TEACHING NOTES ON THEORIES AND STORIES OF GAME THEORY
THEORY OF GAME THEORY from Pindyck and Rubinfield
A game is any situation in which players
(the participants) make strategic decisions — i.e. decisions that take into
account each other's actions and responses.
Strategic decisions result in payoffs to the players:
outcomes that generate rewards or benefits.
A key
objective of game theory is to determine the optimal strategy for each player.
A strategy is a rule or plan of action for playing the game.
The optimal strategy for a player is the
one that maximizes her expected payoff.
We will focus on games involving players
who are rational, in the sense that' they think through the consequences of
their actions. In essence, we are concerned with the following question: If I
believe that my competitors are rational and act to maximize their own payoffs,
how should I take their behaviour into account when making my decisions?
The economic games that firms play can be
either cooperative or non-co-operative. In a cooperative game, players can
negotiate binding contracts that allow them to plan joint strategies. In a non-cooperative
game, negotiation and enforcement of binding contracts are not possible.
Consider the following game devised by
Martin Shubik. A dollar bill is auctioned, but in an unusual way. The highest
bidder receives the dollar in return for the amount bid. However, the
second-highest bidder must also hand over the amount that he or she bid — and
get nothing in return.
In some experiments, the "winning"
bidder has ended up paying more than $3 for the dollar! This happens because
players make the mistake of failing to think through the likely response of the
other players and the sequence of events it implies.
Martin Shubik, Game Theory in the Social
Sciences (Cambridge, MA: MIT Press, 1982)
How can we decide on the be strategy for
playing a game? How can we determine a game's likely outcome?
We begin with the concept of a dominant
strategy - one that is optimal no matter what an opponent does.
The following example illustrates this in
a duopoly setting. Suppose Firms A and B sell competing products and are
deciding whether to undertake advertising campaigns. Each firm will be affected
by its competitor's decision. The possible outcomes of the game are illustrated
by the payoff matrix.
Observe that if both firms advertise,
Firm A will earn a profit of 10 and Firm B a profit of 5. If Firm A advertises
and Firm B does not, Firm A will earn 15 and Firm B zero. The table also shows
the outcomes for the other two possibilities.
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Table 1.1 Payoff Matrix for Advertising Game
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Firm B
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Advertise
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Don’t advertise
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Firm A
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Advertise
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10, 5
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15, 0
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Don’t
advertise
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6, 8
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10, 2
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What strategy should each firm choose?
First consider Firm A. It should clearly advertise because no matter what firm
B does, Firm A does best by advertising. If Firm B advertises, A earns a profit
of 10 if it advertises but only 6 if it does not. If B does not advertise, A
earns 15 if it advertises but only 10 if it doesn't. Thus advertising is a
dominant strategy for Firm A. The same is true for Firm B: No matter what firm
A does, Firm B does best by advertising. Therefore, assuming that both firms
are rational, we know that the outcome for this game is that both firms will
advertise. This outcome is easy to determine because both firms have dominant
strategies.
When every player has a dominant
strategy, we call the outcome of the game an equilibrium in dominant strategies.
Unfortunately, not every game has a
dominant strategy for each player. To see this, let's change our advertising
example slightly. The payoff matrix in Table 2 is the same as in Table 1 except
for the bottom right-hand corner— if neither firm advertises, Firm B will again
earn a profit of 2, but Firm A will earn a profit of 20. (Perhaps Firm A's ads
are expensive and largely designed to refute Firm B's claims, so by not
advertising, Firm A can reduce its expenses considerably.)
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Table 1.2 Modified Advertising Game
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Firm B
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Advertise
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Don’t advertise
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Advertise
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10, 5
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15, 0
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Don’t
advertise
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6, 8
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20, 2
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Now Firm A has no dominant strategy. Its
'optimal decision depends on what Firm B does. It Firm B advertises, Firm A
does best by advertising; but if Firm B does not advertise, Firm A also does
best by not advertising. Now suppose both firms must make their decisions at
the same time. What should Firm A do?
To answer this, Firm A must put itself in
Firm B's shoes. What decision is best from Firm B's point of view, and what is
Firm B likely to do? The answer is clear: Firm B has a dominant
strategy—advertise, no matter what Firm A does. (If Firm A advertises, B earns
5 by advertising and 0 by not advertising; if A doesn't advertise, B earns 8 if
it advertises and 2 if it doesn't.) Therefore, Firm A can conclude that Firm B
will advertise. This means that Firm A should advertise (and thereby earn 10
instead of 6). The logical outcome of the game is that both firms will
advertise because Firm A is doing the best it can given Firm B's decision; and
Firm B is doing the best it can given Firm A's decision.
A Nash equilibrium is a set of strategies
(or actions) such that each player is doing the best it can given the actions
of its opponents. Because each player has no incentive to deviate from its Nash
strategy, the strategies are stable.
In the example shown in Table 2, the Nash
equilibrium is that both firms advertise. Given the decision of its competitor,
each firm is satisfied that it has made the best decision possible, and so has
no incentive to change its decision.
It is helpful to compare the concept of a
Nash equilibrium with that of un equilibrium in dominant strategies:
Dominant
Strategies: I'm doing the best I can no matter what you do.
You're doing the best you can no matter what I do.
You're doing the best you can no matter what I do.
Nash
Equilibrium: I'm doing the best I can given what you are
doing.
You're doing the best you can given what I am doing.
You're doing the best you can given what I am doing.
Note that a dominant strategy equilibrium
is a special case of a Nash equilibrium, i In the advertising game of Table 2,
there is a single Nash equilibrium I both firms advertise. In general, a game
need not have a single Nash equilibrium. Sometimes there is no Nash
equilibrium, and sometimes there are several (i.e., several sets of strategies
are stable and self-enforcing). A few more examples will help to clarify this.
The
Product Choice Problem Consider the following "product
choice” problem. Two breakfast cereal companies face a market in which two new
variations of cereal can be successfully introduced—provided that each
variation is introduced by only one firm. There is a market for a new
"crispy" cereal and a market for a new "sweet" cereal, but
each firm has the resources to introduce only one new product. The payoff
matrix for the
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Table 1.3 Product Choice Problem
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Firm 2
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Crispy
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Sweet
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Firm 1
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Crispy
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-5, -5
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10, 10
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Sweet
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10, 10
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-5, -5
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two firms might look like the one in
Table 3.
In this game, each firm is indifferent
about which product it produces—so long as it does not introduce the same
product as its competitor. If coordination were possible, the firms would
probably agree to divide the market. But what if the firms must behave non-cooperatively?
Suppose that somehow—perhaps through a news release—Firm 1 indicates that it is
about to introduce the sweet cereal, and that Firm 2 (after hearing this)
announces its plan to introduce the crispy one. Given the action that it
believes its opponent to be taking, neither firm has an incentive to deviate
from its proposed action. If it takes the proposed action, its payoff is 10,
but if it deviates—and its opponent's action remains unchanged—its payoff will
be -5. Therefore, the strategy set given by the bottom left-hand corner of the
payoff matrix is stable and constitutes a Nash equilibrium: Given the strategy
of its opponent, each firm is doing the best it can and has no incentive to
deviate.
