Disappointment-aversion in security games

Abstract

Even though players in a game optimize their goals by playing an equilibrium, the perceived payoff per round may (and in most cases will) deviate from the expected average payoff. For the example of loss minimization, an undercut of the expected loss is unproblematic, while suffering more than the expected loss may disappoint the player and lead it to believe that the played strategy is not optimal. In the worst case, this may subsequently cause deviations towards seemingly better strategies, even though the equilibrium cannot be improved in general. Such deviations from the utility maximization principle are subject of bounded rationality research, and this work is a step towards more accurate game theoretic models that include disappointment aversion as an additional incentive. This incentive necessarily creates discontinuities in the payoff functionals, so that Nash’s classical equilibrium theorem is no longer applicable. For games with disappointment aversion (defined in this work) the existence of equilibria can nonetheless be shown, i.e., we are able to find Nash equilibria that comply with disappointment aversion.