In this paper, we introduce a simple coalition formation game in the environment of bidding, which is a special case of the weighted majority game （WMG）, and is named the weighted simple-majority game （WSMG）. In W...In this paper, we introduce a simple coalition formation game in the environment of bidding, which is a special case of the weighted majority game （WMG）, and is named the weighted simple-majority game （WSMG）. In WSMG, payoff is allocated to the winners proportional to the players powers, which can be measured in various ways. We define a new kind of stability： the counteraction-stability （C-stability）, where any potential deviating players will confront counteractions of the other players. We show that C-stable coalition structures in WSMG always contains a minimal winning coalition of minimum total power. For the variant where powers are measured directly by their weights, we show that it is NP-hard to find a C-stable coalition structure and design a pseudo-polynomial time algorithm. Sensitivity analysis for this variant, which shows many interesting properties, is also done. We also prove that it is NP-hard to compute the Holler-Packel indices in WSMGs, and hence in WMGs as well.展开更多
基金supported by National Natural Science Foundationof China(No. 70425004)
文摘In this paper, we introduce a simple coalition formation game in the environment of bidding, which is a special case of the weighted majority game （WMG）, and is named the weighted simple-majority game （WSMG）. In WSMG, payoff is allocated to the winners proportional to the players powers, which can be measured in various ways. We define a new kind of stability： the counteraction-stability （C-stability）, where any potential deviating players will confront counteractions of the other players. We show that C-stable coalition structures in WSMG always contains a minimal winning coalition of minimum total power. For the variant where powers are measured directly by their weights, we show that it is NP-hard to find a C-stable coalition structure and design a pseudo-polynomial time algorithm. Sensitivity analysis for this variant, which shows many interesting properties, is also done. We also prove that it is NP-hard to compute the Holler-Packel indices in WSMGs, and hence in WMGs as well.
