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Game Theory

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I What is Game theory? The Theory of Games and Economic Behaviour by John von Neumann and Oskar Morgenstern (1944). Especially one institution: Princeton University –John Forbes Nash –Albert Tucker A game is defined as any interaction between agents that is governed by a set of rules specifying the possible moves for each participant and a set of outcomes for each possible combination of moves. Discover which strategy is a persons best response to the strategies chosen by others Best strategy: that which gives the a player the maximum payoff, given the strategy the other player has chosen or can be expected to choose. Social interactions or games are characterised by uncertainty since decision making is dependent on anticipating what others will do.

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II The application of game theory and its main assumptions Game theory can be applied as some sort of umbrella theory for the rational side of the social sciences. One single mode of explanation for diverse phenomena like: crossing the road in traffic, disarmament, economic competition, giving to charity, voting etc., all of which could be analysed as if they were games. It is useful mainly because it helps clarify some fundamental issues and debates in social science. Key assumptions: –Agents are instrumentally rational. –Agents have common knowledge of this rationality which leads to a consistent alignment of beliefs. –Agents know the rules of the game.

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III The prisoners dilemma An interaction where the individual pursuit of what seems rational produces a collectively self- defeating result. Outcomes in social life are often less than we might hope and the prisoners dilemma provides one possible key to their understanding. Is it (instrumentally) rational to defect? Important to distinguish between a single decision making period and sequences of simple games (super-games) that are played over a number of periods. Other games: Stag hunt, Chicken, Hawk vs. Dove, Battle of the Sexes Cooperative and non-cooperative games, zero-sum games, dynamic games, evolutionary games, three person games and n-person games etc. Burglar A Burglar B Not confess Confess Not confess 1,15, 0 Confess0, 53,3

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IV Game theory and IR The Game Theory of International Politics (Duncan Snidal 1985) As general approach to international politics, game theory assumes goal-seeking behaviour in the absence of centralised, authoritative institutions. It thereby illuminates the fundamental issues of international anarchy and the implications of different configurations of national interests and political circumstances for international conflict and cooperation. An empirical but not descriptive game theory of international relations A deductive theory which increases our understanding of fundamental processes by simplifying them and producing falsifiable predictions about them. If the underlying assumption of self-interested action by strategically rational states is correct, and preferences, strategies and payoffs can be modelled accurately, then a game theory of International politics could generate important testable predictions.

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Introduction to Game Theory Yale Braunstein Spring 2007.

Introduction to Game Theory Yale Braunstein Spring 2007.

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