An Adaptive Model of Demand Adjustment in Weighted Majority Games

This paper presents a simple adaptive model of demand adjustment in cooperative games and analyzes this model in weighted majority games. In the model, a randomly chosen player sets her demand to the highest possible value subject to the demands of other coalition members being satisfied. This basic process converges to the aspiration set. By introducing some perturbations into the process, we show that the set of separating aspirations, i.e., demand vectors in which no player is indispensable in order for other players to achieve their demands, is the one most resistant to mutations. We then apply the process to weighted majority games. We show that in symmetric majority games and in apex games, the unique separating aspiration is the unique stochastically stable one.

MEASURING THE POWER OF PARTIES WITHIN GOVERNMENT COALITIONS

The paper presents a coalition-structure value that is meant to capture outside options of players in a cooperative game. It deviates from the Aumann-Drèze value by violating the null-player axiom. We use this value as a power index and apply it to weighted majority games.