Note that the upper right-hand corner of
the payoff matrix is also a Nash equilibrium, which might occur if Firm 1
indicated that it was about to produce the crispy cereal. Each Nash equilibrium
is stable because once the strategies are chosen, no player will unilaterally
deviate from them. However, without more information, we have no way of knowing
which equilibrium (crispy/sweet vs. sweet/crispy) is likely to result—or if
either will result. Of course, both firms have a strong incentive to reach one
of the two Nash equilibria—if they both introduce the same type of cereal, they
will both lose money. The fact that the two firms are not allowed to collude
does not mean that they will not reach a Nash equilibrium. As an industry
develops, understandings often evolve as firms "signal" each other
about the paths the industry is to take.
Beach
Location Game Suppose that you (Y) and a competitor (C)
plan to sell soft drinks on a beach in Goa
this summer. The beach is 200 meters long, and sunbathers are spread evenly
across its length. You and your competitor sell the same soft drinks at the
same prices, so customers will walk to the closest vendor. Where on the beach
will you locate, and where do you think your competitor will locate?
If you think about this for a minute, you
will see that the only Nash equilibrium calls for both you and your competitor
to locate at the same spot in the center of the beach. To see why, suppose
your competitor located at some other point (A), which is three quarters of the
way to the end of the beach. In that case, you would no longer want to locate
in the center; you would locate near your competitor, just to the left. You
would thus capture nearly three-fourths of all sales, while your competitor got
only the remaining fourth. This outcome is not an equilibrium because your
competitor would then want to move to the center of the beach, and you would do
the same.
The "beach location game" can
help us understand a variety of phenomena. Have you ever noticed how, along a
two- or three-mile stretch of road, two or^ three gas stations or several car
dealerships will be located close to each other?
Maximin
strategies
The concept of a Nash equilibrium relies
heavily on individual rationality. Each player's choice of strategy depends not
only on its own rationality, but also on the rationality of its opponent. This
can be a limitation, as the example in Table 4 shows.
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Table 1.4 Maximum Strategy
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Firm 2
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Don’t invest
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Invest
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Firm 1
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Don’t
invest
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0, 0
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-10, 10
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Invest
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-100, 0
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20, 10
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In this game, two firms compete in
selling file-encryption software. Because both firms use the same encryption
standard, files encrypted by one firm's software can be read by the other's —an
advantage for consumers. Nonetheless, Firm t has a much larger market share.
(It entered the market earlier and its software has a better user interface.)
Both firms are now considering an investment in a new encryption standard.
Note that investing is a dominant
strategy for Firm 2 because by doing so it will do better regardless of what
Firm 1 does. Thus Firm 1 should expect Firm 2 to invest. In this case, Firm 1
would also do better by investing (and earning Rs 20 crore) than by not
investing (and losing Rs 10 crore). Clearly the outcome (invest, invest) is a
Nash equilibrium for this game, and you can verify that it is the o{y Nash
equilibrium. But note that Firm 1-'s manager had better bb sure that Firm 2's
managers understand the game and are rational. If Firm 2 should happen to make
a mistake and fail to invest, it would be extremely costly to Firm 1. (Consumer
confusion over incompatible standards would arise, and Firm 1, with its
dominant market share, would lose Rs 100 crore.)
If you were Firm 1, what would you do? If
you tend to be cautious—and if you are concerned that the managers of Firm 2
might not be fully informed or rational—you might choose to play "don't invest."
In that case, the worst that can happen is that you will lose Rs 10 crore; you
no longer have a chance of losing Rs 100 crore. This strategy is called a maximin strategy because it maximizes
the minimum gain that can be earned. If both firms used maximin strategies,
the outcome would be that Firm 1 does not invest and Firm 2 does. A maximin
strategy is conservative, but it is not profit-maximizing. (Firm 1, for
example, loses Rs 10 crore rather than earning Rs 20 crore.) Note that if Firm
1 knew for certain that Firm 2 was using a maximin strategy, it would prefer to
invest (and earn Rs 20 crore) instead of following its own maximin strategy of
not investing.
Maximizing
the Expected Payoff If Firm 1 is unsure about what Firm 2 will do
but can assign probabilities to each feasible action for Firm 2, it could
instead use a strategy that maximizes its expected payoff. Suppose, for
example, that Firm 1 thinks that there is only a 10-percent chance that Firm 2
will not invest. In that case, Firm l's expected payoff from investing is
(0.1X-100) + (0.9X20) = Rs 8 crore. Its expected payoff if it doesn't invest is
(0.1)(0) + (0.9X-10) = -Rs 9 crore. In this case, Firm 1 should invest.
On the other hand, suppose Firm 1 thinks
that the probability that Firm 2 will not invest is 30 percent. Then Firm l's
expected payoff from investing is (0.3X-100) + (0.7X20) = -Rs 16 crore, while
its expected payoff from not investing is (0.3)(0) + (0.7X-10) = -Rs 7 crore.
Thus Firm 1 will choose not to invest.
You can see that Firm l's strategy
depends critically on its assessment of the probabilities of different actions
by Firm 2. Determining these probabilities may seem like a tall order.
However, firms often face uncertainty (over market conditions, future costs,
and the behavior of competitors), and must make the best decisions they can
based on probability assessments and expected values.
Mixed
Strategies
In all of the games that we have examined
so far, we have considered strategies in which players make a specific choice
or take a specific action: advertise or don't advertise, set a price of Rs 4 or
a price of Rs 6, and so on. Strategies of this kind are called Pure strategies.
There are games, however, in which a pure strategy is not the best way to
play.
Matching
Pennies An example is the game of "Matching pennies”. In
this game, each player chooses heads or tails and the two players reveal their
coins at the same time. If the coins match (i.e., both are heads or both are
tails), Player A wins and receives a rupee from Player B. If the coins do not
match, Player B wins and receives a rupee from Player A. The payoff matrix is
shown in Table 6.
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Table 1.6 Matching Pennies
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Player B
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Heads
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Tails
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Heads
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1, -1
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-1, 1
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Tails
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-1, 1
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1, -1
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Note that there is no Nash equilibrium in
pure strategies for this game. Suppose, for example, that Player A chose the strategy
of playing heads. "Then Player B would wan! to play tails. But if Player B
plays tails, Player A would also want to play tails. No combination of heads or
tails leaves both players satisfied—one player or the other will always want to
change strategies.
Although there is no Nash equilibrium in
pure strategies, there is a Nash equilibrium in mixed strategies: strategies in
which players make random choice among two or more possible actions, based on
sets of chosen probabilities. In this game, for example, Player A might simply
flip the coin, thereby playing heads with probability 1/2 and playing tails with
probability 1/2. In fact, if Player A follows this strategy a1d Player B does
the same, we will have a Nash equilibrium: Both players will be doing the best
they can given what the opponent is doing. Note that although the outcome is
random, the expected payoff is 0 for each player.
It may seem strange to play a game by
choosing actions randomly. But put yourself in the position of Player A and,
think what would happen if you, followed a strategy other than just flipping
the coin. Suppose you decided to play heads. If Player B knows this, she would
play tails and you would lose. Even if Player B didn't know your strategy, if
the game were played repeatedly, she could eventually discern your pattern of play
and choose a strategy that countered it. Of course, you would then want to
change your strategy— which is why this would not be a Nash equilibrium. Only
ii you and your opponent both choose heads or tails randomly with probability 1/2
would neither of you have any incentive to change strategies. (You can check
that the use of different probabilities, say 3/4 for heads and T/ for tails,
does not generate a Nash equilibrium.)
