Truthfulness in Coalitions : A Sequential Equilibrium Analysis

The paper integrates the formation of coalitions by a standard sequential offer procedure and the truthfulness - cheating strategies of their members, which support sequential equilibria. We derive the probabilities of truthfulness for players in a two - and three - member coalition in terms of the payoffs. It turns out that in a sequential equilibrium, these probabilities are determined by the tension between two basic incentives: the incentive to cheat and the incentive to defend against cheating. Both incentives are expressed in terms of payoffs. Among the results, we find that if the latter dominates the incentive to cheat, honesty is a pure strategy that supports a sequential equilibrium. Also, feasible payoff patterns are identified in which honesty and cheating do not matter; that is, whether the players are honest or not, the same coalitions emerge in a subgame perfect equilibrium. Other well defined payoff patterns are uncovered in which players' truthfulness is associated with different coalition sizes and structures so that honesty and cheating do matter in this sense