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Please use this identifier to cite or link to this item: http://hdl.handle.net/1959.3/204575
 Title
 Applying risk theory to game theory
 Author(s)
 Barnett, Tristan
 Abstract
 The Minimax Theorem is the most recognized theorem for determining strategies in a two person zerosum game. Other common strategies exist such as the maximax principle and minimize the maximum regret principle. All these strategies follow the Von Neumann and Morgenstern linearity axiom which states that numbers in the game matrix must be cardinal utilities and can be transformed by any positive linear function f(x)=ax+b, a>0 without changing the information they convey. This paper describes riskaverse strategies where the linearity axiom may not hold. With connections to gambling theory, there is evidence to show why it can be optimal for the favorable player to adopt riskaverse strategies. This reasoning can then be applied to a two person zerosum game arbitration process to determine an alternative outcome to the solution given by strategies under the Minimax Theorem. Risk analysis is used to show why the uncooperative solution in the Prisoner's Dilemma can be a 'reasonable' outcome to the game, even though the solution is nonPareto optimal, and why cooperation may be implicitly forced in the game. Logical reasoning is given to show why maximin strategies in two person nonzerosum games could be considered as a Nash Equilibria. A riskaverse status quo is devised for the Nash Arbitration scheme as an alternative to the maximin and threat status quo solutions. The analysis and results given in this paper show that it can be 'optimal' for the favorable player to accept less than the amount given by maximizing expectation, due to the risks involved and the possibility of having a negative payout.
 Publication type
 Conference paper
 Source
 Proceedings of the 2nd Brazilian Workshop of the Game Theory Society, Sao Paulo, Brazil, 29 July04 August 2010
 Publication year
 2010
 Keyword(s)
 Gambling theory; Game theory; Minimax Theorem; Riskaverse strategies; Risk theory; Two person zerosum games
 Publisher
 Game Theory Society
 Publisher URL

http://www.gametheorysociety.org/conferences/2010.html
 Copyright
 Copyright © 2010.