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.
The skewness of the return distribution is one of the important features of the security price.In this paper,the authors try to explore the relationship between the skewness and the coefficient ofrisk premium.The coefficient of the risk premium is estimated by a GARCH-M model,and the robustmeasurement of skewness is calculated by Groeneveld-Meeden method.The empirical evidences forthe composite indexes from 33 securities markets in the world indicate that the risk compensationrequirement in the market where the return distribution is positively skewed is virtually zero,andthe risk compensation requirement is positive in a significant level in the market where the returndistribution is negative skewed.Moreover,the skewness is negatively correlated with the coefficient ofthe risk premium.
