April 2013
Beginner
266 pages
6h 11m
English
Content preview from Solutions Manual to Accompany Game Theory: An Introduction, 2nd Edition
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Appendix D: Games in Extensive Form: Sequential Decision Making
Definition D.1 A subgame perfect equilibrium for an extensive form game is a Nash equilibrium whose restriction to any subgame is also a Nash equilibrium of this subgame.
Theorem D.2 Any finite tree game in extensive form has at least one subgame perfect equilibrium.
Theorem D.3 (1) Any finite game in extensive form with perfect information has at least one subgame perfect equilibrium in pure strategies.
(2) Suppose all payoffs at all terminal nodes are distinct for any player. Then there is one and only one subgame perfect equilibrium.
(3) If a game has no proper subgames, then every Nash equilibrium is subgame perfect.
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