PPT-Math Intro: Matrix Form Games and Nash Equilibrium

Lets start with an informal discussion of what a game is and when its useful Components of a game Players Eg animals people firms countries Strategies Eg attack S. Christodoulou and . Koutsoupias. ,. Roughgarden. Slides stolen/modified from Tim . Roughgarden. TexPoint fonts used in EMF. . Read the TexPoint manual before you delete this box.: . A. A. A. A. A. A. Econ 171. The Hawk-Dove Game. Animals meet encounter each other in the woods and must decide how to share a resource.. There are two possible strategies. . Hawk: Demand the entire resource and be prepared to fight for it.. ECO 54 History of Economic Thought. Udayan. Roy. What is Game Theory?. Game theory looks at rational behavior when each decision maker’s well-being depends on the decisions of others as well as her own. Fall 2011. Constantinos Daskalakis. Lecture 11. Last. . Lecture. .... 0. n. Generic PPAD. Embed PPAD graph in [0,1]. 3. 3D-SPERNER. canonical . p. .w. . linear . BROUWER. multi-player. NASH. 4-player. Theorem. (Nash, 1951): . Every finite game (finite number of players, finite number of pure strategies) has at least one mixed-strategy Nash equilibrium.. Nash, John.  (1951) "Non-Cooperative Games" . 1 2 III. Extensive-Form Games Strategies are Lecture 12. Constantinos Daskalakis. The Lemke-. Howson. Algorithm. The Lemke-. Howson. Algorithm (1964). Problem:. Find an exact equilibrium of a 2-player game.. Since there exists a rational equilibrium this task is feasible.. Econ 171. The Hawk-Dove Game. Animals meet encounter each other in the woods and must decide how to share a resource.. There are two possible strategies. . Hawk: Demand the entire resource and be prepared to fight for it.. Microeconomics C. Amine Ouazad. Who am I. Assistant prof. at INSEAD since 2008.. Teaching . Prices and Markets in the MBA . program, Econometrics A, B, Microeconometrics, in the PhD program.. Research:. Short introduction to game theory. 1. 2. Decision . Theory (reminder). (How to make decisions). Decision Theory = . Probability theory + Utility Theory. (deals with chance) (deals with outcomes). Fall 2016. Yang Cai. Lecture . 05. Overview so far. Recap:. Games, . rationality, . solution concepts. Existence Theorems for Nash equilibrium: . Nash’s theorem for general games (via . Brouwer. solution concepts, and . Refinements of NASH Equilibrium. Tuomas Sandholm. The heart of the problem. In a 1-agent setting, agent. ’. s expected utility maximizing strategy is well-defined. But in a multiagent system, the outcome may depend on others. competitiON. P.V. Viswanath. FIN 663, . Financial Strategy and Business Decisions. Why Game Theory?. equilibria. We saw previously (in the module on Capital Structure and Stockholder Incentives) that the existence of debt could cause debt overhang... solution concepts, and . Refinements of NASH Equilibrium. Tuomas Sandholm. The heart of the problem. In a 1-agent setting, agent. ’. s expected utility maximizing strategy is well-defined. But in a multiagent system, the outcome may depend on...