Common agency and computational complexity: theory and experimental evidence

In a common agency game, several principals try to in°uence the behavior of an agent. Common agency games typically have multiple equilibria. One class of equilibria, called truthful, has been identi¯ed by Bernheim and Whinston and has found widespread use in the political economy literature. In this paper we identify another class of equilibria, which we call natural. In a natural equilibrium, each principal o®ers a strictly positive contribution on at most one alternative. We show that a natural equilibrium always exists and that its computational complexity is much smaller than that of a truthful equilibrium. To compare the predictive power of the two concepts, we run an experiment on a common agency game for which the two equilibria predict a di®erent equilibrium alternative. The results strongly reject the truthful equilibrium. The alternative predicted by the natural equilibrium is chosen in 65% of the matches, while the one predicted by the truthful equilibrium is chosen in less than 5% of the matches.