One reason to consider mixed strategies
is that some games (such as "Matching Pennies") do not have any Nash
equilibria in pure strategies. It can be shown, however, that once we allow for
mixed strategies, every game has at least one Nash equilibrium. Mixed
strategies, therefore, provide solutions to games when pure strategies fail. Of
course, whether solutions involving mixed strategies are reasonable will depend
on the particular game and players. Mixed strategies are likely to be very
reasonable for "Matching Pennies," poker, and other such games. A
firm, on the other hand, might not find it reasonable to believe that its
competitor will set its price randomly.
The Battle
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Raman
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Movie
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Opera
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Radhika
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Movie
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2, 1
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0, 0
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Opera
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0, 0
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1, 2
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First, note that there are two Nash
equilibria in pure strategies for this game—the one in which Raman and Radhika
both watch movie, and the one in which they both go to the opera. Radhika, of
course, would prefer the first of these outcomes and Raman the second, but both
outcomes are equilibria — neither Raman nor Radhika would want to change his or
her decision, given the decision of the other.
This game also has an equilibrium in
mixed strategies: Radhika chooses movie with probability 2/3 and opera with
probability 1/3, and Raman chooses movie with probability 1/3 and opera with
probability 2/3. You can check that if Radhika uses this strategy, Radhika
cannot do better with any other strategy, and vice versa. The outcome is
random, and Raman and Radhika will each have an expected payoff of 2/3.
In real life, firms play repeated games:
Actions are taken and payoffs received over and over again.
Robert Axelrod, The Evolution of
Cooperation (New York: Basic Books, 1984)
Infinitely Repeated Game Suppose the game
is infinitely repeated. In other words, my competitor and I repeatedly set
prices month after month, forever. Cooperative behavior (i.e., charging a high
price) is then the rational response to a tit-for-tat strategy. (This assumes
that my competitor knows, or can figure out, that I am using a tit-for-tat
strategy.
With infinite repetition of the game, the
expected gains from cooperation will outweigh those from undercutting. This
will be true even if the probability that I am playing tit-for-tat (and so
will continue cooperating) is small.
Now suppose the game is repeated a finite
number of times—say, N months. (N can be large as long as it is finite.) If my
competitor (Firm 2) is rational and believes that I am rational, he will reason
as follows: "Because Firm 1 is playing tit-for-tat, I (Firm 2) cannot
undercut—that is, until the last month. I should undercut the last month because
then I can make a large profit that month, and afterward the game is over, so
Firm 1 cannot retaliate. Therefore, I will charge a high price until the last
month, and then I will charge a low price."
However, since I (Firm 1) have also
figured this out, I also plan to charge a low price in the last month. Of
course, Firm 2 can figure this out as well, and therefore knows that I will
charge a low price in the last month. But then what about the next-to-last
month? Because there will be no cooperation in the last month, anyway, Firm 2
figures that it should undercut and charge a low price in the next-to-last
month. But, of course, I have figured this out too, so I also plan to charge a
low price in the next-to-last month. And because the same reasoning applies to
each preceding month, the game unravels: The only rational outcome is for both
of us to charge a low price every month.
Tit-for-Tat
in Practice Since most of us do not expect to live
forever, the unravelling argument would seem to make the tit-for-tat strategy
of little value, leaving us stuck in the prisoners' dilemma. In practice,
however, tit-for-tat can sometimes work and cooperation can prevail. There are
two primary reasons.
First, most managers don't know how long
they will be competing with their rivals, and this also serves to make
cooperative behavior a good strategy. If the end point of the repeated game is
unknown, the unravelling argument that begins with a clear expectation of
undercutting in the last month no longer applies. As with an infinitely
repeated game, it will be rational to play tit-for-tat.
Second, my competitor might have some
doubt about the extent of my rationality. Suppose my competitor thinks (and he
need not be certain) that I am playing tit-for-tat. He also thinks that perhaps
I am playing tit-for-tat "blindly," or with limited rationality, in
the sense that I have failed to work out the logical implications of a finite
time horizon as discussed above. My competitor thinks, for example, that
perhaps I have not figured out that he will undercut me in the last month, so
that I should also charge a low price in the last month, and so on. "Perhaps,"
thinks my competitor, "Firm 1 will Play tit-for-tat blindly, charging
a high price as long as I charge a high price." Then (if the time horizon
is long enough), it is rational for my competitor to maintain a high price
until the last month (when he will undercut me).
Note that we have stressed the word perhaps.
My competitor need not be sure that I am playing tit-for-tat “blindly” or even
that I am playing tit-for-tat at all. Just the possibility can make cooperative
behavior a good strategy (until near the end) if the time horizon is long
enough. Although my competitor's conjecture about how I am playing the game
might be wrong, cooperative behavior is profitable in expected value terms. With
a long time horizon, the sum of current and future profits, weighted by the
probability that the conjecture is correct, can exceed the sum of profits from
price competition, even if my competitor is the first to undercut. After all,
if I am wrong and my competitor charges a low price, I can shift my strategy at
the cost of only one period's profit—a minor cost in light of the substantial
profit that I can make if we both choose to set a high price.
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Table 1.5 Prisoners’ Dilemma
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Prisoner B
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Confess
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Don’t confess
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Prisoner A
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Confess
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-5, -5
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-1, -10
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Don’t
confess
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-10, -1
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-2, -2
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Thus, in a repeated game, the prisoners'
dilemma can have a cooperative outcome. In most markets, the game is in fact
repeated over a long and uncertain length of time, and managers have doubts
about how "perfectly rationally" they and their competitors operate.
As a result, in some industries, particularly those in which only in few firms
compete over a long period under stable demand and cost conditions, cooperation
prevails, even though no contractual arrangements are made. (The water meter
industry, discussed below, is an example.) In many other industries, however,
there is little or no cooperative behavior.
Sometimes cooperation breaks down or
never begins because there are too many firms.
More often, failure to cooperate is the
result of rapidly shifting demand or cost conditions. Uncertainties about
demand or costs make it difficult for the firms to reach an implicit
understanding of what cooperation should entail. (Remember that an explicit understanding,
arrived at through meetings and discussions, could lead to an antitrust
violation.) Suppose, for example, that cost differences or different beliefs
about demand lead one firm to conclude that cooperation means charging Rs 50
while a second firm thinks it means Rs 40. If the second firm charges Rs 40, the
first firm might view that as a grab for market share and respond in tit-for-tat
fashion with a Rs 35 price. A price war could then develop.
In most of the games we have discussed so
far, both players move at the same time.
In sequential
games, players move in turn.
There are many other examples: an
advertising decision by one firm and the response by its competitor;
entry-deterring investment by an incumbent firm and the decision whether to
enter the market by a potential competitor; or a new government regulatory
policy and the investment and output response of the regulated firms.
As a simple example, let's return to the
product choice problem first discussed in Section 12.3.
This time, let's change the payoff matrix
slightly.
