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Please use this identifier to cite or link to this item: http://hdl.handle.net/1959.3/204575
- Applying risk theory to game theory
- Barnett, Tristan
- The Minimax Theorem is the most recognized theorem for determining strategies in a two person zero-sum 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 risk-averse 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 risk-averse strategies. This reasoning can then be applied to a two person zero-sum 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 non-Pareto optimal, and why cooperation may be implicitly forced in the game. Logical reasoning is given to show why maximin strategies in two person nonzero-sum games could be considered as a Nash Equilibria. A risk-averse 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
- Proceedings of the 2nd Brazilian Workshop of the Game Theory Society, Sao Paulo, Brazil, 29 July-04 August 2010
- Publication year
- Gambling theory; Game theory; Minimax Theorem; Risk-averse strategies; Risk theory; Two person zero-sum games
- Game Theory Society
- Publisher URL
- Copyright © 2010.