Thursday 24 November 2011

ADAPTING GAME THEORY TO THE CLASSROOM-TEACHING NOTES ON THINKING STRATEGICALLY



“Strategic thinking is the art of outdoing an adversary, knowing that the adversary is trying to do the same to you”(Dixit, Avinash and Nalebuff Barry, Norton 1991).Strategic Thinking has been studied in various books, notably in Michael Porter’s Competitive Strategy (Porter, Michael, Free Press, 1991). However our focus is on Dixit and Nalebuff’s classic “Thinking Strategically-The Competitive Edge in Business, Politics and Everyday Life”
A). Ten Tales of Strategy
1. The Hot Hand: People including commentators and bettors believe that players experience the “hot hand, while observing basketball players scoring baskets, they believe that there exists a positive autocorrelation between successful baskets when there is infact no empirical evidence of that..Sports announcers see long streaks of consecutive successes and proclaim that the athelete has a “hot hand.” Yet according to certain psychology professors, this is a misperception of reality.(Gilovich, Thomas, Vallone, Robert and Tversky, Amos, 1985).
They propose a more rigorous test. In basketball, they look at all the instances of a player’s baskets, and observe the percentage of times that player’s next shot is also a basket.A similar calculation is made for the shots immediately following misses.If a baket is more likely to follow a basket than to follow a miss, then there really is something to the theory of the hot hand.
They conducted this test on a basketball team. The results contradicted the ‘hot hand’ view. When a player made his last shot, he was less likely to make his next; when he missed his previous attempt, he was more likely to make his next. Does this mean we should be talking of the ‘stroboscopic hand,” like the strobe light that alternates between on and off?
Game theory suggests a different interpretation. While the statistical evidence denies the presence of streak shooting, it does not refute the possibility that a ‘hot’ player might warm up the game in some other way. The difference between streak shooting and a hot hand arises because of the interaction between offensive and defensive strategies. Suppose a player does have a truly hot hand. Surely the other side would start to crowd him. This could easily lower his shooting percentage.
That is not all. When the defense focuses on this player, one of his teammates is left unguarded and is more likely to shoot successfully. Thus we might test for hot hands by looking for streaks in team success.
A player may even assist himself when one hot hand warms up the other. The Boston Celtics star, Larry Bird, prefers shooting with his right hand.
What happens when Bird spends his off season working to improve his left-handed shooting? The defense responds by spending more time covering his left-handed shots. The result is that this frees his right hand more often.
Going one step further, we show that when the left hand is stronger it may even be usedless often. If your backhand is much weaker than your forehand, your opponents will learn to play to your backhand. Eventually, as a result of all this backhand practice, your backhand will improve. As your two strokes become more equal, opponents will play more evenly between forehands and backhands. You get to use your better forehand more often; this could be the real advantage of improving your backhand.
2. When it pays to move second-In two competitor sailboat racing an interesting reversal of a “follow the leader” strategy is seen. The leading sailboat usually copies the strategy of the trailing boat. If you have the lead, the surest way to stay ahead is to play monkey see, monkey do. So we come to our second tale-
                                             “To lead or not to lead.”
After the first four races in the 1983 America’s Cup finals, Dennis Conner’s Liberty led 3-1 in a best-of-seven series. On the morning of the fifth race, there was anticipation of having prolonged the United States’ winning streak to 132 years. It was not to be.
At the start, Liberty got off  to a 37-second lead when Australia II  jumped the gun and had to recross the starting line. The Australian skipper, John Bertrand, tried to catch up by sailing way over to the left of the course in the hopes of catching a wind shift. Dennis Conner chose to keep Liberty on the right-hand side of the course. Bertrand’s gamble paid off. Conner was criticized for his strategic failure to follow Australia II’s path. Two races later, Australia II won the series.
The leader imitates the follower even when the follower is clearly pursuing a poor strategy. Why? Because in sailboat racing: only winning matters.
3.Do what you want we will not bribe you-Consider two companies both in a position where they have to bribe a Government department, now one company will think the other company is going to bribe so I will benefit by bribing, he can also think even if the other company does not bribe I will benefit by bribing.The other company will also think in a similar manner so both will end up bribing the government department. However both companies would have benefitted by making an agreement not to bribe. This is an example of Prisoners Dilemna
4. Be selectively inflexible-there is a power in intransigence , but how can one achieve the necessary degree of intransigence? There are various means by which commitment can be achieved and sustained.
5. Hostages dilemma-a prisoners dilemma with more than two people-Why is a planeload of people powerless before a single hijacker with a gun? The question is who is going to bell the cat?
6. Look at the whole picture-Decisions made on a case by case basis can lead to undesireable results overall.In fact a sequence of majority votes can lead to an outcome that everyone regards as worse than the status-quo.
7. Be wary of a commitment-once you get into a situation it is difficult to get out of it. Strategists who foresee such consequences will use their bargaining power while it exists, namely, before they get into the commitment.
8. Mix your plays-If you do the same thing all the time, the opposition will be able to counter you more effectively by concentrating its resources on the best response to your one strategy. It is unpredictability that is important when mixing.
9. Use information to guide your own action.-The strategic insight is that other people’s actions tell us something about what they know, and we should use such information to guide our own action. Of course, we should use this in conjunction with our own information concerning the matter and use all strategic devices to elicit more from others.
10.Pride and irrationality cannot be ignored-It is foolhardy to deal with people who are not rational in terms of bargaining, negotiations and strategy. Even if you deal with such people do not pre-commit yourself.
B)A few Morals:
The Hot hand-we cannot assume that when we change our behavior everything else will remain unchanged.
When it pays to move second-In technology races no less than in sailboat races, those who trail tend to employ more innovative strategies; the leaders tend to imitate the followers.
Be selectively inflexible-“The stuck wheel gets the grease”
Belling the cat-the difficulty of obtaining outcomes that require coordination and individual sacrifice.
Look at the whole picture-the danger of solving problems piece by piece.
Mix your plays-tennis and tax audits point out the strategic advantage of being unpredictable.
C.) Moral of Case Study 1-In games it is not always an advantage to seize the initiative and move first. This reveals your hand, and the other players can use this to their advantage and your cost. Second movers maybe in the stronger strategic position.
References;
Dixit, Avinash, Nalebuf Barry, “Thinking Strategically-The Competitive Edge in Business, Politics and Everyday Life” Norton 1991.

Gilovich, Thomas, Vallone, Robert and Tversky, Amos,”The Hot Hand in Basketball:On the misperception of Random Sequences,” Cognitive Psychology 17,1985:295-314.

Porter, Michael, Competitive Strategy,Free Press, 1991

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