The new sweet cereal will inevitably be a
better seller than the new crispy cereal, earning a profit of 20 rather than 10
(perhaps because consumers prefer sweet things to crispy things). Both new cereals
will still be profitable, however, as long as each is introduced by only one firm.
Suppose that both firms, in ignorance of
each other's intentions, must announce their decisions- independently and
simultaneously. In that case, both s will probably introduce the sweet cereal—and
both will lose money.
Now suppose that Firm 1 can gear up its
production faster and introduce in new cereal first. We now have a sequential
game: Firm 1 introduces a new cereal, and then Firm 2 introduces one. What will
be the outcome of this game? When making its decision, Firm 1 must consider the
rational response of its competitor. It knows that whichever cereal it
introduces, Firm 2 will introduce the other kind. Thus it will introduce the
sweet cereal, knowing that Firm 2 will respond by introducing the crispy one.
Although this outcome can be deduced from
the payoff matrix in Table 12.9, sequential games are sometimes easier to
visualize if we represent the possible moves in the form of a decision tree.
This representation is called the extensive form of a game. It shows the
possible choices of Firm 1 (introduce a crispy or a sweet cereal) and the possible
responses of Firm 2 to each of those choices. The resulting payoffs are given
at the end of each branch. For example, if Firm 1 produces a crispy cereal and
Firm 2 responds by also producing a crispy cereal, each firm will have a payoff
of -5.
In this product-choice game, there is a
clear advantage to moving first: By introducing the sweet cereal. Firm 1
leaves Firm 2 little choice but to introduce the crispy one.
What actions can a firm take to gain
advantage in the market place? For example, how might a firm deter entry by
potential competitors, or induce existing competitors to raise prices reduce
output, or leave the market altogether?
Making a commitment—constraining its future
behavior—is crucial. To see why, suppose that the first mover (Firm 1) could
later change its mind in response to what Firm 2 does. What would happen?
Clearly, Firm 2 would produce a large output. Why? Because it knows that Firm 1
will respond by reducing the output that it first announced. The only way that
Firm 1 can gain a first-mover advantage is by committing itself. In effect, Firm
1 constrains Firm 2's behavior by constraining its own behaviour.
The idea of constraining your own
behavior to gain an advantage may seem paradoxical, but we will soon see that
it is not. Let's consider a few examples. First, let's return once more to the
product-choice problem shown in Table 12.9.
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Firm 2
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Crispy
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Sweet
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Firm 1
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Crispy
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10, 10
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100, -50
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Sweet
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-50, 100
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50, 50
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The firm that introduces its new
breakfast cereal first will do best. But which firm will introduce its cereal first?
Even if both firms require the same amount of time to gear up production, each
has an incentive to commit itself first to the sweet cereal. The key word is
commit If Firm 1 simply announces it will produce the sweet cereal, Firm 2 will
have little reason to believe it. After all, Firm 2, knowing the incentives,
can make the same announcement louder and more vociferously, Firm 1 must
constrain its own behavior in some way that convinces Firm 2 that Firm t has no
choice but to produce the sweet cereal. Firm 1 might launch an expensive
advertising campaign describing the new sweet cereal well before its
introduction, thereby putting its reputation on the line. Firm 1 might also
sign a contract for the forward delivery of a large quantity of sugar (and make
the contract public, or at least send a copy to Firm 2). The idea is for Firm
7 to commit itself to produce the sweet cereal. Commitment is a strategic move
that will induce Firm 2 to make the decision that Firm 1 wants it to make—namely,
to produce the crispy cereal.
Why can't Firm 1 simply threaten Firm 2,
vowing to produce the sweet cereal even if Firm 2 does the same? Because Firm 2
has little reason to believe the threat—and can make the same threat itself. A
threat is useful only if it is credible. The following example should help
make this clear.
Empty
Threats
Suppose Firm 1 produces personal
computers that can be used both as word processors and to do other tasks. Firm
2 produces only dedicated word processors. As the payoff matrix in Table 11
shows, as long as Firm 1 charges a high price for its computers, both firms can
make a good deal of money. Even if Firm 2 charges a low price for its word
processors, many people will still buy Firm l's computers (because they can do so
many other things), although some buyers will be induced by the price
differential to buy the dedicated word processor instead. However, if Firm 1
charges a low price, Firm 2 will also have to charge a low price (or else make
zero profit), and the profit of both firms will be significantly reduced.
|
Table 1.11 Pricing of computers and word
processors
|
||||
|
|
|
Firm 2
|
|
|
|
|
|
High Price
|
Low Price
|
|
|
|
|
|
|
|
|
Firm 1
|
High
price
|
100, 80
|
80, 100
|
|
|
Low price
|
20, 0
|
10, 20
|
|
|
|
|
|
|
|
|
Firm 1 would prefer the outcome in the
upper left-hand corner of the matrix. For Firm 2, however, charging a low price
is clearly a dominant strategy. Thus the outcome in the upper right-hand corner
will prevail (no matter which firm sets its price first).
Firm 1 would probably be viewed as the
"dominant" firm in this industry because its pricing actions will
have the greatest impact on overall industry profits. Can Firm 1 induce Firm 2
to charge a high price by threatening to charge a low price if Firm 2 charges a
low price? No, as the payoff matrix in Table 12.11 makes clear: Whatever Firm 2
does, Firm 1 will be much worse off if it charges a low price. As a result, its
threat is not credible.
Commitment
and Credibility
Sometimes firms can make threats
credible. To see how, consider the following example. Race Car Motors, Inc.,
produces cars, and Far Out Engines, Ltd., produces specialty car engines. Far
Out Engines sells most of its engines to Race Car Motors, and a few to a
limited outside market. Nonetheless, it depends heavily on Race Car Motors and
makes its production decisions in response to Race Car's production plans.
|
Table 1.12(a) Production choice problem
|
||||
|
|
|
Race Car Motors
|
|
|
|
|
|
Small cars
|
Big cars
|
|
|
|
|
|
|
|
|
Far Out Engines
|
Small
engines
|
10, 10
|
100, -50
|
|
|
Big
engines
|
-50, 100
|
50, 50
|
|
|
|
|
|
|
|
|
We thus have a sequential game in which
Race Car is the "leader." It will decide what kind of cars to build,
and Far Out Engines will then decide what kind of engines to produce. The
payoff matrix in Table 12.12(a) shows the possible outcomes of this game.
(Profits are in hundred crore of rupees.) Observe that Race Car will do best by
deciding to produce small cars. It knows that in response to this decision, Far
Out will produce small engines, most of which Race Car will then buy. As a
result, Far Out will make Rs 300 crore and Race Car Rs 600 crore.
Far Out, however, would much prefer the
outcome in the lower right-hand corner of the payoff matrix. If it could
produce big engines, and if Race Car produced big cars and thus bought the big
engines, it would make Rs 800 crore. (Race Car, however, would make only Rs 300
crore.) Can Far Out induce Race Car to produce big cars instead of small ones?
Suppose Far Out threatens to produce big
engines no matter what Race Car does; suppose, too, that no other engine
producer can easily satisfy the needs of Race Car. If Race Car believed Far
Out's threat, it would produce big cars: Otherwise, it would have trouble
finding engines for its small cars and would earn only Rs 100 crore instead of
Rs 300 crore. But the threat is not credible: once Race Car responded by
announcing its intentions to produce small cars, Far out would have no
incentive to carry out its threat.
