Title: An Axiomatic Theory of a Risk Dominance Measure for Bipolar Games with Linear Incentives
Abstract: Bipolar games are normal form games with two pure strategies for each player and with two strict equilibrium points without common equilibrium strategies. A normal form game has linear incentives, if for each player the difference between the payoffs for any two pure strategies depends linearly on the probabilities in the mixed strategies used by the other players. A measure of risk dominance between two strice equilibrium points of a bipolar game with linear incentives is characterized by eleven axioms. The measure has the purpose to serve as a structural element of a not yet fully specified equilibrium selection theory for games with linear incentives. This class contains all two-person games but also those n-person games which arise from two-person normal forms with incomplete information by looking at the types as separate players. The measure is a weighted average of deviation loss ratio logarithms with weights derived from influence matrices whose elements describe one player´s relative influence on another player's payoff difference.
Creation-Date: August 1993
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