Game theory: concepts and applications by Frank C. Zagare

By Frank C. Zagare

The thoughts of online game idea (rationality and so on) now pervade a lot of social technology, in order that Professor Zagare's exposition of video game concept and its purposes (intended to "convert the unconverted and begin the uninitiated") is particularly welcome. He offers tools for analysing the constitution of the sport; considers 0 and nonzero-sum video games and the basic 'minimax theorem'; and investigates video games with greater than avid gamers, together with the potential of coalitions among avid gamers. varied examples provide the reader an concept of the way the idea could be utilized to quite a lot of occasions.

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If you have heard of zero-sum games, mixed strategies, Prisoners' Dilemmas, and minimax strategies, but feel that you should know more about these topics, Zagare's introduction will add greatly to your understanding of many aspects of modern social science. RICHARD G. NIEMI SERIES CO-EDITOR Page 7 Introduction Game theory is formally a branch of mathematics developed to deal with conflict of interest situations in social science. Although the origins of the theory can be traced to early articles in the 1920s by mathematicians Emile Borel (1921, 1924) and John von Neumann (1928), the field was only definitely established when von Neumann and economist Oskar Morgenstern published Theory of Games and Economic Behavior (1944[1953]).

While this outcome cannot be considered satisfactory by any reasonable standard, the strategies that brought it about were optimal, and game-theoretically sound, in the sense that they were the best choices either side could make, given the structure of the game they played. Needless to say, had either side been able to foresee the consequences of their action (both coalitions believed that the war would remain localized and limited in scope and duration) they might have evaluated the outcomes differently and been able to avoid war.

It seems safe to assume, then, that a player, if rational, will not select a dominated strategy, and that the search for an optimal strategy can confidently be limited to each player's set of undominated strategies. 3, a reduced version of the Battle of Avranches-Gap is provided, listing only the undominated strategies of the two players and Bradley's evaluation of the associated outcomes. The question remains: What strategy should each player choose? Each could choose the (pure) strategy8 that maximizes his security level, but these strategies are not in equilibrium, as is easily demonstrated.

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