Far out can make its threat credible by
visibly and irreversibly reducing some of its own payoffs in the matrix,
thereby constraining its own choices. In particular; Far Out must reduce its
profits from small engines (the payoffs in the top row of the matrix). It might
do this by shutting down or destroying some of its small engine production
capacity. This would result in the payoff matrix shown in Table 12(b). Now Race
car knows that whatever kind of car it produces, Far out will produce big engines.
If Race Car produces the small cars, Far
out will sell the big engines as best it can to other car producers and settle
for making only Rs 100 crore' But this is better than making no profits
producing small engines. Because Race Car will have to look elsewhere for
engines, its profit will also be lower (Rs 100 crore). Now it is clearly in
Race Car's interest to produce large cars. By taking an action that seemingly puts
itself at a disadvantage, Far out has improved its outcome in the game.
|
Table 1.12(b) Modified Production Choice Problem
|
||||
|
|
|
Race Car Motors
|
|
|
|
|
|
Small cars
|
Big cars
|
|
|
|
|
|
|
|
|
Far Out Engines
|
Small
engines
|
0, 6
|
0, 0
|
|
|
Big
engines
|
1, 1
|
8, 3
|
|
|
|
|
|
|
|
|
Although strategic commitments of this
kind can be effective, they are risky and depend heavily on having accurate
knowledge of the payoff matrix and the industry. Suppose, for example, that Far
out commits itself to producing big engines but is surprised to find that another
firm can produce small engines at a low cost. The commitment may then lead Far
Out to bankruptcy rather than continued high profits.
The
Role of Reputation Developing the right kind of reputation can
also give one a strategic advantage' Again, consider Far Out Engines' desire to
produce big engine for Race Car Motors' big cars suppose that the managers of
Far out Engines develop a reputation for being irrational — perhaps downright
crazy. They threaten to produce big- engines no matter what Race Car Motors
does (refer to Table 12a). Now the threat might be credible without any further
action; after all' you can't be sure that an irrational manager will always
make a profit-maximizing decision. In gaming situations, the party that is
known (or thought) to be a little crazy can have a significant advantage.
Developing a reputation can be an
especially important strategy in a repeated game. A firm might find it advantageous
to behave irrationally for several plays of the game. This might give it a
"reputation that will allow it to increase its long-run profits
substantially. Bargaining Strategy
Our discussion of commitment and
credibility also applies to bargaining problems. The outcome of a bargaining
situation can depend on the ability of either side to take an action that alters
its relative bargaining position.
|
Table 1.13 Production Decision
|
||||
|
|
|
Firm 2
|
|
|
|
|
|
Produce A
|
Produce B
|
|
|
|
|
|
|
|
|
Firm 1
|
Produce A
|
40, 5
|
50, 50
|
|
|
Produce B
|
60, 40
|
5, 45
|
|
|
|
|
|
|
|
|
For example, consider two firms that are
each planning to introduce one of two products which are complementary goods. As
the payoff matrix in Table 13 shows, Firm 1 has a cost advantage over Firm 2 in producing A. Therefore,
if both firms produce A, Firm 1 can maintain a lower price and earn a higher
profit. Similarly, Firm 2 has a cost advantage over Firm 1 in producing product B. If
the two firms could agree about who will produce what, the rational outcome
would be the one in the upper right-hand corner: Firm 1 produces A, Firm 2
produces B, and both firms make profits of 50. Indeed, even without
cooperation, this outcome will result whether Firm 1 or Firm 2 moves first or
both firms move simultaneously. Why? Because producing B is a dominant
strategy for Firm 2, so (A, B) is the only Nash equilibrium.
Firm 1, of course, would prefer the
outcome in the lower left-hand corner of the payoff matrix. But in the context
of this limited set of decisions, it cannot achieve that outcome. Suppose,
however, that Firms 1 and 2 are also bargaining over a second issue—whether to
join a research consortium that a third firm is trying to form. Table 12.14
shows the payoff matrix for this decision problem. Clearly, the dominant
strategy is for both firms to enter the consortium, thereby increasing profits
to 40.
Now suppose that Firm 1 links the two
bargaining problems by announcing that it will join the consortium only if Firm
2 agrees to produce product A. In this case, it is indeed in Firm 2's interest to
produce A (with Firm 1 producing B) in return for Firm l's participation in the
consortium. This example illustrates how combining issues in a bargaining
agenda can sometimes benefit one side at the other's expense.
As another example, consider bargaining
over the price of a house. Suppose I, as a potential buyer, do not want to pay
more than Rs 2,00,000 for a house that is actually worth Rs 2,50,000 to me. The
seller is willing to part with the house at any price above Rs 1,80,000 but
would like to receive the highest price she can. If I am the only bidder for
the house, how can I make the seller think that I will walk away rather than
pay more than Rs 2,00,000?
I might declare that I will never, ever
pay more than Rs 2,00,000 for the house. But is such a promise credible? It may
be if the seller knows that I have a reputation for toughness and that I have
never reneged on a promise of this sort. But suppose I have no such reputation.
Then the seller knows that I have every incentive to make the promise (making
it costs nothing) but little incentive to keep it. (This will probably be our
only business transaction together.) As a result, this promise by itself is not
likely to improve my bargaining position.
The promise can work, however, if it is
combined with an action that gives it credibility. Such an action must reduce
my flexibility—limit my options—so that I have no choice but to keep the
promise. One possibility would be to make an enforceable bet with a third
party—for example, "If I pay more than Rs 2,00,000 for that house, I'll
pay you Rs 60,000." Alternatively, if I am buying the house on behalf of
my company, the company might insist on authorization by the Board of Directors
for a price above Rs 2,00,000, and announce that the board will not meet again
for several months. In both cases, my promise becomes credible because I have
destroyed my ability to break it. The result is less flexibility—and more
bargaining power.
