k -Prize Weighted Voting Game

We introduce a natural variant of weighted voting games, which we refer to as 𝑘-Prize Weighted Voting Games. Such games consist of 𝑛 players with weights, and 𝑘 prizes, of possibly differing values. The players form coalitions, and the 𝑖-th largest coalition (by the sum of weights of its members) wins the 𝑖-th largest prize, which is then shared among its members. We present four solution concepts to analyse the games in this class, and characterise the existence of stable outcomes in games with three players and two prizes, and in games with uniform prizes. We then explore the efficiency of stable outcomes in terms of Pareto optimality and utilitarian social welfare. Finally, we study the computational complexity of finding stable outcomes.

Authors

• Wei-Chen Lee University of Oxford
• David Hyland University of Oxford
• Alessandro Abate University of Oxford
• Edith Elkind Northwestern University
• Jiarui Gan
• Julian Gutierrez
• Paul Harrenstein
• Michael Wooldridge University of Oxford

Keywords

• Coalition formation
• Cooperative game theory
• Cooperative games
• with externalities
• Core
• Efficiency
• Partition function form
• Stability
• Weighted Voting Game.