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What is game theory? Game theory is optimal decision-making in the presence of others with different objectives. Game theory is the mathematical theory of conflicts. A conflict is an interactive situation in which a) several agents make decisions, b) the final outcome depends on the decision of all agents, and c) every agent has his own preferences on the set of possible outcomes.

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**Mathematical Decision Theory**

One Objective Several Objectives One Decision-Maker One-person Decision Theory Multiobjective Decision Theory Several Decision-Makers Cooperative Game Theory Non-Cooperative Game Theory

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**Cooperative versus non-cooperative game theory**

Cooperative models assume that agents have cooperative mechanisms (to make binding commitments) outside the specified rules of the game. Cooperative solutions focus on how to allocate the benefits resulting from the cooperation. Non-cooperative models assume that players do not have cooperative mechanisms (to make binding commitments) outside the specified rules of the game. Non-cooperative solutions focus on how to behave strategically.

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**Some non-cooperative models Some cooperative models**

Strategic games (including finite games, zero-sum games, bimatrix games, matrix games,…) Extensive games: perfect information games, perfect and imperfect recall games, incomplete information games,... Dynamic games: repeated games, differential games, stochastic games,… Some cooperative models Bargaining problems. TU and NTU games.

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**“Handbook of Game Theory”. R. Aumann and S. Hart (eds. ). Elsevier**

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**Some milestones in the history of game theory**

Ancestors: Cournot, Zermelo, Borel. 1928. John von Neumann proves the minmax theorem.

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**John von Neumann Born in December 28, 1903 in Budapest, Hungary.**

Died in February 8, 1957 in Washington DC, USA.

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**Some milestones in the history of game theory**

Ancestors: Cournot, Zermelo, Borel. 1928. John von Neumann proves the minmax theorem. 1944. “Theory of Games and Economic Behavior”. John von Neumann and Oskar Morgenstern.

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“...it is apparent from the evidence presented above that all the technical aspects of the theory may be credited to von Neumann.” “Morgenstern’s role was crucial. (…) He focused the latter (von Neumann) attention, he acted as a spark.” Leonard RJ (1995) From Parlor Games to Social Science: von Neumann, Morgenstern and the Creation of Game Theory. Journal of Economic Literature 33,

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**Some milestones in the history of game theory**

Ancestors: Cournot, Zermelo, Borel. 1928. John von Neumann proves the minmax theorem. 1944. “Theory of Games and Economic Behavior”. John von Neumann and Oskar Morgenstern. 1950. Nash introduces his equilibrium concept.

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**Born in June 13, 1928 in Bluefield, USA.**

John Nash Born in June 13, 1928 in Bluefield, USA.

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**Some milestones in the history of game theory**

Ancestors: Cournot, Zermelo, Borel. 1928. John von Neumann proves the minmax theorem. 1944. “Theory of Games and Economic Behavior”. John von Neumann and Oskar Morgenstern. 1950. Nash introduces his equilibrium concept. 1971. Starting of International Journal of Game Theory. 1989. Starting of Games and Economic Behavior. 1994. Nobel Prize for Harsanyi, Nash and Selten.

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**Nobel Prize in Economic Sciences 1994**

John Harsanyi ( ) John Nash (1928-) Reinhard Selten (1930-)

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**Some milestones in the history of game theory**

Ancestors: Cournot, Zermelo, Borel. 1928. John von Neumann proves the minmax theorem. 1944. “Theory of Games and Economic Behavior”. John von Neumann and Oskar Morgenstern. 1950. Nash introduces his equilibrium concept. 1971. Starting of International Journal of Game Theory. 1989. Starting of Games and Economic Behavior. 1994. Nobel Prize for Harsanyi, Nash and Selten. 1999. The ISDG launches the International Game Theory Review. 2000. First World Conference on Game Theory (IGTS). 2005. Nobel Prize for Aumann and Schelling.

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**Nobel Prize in Economic Sciences 2005**

“Robert Aumann and Thomas Schelling have contributed to enhancing our understanding of conflict and cooperation. They have achieved this by extending and applying game theory –a method used to analyze strategic interaction among different agents. Their work has transformed the social sciences far beyond the boundaries of economics. Aumann’s and Schelling’s research continues to shape the debate on the formation of social institutions.” The Royal Swedish Academy of Sciences Thomas C. Schelling (1921-) Robert J. Aumann (1930-)

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