EXAMPLE 12.3
Wal-Mart Stores' Preemptive Investment Strategy
Wal-Mart Stores' Preemptive Investment Strategy
Wal-Mart Stores, Inc., is an enormously
successful chain of discount retail stores in the United States started by Sam
Walton in 1969.n Its success was unusual in the industry. During the 1960s and
1970s, rapid expansion by existing firms and the entry and expansion of new
firms made discount retailing increasingly competitive. During the 1970s and
1980s, industry-wide profits fell, and large discount chains—including such
giants as King's, Korvette's, Mammoth Mart, W. T. Grant, and Woolco—went
bankrupt. Wal-Mart Stores, however, kept on growing and became even more
profitable. By the end of 1985, Sam Walton was one of the richest people in the
United States
How did Wal-Mart Stores succeed where
others failed? The key was Wal-Mart's expansion strategy. To charge less than
ordinary department stores and small retail stores, discount stores rely on
size, no frills, and high inventory turnover. Through the 1960s, the
conventional wisdom held that a discount store could succeed only in a city
with a population of 100,000 or more. Sam Walton disagreed and decided to open
his stores in small Southwestern towns; by 1970, there were 30 Wal-Mart stores
in small towns in Arkansas , Missouri ,
and Oklahoma
By the mid-1970s, other discount chains
realized that Wal-Mart had a profitable strategy: Open a store in a small town
that could support only one discount store and enjoy a local monopoly. There
are a lot of small towns in the United
States
This game has two Nash equilibria—the
lower left-hand corner and the upper right-hand corner. Which equilibrium
results depend on who moves first. If Wal-Mart moves first, it can enter,
knowing that the rational response of Company X will be not to enter, so that
Wal-Mart will be assured of earning 20. The trick, therefore, is to preempt—to
set up stores in other small towns quickly, before Company X (or Company Y or
Z) can do so. That is exactly what Wal-Mart did. By 1986, it had 1009 stores in
operation and was earning an annual profit of $450 million. And while other
discount chains were going under, Wal-Mart continued to grow. By 1999, Wal-Mart
had become the world's largest retailer, with 2454 stores in the United States
In recent years, Wal-Mart has continued
to preempt other retailers by opening new discount stores, warehouse stores
(such as Sam's Club), and combination discount and grocery stores (Wal-Mart
Supercenters) all over the world. Wal-Mart has been especially aggressive in
applying its preemption strategy in other countries. As of 2007, Wal-Mart had
about 3800 stores in the United States
and about 2800 stores throughout Europe, Latin America, and Asia .
Wal-Mart had also become the world's largest private employer, employing more
than 1.6 million people worldwide.
|
Table 1.15 The Discount Store Preemption Game
|
||||
|
|
|
Company X
|
|
|
|
|
|
Enter
|
Don’t enter
|
|
|
|
|
|
|
|
|
Wal-Mart
|
Enter
|
10, 10
|
10, 20
|
|
|
Don’t
enter
|
20, 10
|
40, 40
|
|
|
|
|
|
|
|
|
Barriers to entry, which are an important
source of monopoly power and profits, sometimes arise naturally. For example,
economies of scale, patents and licenses, or access to critical inputs can
create entry barriers. However, firms themselves can sometimes deter entry by
potential competitors.
To deter entry, the incumbent firm must
convince any potential competitor that entry will be unprofitable. To see how
this might be done, put yourself in the position of an incumbent monopolist
facing a prospective entrant, Firm X. Suppose that to enter the industry, Firm
X will have to pay a (sunk) cost of Rs 80 crore to build a plant. You, of
course, would like to induce Firm X to stay out of the industry. If X stays
out, you can continue to charge a high price and enjoy monopoly profits. As
shown in the upper right-hand corner of the payoff matrix in Table 16 (a), you
would earn Rs 200 crore in profits.
|
|
|
Potential Entrant
|
|
|
|
|
|
Enter
|
Stay out
|
|
|
|
|
|
|
|
|
Incumbent
|
High price (accommodation)
|
100, 20
|
200, 0
|
|
|
Low price
(warfare)
|
70, -10
|
130, 0
|
|
|
|
|
|
|
|
|
If Firm X does enter the market, you must
make a decision. You can be "accommodating, " maintaining a high
price in the hope that X will do the same. In that case, you will earn only Rs
100 crore in profit because you will have to share the market. New entrant X
will earn a net profit of Rs 20 crore: Rs 100 crore minus the Rs 80 crore cost
of constructing a plant. (This outcome is shown in the upper left-hand corner
of the payoff matrix.) Alternatively, you can increase your production
capacity, produce more, and lower your price. The lower price will give you a
greater market share and a Rs 20 crore increase in revenues. Increasing
production capacity, however, will cost Rs 50 crore, reducing your net profit to
Rs 70 crore. Because warfare will also reduce the entrant's revenue by Rs 30
crore, it will have a net loss of Rs 10 crore. (This outcome is shown in the
lower left-hand corner of the payoff matrix.) Finally, if Firm X stays out but
you expand capacity and lower price nonetheless, your net profit will fall by
Rs 70 crore (from Rs 200 crore to Rs 130 crore): the Rs 50 crore cost of the
extra capacity and a Rs 20 crore reduction in revenue from the lower price
with no gain in market share. Clearly this choice, shown in the lower
right-hand corner of the matrix, would make no sense.
If Firm X thinks you will be
accommodating and maintain a high price after it has entered, it will find it
profitable to enter and will do so. Suppose you threaten to expand output and
wage a price war in order to keep X out. If X takes the threat seriously, it
will not enter the market because it can expect to lose Rs 10 crore. The
threat, however, is not credible. As Table 16(a) shows (and as the potential
competitor knows), once entry has occurred, it will be in your best interest to
accommodate and maintain a high price. Firm Xs rational move is to enter the
market; the outcome will be the upper left-hand corner of the matrix.
But what if you can make an irrevocable
commitment that will alter your incentives once entry occurs—a commitment that
will give you little choice but to charge a low price if entry occurs? In
particular, suppose you invest the Rs 50 crore now, rather than later, in the
extra capacity needed to increase output and engage in competitive warfare
should entry occur. Of course, if you later maintain a high price (whether or
not X enters), this added cost will reduce your payoff.
We now have a new payoff matrix, as shown
in Table 16(b).
|
Table 1.16(b) Entry Deterrence
|
||||
|
|
|
Potential Entrant
|
|
|
|
|
|
Enter
|
Stay out
|
|
|
|
|
|
|
|
|
Incumbent
|
High price (accommodation)
|
50, 20
|
150, 0
|
|
|
Low price
(warfare)
|
70, -10
|
130, 0
|
|
|
|
|
|
|
|
|
As
a result of your decision to invest in additional capacity, your threat to
engage in competitive warfare is completely credible. Because you already have
the additional capacity with which to wage war, you will do better in
competitive warfare than you would by maintaining a high price. Because the
potential competitor now knows that entry will result in warfare, it is
rational for it to stay out of the market. Meanwhile, having deterred entry you
can maintain a high price and earn a profit of Rs 150 crore.
Can an incumbent monopolist deter entry
without making the costly move of installing additional production capacity?
Earlier we saw that a reputation for irrationality can bestow a strategic
advantage. Suppose the incumbent firm has such a reputation. Suppose also that
by means of vicious price-cutting, this firm has eventually driven out every
entrant in the past, even though it incurred losses in doing so. Its threat
might then be credible: The incumbent's irrationality suggests to the
potential competitor that it might be better off staying away.
Of course, if the game described above
were to be indefinitely repeated, then the incumbent might have a rational
incentive to engage in warfare whenever entry actually occurs. Why? Because
short-term losses from warfare might be outweighed by longer-term gains from
preventing entry. Understanding this, the potential competitor might find the
incumbent's threat of warfare credible and decide to stay out. Now the
incumbent relies on its reputation for being rational—and far-sighted—to
provide the credibility needed to deter entry. The success of this strategy
depends on the time horizon and the relative gains and losses associated with
accommodation and warfare.
We have seen that the attractiveness of
entry depends largely on the way incumbents can be expected to react. In
general, once entry has occurred, incumbents cannot be expected to maintain
output at their pre-entry levels. Eventually, they may back off and reduce
output, raising price to a new joint profit-maximizing level. Because potential
entrants know this, incumbent firms must create a credible threat of warfare to
deter entry. A reputation for irrationality can help. Indeed, this seems to be
the basis for much of the entry-preventing behavior that goes on in actual
markets. The potential entrant must consider that rational industry discipline
can break down after entry occurs. By fostering an image of irrationality and
belligerence, an incumbent firm might convince potential entrants that the risk
of warfare is too high.
