Risk limits, conflict, and equilibrium selection in games with multiple equilibria

Abstract

A risk limit conflict measure is developed as the product of the two players’ maximum probabilities of being recalcitrant when pursuing a preferred equilibrium. Although the justification for it is different, the measure is equivalent to Axelrod’s (1970) measure, which is the ratio of infeasible joint demand and joint demand above the threat point which he illustrated graphically. Axelrod did not justify his measure beyond informal verbal descriptions. The article furthermore offers an equilibrium selection in favour of the player with the largest risk limit. The equilibrium selection is different from Harsanyi and Selten’s (1988, p.90) equilibrium selection, which assigns equal weight to four payoff differences, which the article argues is not realistic. The equilibrium selection is also compared with Hausken (2007).