La Teor

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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

• 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. 1992/1994/2002
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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.
Morgensterns 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, 730-761.
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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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John Nash
Born in June 13, 1928 in Bluefield, USA.
www.nobel.se/economics/laureates
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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 (1920-2000)
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. Aumanns and Schellings 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-)