There is an analogy here to nuclear
deterrence Consider the use of a nuclear threat to deter the former Soviet
Union from invading Western Europe during the Cold War If it invaded, would the
United States actually react with nuclear weapons, knowing that the Soviets
would then respond in kind7 Because it is not rational for the United States to
react this way, a nuclear threat might not seem credible But this assumes that
everyone is rational, there is a reason to fear an irrational response by the
United States Even if an irrational response is viewed as very improbable, it
can be a deterrent, given the costliness of an error The United States can thus
game by promoting the idea that it might act irrationally, or that events might
get out of control once an invasion occurs This is the "rationality of irrationality"
See Thomas Schilling, The Strategy of Conflict (Harvard University Press,
1980).
STORIES OF GAME
THEORY from Thinking Strategically by Dixit
Tit-for-tat is a variation of the “eye for an eye” rule of
behaviour: do unto others as they have done onto you. More precisely, the
strategy cooperates in the first period and from then on mimics the rival’s
action from the previous period.
Tit-for-tat is as clear and simple as you can get. It is nice
in that it never initiates cheating. It is provocable, that is, it never lets
cheating go unpunished. And it is forgiving, because it does not hold a grudge
for too long and is willing to restore cooperation.
In spite of all this, we believe that tit-for-tat is a flawed
strategy. The slightest possibility of misperceptions results in a complete
breakdown in the success of tit-for-tat.
For instance, in 1982 the United
States responded to the Soviet spying and wiretapping of
the U.S. embassy in Moscow by reducing the number of Soviet diplomats
permitted to work in the United
States Soviet Union . In the end, both countries
were bitter, and future diplomatic cooperation was more difficult.
The problem with tit-for-tat is that any mistake “echoes”
back and forth. One side punishes the other for a defection, and this sets off
a chain reaction. The rival responds to the punishment by hitting back. This
response calls for a second punishment. At no point does the strategy accept a
punishment without hitting back. The Israelis punish the Palestinians for an
attack. The Palestinians refuse to accept the punishment and retaliate. The
circle is complete and the punishments and reprisals become self-perpetuating.
What tit-for-tat lacks is a way of saying, “Enough is enough”.
It is dangerous to apply this simple rule in situations in which misperceptions
are endemic. Tit-for-tat is too easily provoked. You should be more forgiving
when a defection seems to be a mistake rather than the rule. Even if the
defection was intentional, after a long-enough cycle of punishments it may
still be time to call it quits and try reestablishing cooperation. At the same
time, you don't want to be too forgiving and risk exploitation. How do you make
this trade-off?
But what happens if t{ere is a chance that one side
misperceives the other's move?
No matter how unlikely a misperception is (even if it is one
in ir trillion), in the long run tit-for-tat will spend half of its time
cooperating and half defecting, just as a random strategy does. When the
probability of a misperception is small, it will take a lot longer for the trouble
to arise. But then once a mistake happens, it will also take a lot longer to
clear it up.
The possibility of misperceptions means that you have to be
more forgiving, but not forgetting, than simple tit-for-tat. This is true when
there is a presumption that the chance of a misperception is small, say five
percent. But what strategy would you adopt in a prisoners, dilemma in which
there is a fifty percent chance that the other side will misinterpret (reverse)
your actions? How forgiving should you be?
Once the probability of misunderstanding reaches fifty per cent
there is no hope for achieving any cooperation in the prisoners' dilemma. You
should always defect. Why? Consider two extremes. Imagine that you always
cooperate. Your opponent will misinterpret your moves half the time. As a
result, he will believe that you have defected half the time and cooperated
half the time. What if you always defect? Again, you will be misinterpreted
half the time. Now this is to your benefit, as the opponent believes that you
spend half your time cooperating.
No matter what strategy you choose, you cannot have any
effect on what your partner sees. It is as if your partner flips a coin to
determine what he thinks you did. There is simply no connection with reality
once the probability of a mistake reaches fifty percent. Since you have no hope
of influencing your partner's subsequent choices, you might as well defect.
Each period you will gather a higher payoff and it won’t hurt you in the
future.
The moral is that it pays to be more forgiving up to a point.
Once the probability of mistakes gets too high, the possibility of maintaining
cooperation in a prisoners’ dilemma breaks down. It is just too easy to be
taken advantage of. The large chance of misunderstandings makes it impossible
to send clear messages through your actions' Without an ability to communicate
through deeds, any hope for cooperation disappears.
A 50 percent chance of a misperception is the worst possible
case. If misperceptions were certain to occur you would interpret every message
as its opposite, and there would be no misunderstandings.
Credibility is a problem with all strategic moves. If your
unconditional move, or threat or promise, is purely oral, why should you carry
it out if it turns out not to be in your interest to do so? But then others
will look forward and reason backward to predict that you have no incentive to
follow through, and your strategic move will not have the desired effect.
Establishing credibility in the strategic sense means that
you are expected to carry out your unconditional moves, keep your promises, and
make good on your threat.
The Eightfold Path to Credibility
Making your strategic moves credible is not easy. But it is
not impossible, either to make a strategic move credible, you must take a
supporting or collateral action such an action is called commitment.
Offer eight devices for achieving credible commitments. Like
the Buddhist prescription for Nirvana, they call this the "eightfold
path" to credibility. Depending on the circumstances, one or more of
these tactics may prove effective for you. Behind this system are three
underlying principles.
The first principle is to change the payoffs of the game. The
idea is to make it in your interest to follow through on your commitment: turn
a threat into a warning, a promise into an assurance. This can be done through
a variety of ways.
1. Establish and use a
reputation.
2. Write contracts.
Both these tactics make it more costly to break the commitment
than to keep it.
A second avenue is to change the game to limit your ability
to back out of a commitment. In this category, we consider three possibilities.
The most radical is simply to deny yourself any opportunity to back down,
either by cutting yourself off from the situation or by destroying any avenues
of retreat. There is even the possibility of removing yourself from the decision-making
position and leaving the outcome to chance.
3. Cut off
communication.
4. Burn bridges behind
you.
5. Leave the outcome
to chance.
These two principles can be combined: both the possible
actions and their outcomes can be changed. If a large commitment is broken
down into many smaller ones, then the gain from breaking a little one may be
more than offset by the loss of the remaining contract. Thus we have
6. Move in small
steps.
A third route is to use others to help you maintain commitment.
A team may achieve credibility more easily than an individual. Or you may
simply hire others to act in your behalf.
7. Develop credibility
through teamwork.
8. Employ mandated
negotiating agents.
Reputation
If you try a strategic move in a game and then back off, you may lose your
reputation for credibility. In a once-in-a-lifetime situation, reputation may
be unimportant and therefore of little commitment value. But, you typically
play several games with different rivals at the same time, or the same rivals
at different times. Then you have an incentive to establish a reputation, and
this serves as a commitment that makes your strategic moves credible.
During the Berlin crisis in
1961, John F. Kennedy explained the importance of the U.S.
