Game Theory

Game Theory
Sociologyindex	Books On Game Theory	Sociology Books 2008
Game theory develops general mathematical formulas and algorithms to identify optimal strategies and to predict the outcome of interactions. Game Theory is the science of strategy and attempts to determine what actions different players such as trading partners, employers, unions or even organised crime groups should take to secure the best outcome for themselves. Game theory studies strategic interaction in competitive and cooperative environments. Only fifty years old, it has already revolutionized economics, and is spreading rapidly to a wide variety of fields including conflict and war. Oskar Morgenstern and mathematician John von Neumann also contributed immensely. Game theory applied to penalty kicks in a tie-breaker Nobel laureates John Nash, Robert Aumann and Thomas Schelling have done pioneering work in the field of game theory. The 2005 Nobel prize for economics was given to Thomas Schelling and Robert Aumann for their work on "game theory", for work that found uses in "security and disarmament policies, price formation on markets, as well as economic and political negotiations." Robert Aumann has been cited for his analysis of "infinitely repeated games" to identify what outcomes can be maintained over time. "Insights into these issues help explain economic conflicts such as price wars and trade wars, as well as why some communities are more successful than others in managing common-pool resources." Robert Aumann believes that "game theory had become a cornerstone of economics worldwide. "I think game theory creates ideas that are important in solving and approaching conflict in general" - Robert Aumann. On winning the Nobel prize Robert Aumann has said "This is a badge of honour for this branch of science, for game theory." Thomas Schelling who has said "I'm not really a game theorist" has applied game theory to global security and the cold war arms race. Thomas Schelling has also used examples from everyday life, such as the difficulty in trying to get ice-hockey players to overcome their fear of being at competitive disadvantage and wear helmets, even though it would protect their heads. Game Theory Society - Founded in January 1999, the society aims to promote the investigation, teaching and application of game theory. gametheorysociety.org/intro.html

Game theory applied to penalty kicks in a tie-breaker

Ever heard of sportsmen applying a combination of economics and mathematics to win the game. Game Theory was originally devised to help anything from pay negotiations to waging war. Morgenstern and von Neumann didn’t target footballers or gamblers.

‘World Cup Game Theory,’ an article in Slate magazine, decodes Game Theory and analyses how it works.

Using Game Theory we can mathematically analyse ‘‘situations of strategic interaction, that is, any situation where participants have to take into account the other side’s responses. Here, strategic interaction would be a soccer penalty, not a free throw in basketball. the strategic question could be translated into Game Theory’s mathematical language, solved like any old mathematical problem, and then translated back into the real world to explain what to do.

Tim Harford, author of bestselling 'The Undercover Economist' highlights this with an example. ‘‘Let’s say a right-footed striker always shoots to the right. The keeper will always anticipate the shot and the striker would be better off occasionally shooting to the left, because even with a weaker shot it is best to shoot where the goalie isn’t.

On the other hand, if the striker chooses a side by tossing a coin, the keeper will always dive to the striker’s left: Since he can’t guess where the ball will go, best to go where the shot will be weak if it does come. But then the striker should start favouring his stronger side again.’’

It is in such a situation that Game Theory works, a ‘‘mathematical description of how all the possible payoffs to the different players vary with their different strategies — so if the goalkeeper jumps to his left while the striker shoots to the keeper’s right, the striker will get a high payoff and the goalkeeper will get a low one.’’

He explains that if the striker and the keeper are behaving optimally, neither will have a predictable strategy. The striker might favour his stronger side, of course, but that does not mean that there will be a pattern to the bias. The striker might shoot to the right two times out of three, but we cannot then conclude that it will have to be to the left next time. each choice of shot should be equally likely to succeed, weighing up the advantage of shooting to the stronger side against the disadvantage of being too predictable.
If shots to the right score three-quarters of the time and shots to the left score half the time, you should be shooting to the right more often. Shots to the right will become less successful and those to the left more successful. It might sound strange that at this point any choice will do, but it is analogous to saying that if you are at the summit of the mountain, no direction is up.