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Notes for Session 4, Classical Game Theory, Summer School 2011 T.Seidenfeld 1 Session 4: Classical Game Theory von Neumann and Nash
 

Summary: Notes for Session 4, Classical Game Theory, Summer School 2011 T.Seidenfeld 1
Session 4: Classical Game Theory von Neumann and Nash
4.1: See the attached material taken from Luce and Raiffa's (1957) wonderful book,
Games and Decisions appendices 2-4 about von Neumann's Minimax Theorem for
Two-person, Zero-sum games. In class we'll concentrate on the opening to
Appendix 2 and the geometric argument of Appendix 3.
4.2: Limitations of the von Neumann Minimax Theorem.
4.2.1: Non-zero sum games multiple non-equivalent equilibria (BoS game)
4.2.2: More than 2 players no stability against coalitions. (Divide a dollar.)
4.3 Nash's Theory Preserve equilibria
4.4 Prisoner's Dilemma Pareto versus Strict Dominance
4.5 Strictly dominating non-Bayes decisions.
Notes for Session 4, Classical Game Theory, Summer School 2011 T.Seidenfeld 2
4.1 von Neumann's Minimax Theorem for 2 person, 0 sum games.
4.2.1: Multiple, non-equivalent equilibria in 2-person, non-zero sum games.
Bach Stravinsky
Bach (2,1) (0,0)
Stravinsky (0,0) (1,2)
Equilibria pairs are: (B,B) and (S,S).
These have different values to the players.

  

Source: Andrews, Peter B. - Department of Mathematical Sciences, Carnegie Mellon University

 

Collections: Mathematics