Another example is Israel Israel Israel Israel
Reputation effect is a two-edged sword for commitment.
Sometimes destroying your reputation can create the possibility for a
commitment. Destroying your reputation commits you not to take actions in the
future that you can predict will not be in your best interests.
The question of whether to negotiate with hijackers helps
illustrate the point. Before any particular hijacking has occurred, the
government might decide to deter hijackings by threatening never to negotiate.
However the hijackers predict that after they commandeer the jet, the
government will find it impossible to enforce a no-negotiation posture. How can
a government deny itself the ability to negotiate with hijackers? One answer is
to destroy the credibility of its promises. Imagine that after reaching a
negotiated settlement, the government breaks its commitment and attacks the
hijackers. This destroys any reputation the government has for trustworthy
treatment of hijackers. It loses the ability to make a credible promise, and
irreversibly denies itself the temptation to respond to a hijacker's threat.
This destruction of the credibility of a promise makes credible the threat
never to negotiate.
Contracts
A straightforward way to make your commitment credible is to
agree to a punishment if you fail to follow through. If your kitchen remodeler
gets a large payment up front, he is tempted to slow down the work. But a
contract that specifies payment linked to the progress of the work and penalty
clauses for delay can make it in his interest to stick to the schedule. The
contract is the commitment device.
Actually, it's not quite that simple. Imagine that a dieting
man offers to pay $500 to anyone who catches him eating fattening food. Every
time the man thinks of a dessert he knows that it just isn't worth $500. Don't
dismiss this example as incredible; just such a contract was offered by a Mr.
Nick Russo — except the amount was $25,000. According to the Wall Street Journal:
So, fed up with various weight-loss programs, Mr. Russo
decided to take his problem to the public. In addition to going on a
1,000-cirlorie-a-day diet, he is offering a bounty —$25,000 to the charity of one's
choosing — to anyone who spots him eating in a restaurant. He has peppered
local eateries ... with "wanted" pictures of himself.
But this contract has a fatal flaw: there is no mechanism to
prevent renegotiation. With visions of éclairs dancing in his head, Mr. Russo
should argue that under the present contractual agreement, no one will ever get
the $25,000 penalty since he will never violate the contract. Hence, the
contract is worthless. Renegotiation would be in their mutual interest. For
example, Mr. Russo might offer to buy a round of drinks in exchange for being
released from the contract. The restaurant diners prefer a drink to nothing and
let him out of the contract.
For the contracting approach to be successful, the party that
enforces the action or collects the penalty must have some independent incentive
to do so. In the dieting problem, Mr. Russo's family might also want him to be
skinnier and thus not be tempted by a mere free drink.
The contracting approach is better suited to business dealings.
A broken contract typically produces damages, so that the injured party is not
willing to give up on the contract for naught. For example, a producer might
demand a penalty from a supplier who fails to deliver. The producer is not
indifferent about whether the supplier delivers or not. He would rather get
his supply than receive the penalty sum. Renegotiating the contract is no
longer a mutually attractive option.
Cutting off Communication
Cutting off communication succeeds as a credible commitment
device because it can make an action truly irreversible. An extreme form of
this tactic arises in the terms of a last will and testament. Once the party
has died, renegotiation is virtually impossible. (For example, it took an act
of the British parliament to change Cecil Rhodes's will in order to allow
female Rhodes Scholars.) In general, where there is a will, there is a way to
make your strategy credible.
For example, most universities set a price for endowing a chair.
The going rate is about $1.5 million. These prices are not carved in stone (nor
covered with ivy). Universities have been known to bend their rules in order to
accept the terms and the money of deceased donors who fail to meet the current
prices.
Burning
Bridges behind You
Armies often achieve commitment by denying themselves an
opportunity to retreat. This strategy goes back at least to 1066, when WiIIiam
the Conqueror's invading army burned its own ships, thus making an
unconditional commitment to fight rather than retreat. Cort6s followed the same
strategy in his conquest of Mexico Cempoalla ,
Mexico
Leaving the Outcome beyond Your Control
The doomsday device in the movie Dr. Strangelove consisted of
large buried nuclear bombs whose explosion would emit enough radioactivity to
exterminate all life on earth. The device would be detonated automatically in
the event of an attack on the Soviet Union .
When President Milton Muffley of the United States
The device is such a good deterrent because it makes aggression
tantamount to suicide. Faced with an American attack, Soviet premier Dimitri
Kissov might refrain from retaliating and risking mutually assured
destruction. As long as the Soviet premier has the freedom not to respond, the
Americans might risk an attack. But with the doomsday device in place, the
Soviet response is automatic and the deterrent threat is credible.
However, this strategic advantage does not come without a
cost. There might be a small accident or unauthorized attack, after which the
Soviets would not want to carry out their dire threat, but have no choice as
execution is out of their control. This is exactly what happened in Dr.
Strangelove.
To reduce the consequences of errors, you want a threat that
is no stronger than is necessary to deter the rival. What do you do if the
action is indivisible, as a nuclear explosion surely is? You can make the
threat milder by creating a risk, but not a certainty, that the dreadful event
will occur. This is Thomas Schelling's idea of brinkmanship.
Moving
in Steps
Although two parties may not trust each other when the stakes
are large, if the problem of commitment can be reduced to a small-enough scale,
then the issue of credibility will resolve itself. The threat or promise is
broken up into many pieces, and each one is solved separately.
Honor among thieves is restored if they have to trust each
other only a little bit at a time. Consider the difference between making a
single $1 million payment to another person for a kilogram of cocaine and
engaging in 1,000 sequential transactions with this other party, with each
transaction limited to $1,000 worth of cocaine. While it might be worthwhile
to double-cross your "partner" for $1 million, the gain of $1,000 is
too small, since it brings a premature end to a profitable ongoing
relationship.
Whenever a large degree of commitment is infeasible, one
should make do with a small amount and reuse it frequently.
Teamwork
Often others can help us achieve credible commitment. Although
people may be weak on their own, they can build resolve by forming a group.
The successful use of peer pressure to achieve commitment has been made famous
by Alcoholics Anonymous (and diet centers too). The AA approach changes the
payoffs from breaking your word. It sets up a social institution in which
pride and self-respect are lost when commitments are broken.
Mandated Negotiating Agents
If a worker says he cannot accept any wage increase less than
5 percent, why should the employer believe that he will not subsequently back
down and accept 4 percent? Money on the table induces people to try negotiating
one more time.
The worker's situation can be improved if he has someone else
negotiate for him. When the union leader is the negotiator, his position may
be less flexible. He may be forced to keep his promise or lose support from his
electorate. The union leader may secure a restrictive mandate from his members,
or put his prestige on the line by declaring his inflexible position in public.
In effect, the labor leader becomes a mandated negotiating agent. His
authority to act as a negotiator is based on his position. In some cases he
simply does not have the authority to compromise; the workers, not the leader,
must ratify the contract. In other cases, compromise by the leader would result
in his removal.
In practice we are concerned with the means as well as the
ends of achieving commitment. If the labor leader voluntarily commits his
prestige to a certain position, should you (do you) treat his loss of face as
you would if it were externally imposed? Someone who tries to stop a train by
tying himself to the railroad tracks may get less sympathy than someone else
who has been tied there against his will.
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