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		PDO: From Decision Theory to Game Theory with Mike Jones

Description:		This workshop is part of the New York City-based Professional Development and Outreach (PDO) Group 2010-2011 course on "Mathematics and Fairness," sponsored by Math for America and the IAS/Park City Mathematics Institute. Session description: Anytime one person's decision not only affects her own outcome, but another person's outcome, is a situation that may be modeled by game theory. This cocktail party description suggests that game theory is a collection of tools and techniques for modeling and analyzing behavior in diverse applications. Because the players interests may be diametrically opposed, perfectly aligned, or anywhere in between, 2007 Nobel Prize of Economics winner Roger Myerson suggested that game theory should instead be called the "analysis of conflict and cooperation." To introduce game theory terminology, the session will begin with decision theory in which a single player's decision affects only his own outcome or instances in which players' interests are perfectly aligned. As an application, we'll consider a contestant's decision whether to accept a deal or not in the television game show Deal or No Deal. When two players' interests are diametrically opposed, then the game is called a zero-sum game. In 1928, Von Neumann proved that there is always a pair of equilibrium strategies that describe the optimal behavior of the two players when they move simultaneously. We'll use geometry to determine these strategies for small games that model pitcher-batter interactions in baseball. Further, we'll consider non-zero sum games for 2 or more players. Nash generalized Von Neumann's result to solve these types of games, earning him the 1994 Nobel Prize in Economics. For 2-player games, I will explain how Nash's solution concept generalizes both optimization (from decision theory) and Von Neumann's Minimax Theorem (for zero-sum games). Decision theory (or games in which players have identical preferences; cooperative situations) and zero-sum games (or games in which players have opposite preferences; conflict situations) form the two endpoints of the spectrum of two-player, simultaneous move games. Nash's equilibrium allows the games in this spectrum, as well as others, to be analyzed. We'll end with additional applications that demonstrate how game theory can be used to analyze fair division procedures that model divorce settlements, inheritances, and allocations of travel funds among faculty. A benefit of this analysis is that ideas about optimization can be introduced to students with only a background in algebra.

When:		8/27/10 9:00 AM EDT

Duration:		6 Hours 30 Minutes

Location:		MfA office, 160 5th Avenue, 8th Floor, (Entrance on 21st St.) New York, NY, 10010, USA

Type:		General Public

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