Revealed Aspirations and Reciprocal Loyalty in Apex Games

Summary

In this paper a new model for one-step characteristic function games is introduced which explicitly models bargaining chains as chains of stepwise dominating bargaining states. This process model includes the description of reciprocal loyalty and revealed aspirations. Reciprocal loyalty can be developed in groups of “similar players”. The effect of reciprocal loyalty is that a player of the group does not break a joint coalition of the group (and thereby does not “betray” players of the group) unless by the defection he increases his outcome for more than a given amount R, which is the same for all players of the group. It should be remarked that reciprocal loyalty does not have the character of an additional utility. It only gets the character of an additional payoff when a player leaves a coalition, and not when he enters it. By means of revealed aspirations a consistency condition for bargaining chains is defined. It is assumed that by every state of the bargaining process the players reveal information about their aspirations they want to see fulfilled if they are in a coalition. Here it is modeled that a player who changes from one state to another, and thereby improves his payoff shows that his aspiration is higher than his outcome in the preceding state.