ABSTRACT
Introduction Predicting the equilibrium in economics often involves severe computational problems (see Velupillai 2000). However, even if the set of equilibria is simple to calculate, frequently a coordination problem remains to be solved. Such coordination problems can result in inferior outcomes even in mutual interest games. If we consider the pure coordination game in Figure 13.1 in its existential form (as described by Sugden 1995), then without communication the game theoretical prediction of the average behaviour of a population would be the mixed strategy equilibrium where both players choose each strategy with proba bility 0.5. The average payoff would be 100 in this equilibrium. However, Schelling (1960) has argued convincingly that the expected payoff can be improved upon by letting the players use contextual information about the game, like the strategy labels. Thus, for instance by denoting strategies C1 and R1 by ‘Heads’ and C2 and R2 by ‘Tails’ experimental results demonstrate that the majority of subjects are able to coordinate in the (Heads, Heads) equilibrium (see e.g. Mehta et al. 1994). Schelling’s (1960) theory of focal points has become a standard reference in textbooks in game theory (see e.g. Fudenberg and Tirole 1991; Binmore 1992) and it has been developed further by e.g. Bacharach (1993) and Sugden (1995). It has also been confirmed in various experiments (e.g. Mehta et al. 1994; Holm 2000). Thus, few would argue that the ideas put forth by Schelling (1960) are unimportant in coordination situations, especially when one considers that some
contextual information is always present in real strategic situations. This leads to a dilemma: at the same time as contextual information enriches game theory by making it possible to predict a unique focal equilibrium, the importance of con textual information also challenges the very foundation of any theory intended to be applicable to different contexts. It is therefore somewhat strange that so little effort has been directed in trying to find out how important this type of informa tion is compared to payoffs which are captured by the existential game form. Our experiment can be seen as a simplistic step in this direction. The purpose of this chapter is to study the strength of a focal point induced by strategy labels when a small payoff asymmetry is introduced.2 The asym metry is designed so that the non focal equilibrium in the original game becomes payoff salient in the new game by letting it be both Pareto dominant and risk dominant.3 In this way the subjects are forced to select what principle to believe in (and believe that others believe in, etc.), strategy label saliency or payoff saliency.
