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Nash Equilibrium

If gordon does not enter tony will then lead the

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Unformatted text preview: party to a victory at the next election, and Tony will unanimously be remembered as a wise leader and will retain strong in influence over the party. If Gordon does not enter, Tony will then lead the party at the next election and he also has good chances of winning and retain Gordon as the chancellor. NORMAL FORM REPRESENTATION OF THE LEADERSHIP GAME  ­ There are 2 Nash Equilibria: {Stay Out, Fight} and {Enter, Accept}  ­Normal form representation is appropriate for games with simultaneous moves. The two NE, however, in this case hide a non ­credible treat: once Gordon enters the race, it is not credible that Tony will fight.  ­If the order of moves is such that Gordon moves first, then there is a problem with the first NE. We need a stronger equilibrium concept, a "refinement" of NE. Subgame perfect equilibrium  ­A refinement of Nash equilibrium  ­A strategy is now not just an action but a contingent plan of actions  ­ Strategies form a NE in correspondence of any subgame (i.e. starting from any node of the game)  ­Solution usually found by backward induction Summary of Lecture  ­ defined what decision theory and game theory are  ­ analyzed static games with complete information  ­ Examined simple solution concepts for games such as IDSDS and Nash Equilibrium  ­ analyzed dynamic games with complete information and the time ­consistency (credibility) problem...
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