The Probability Of Inefficient Allocation And The Loss Of Social Welfare In The Process Of Unfair Contests

The contests are usually "unfair" in the sense that outperforming all rivals may not be enough to be the winner, because some contestants are favored by the allocation rule, while others are handicapped. However, the contestant who is favored by the allocation rule at beginning of the contest is possibly handicapped with the passage of time, which means the roles of the contestants can have a transformation. An unfair, two-player discriminatory contest where the roles of the contestants have a transformation, is analyzed. Based on the closed form solutions of the equilibrium strategies to the unfair contests, the work did by Feess et al.(2008) and Duan et al.(2012) is extended and deepened, the probability of an inefficient allocation and the loss of social welfare in the unfair contest are analyzed and their explicit mathematical formulas are obtained, which present they are the strictly monotonic increasing functions of the unfair degrees of the rules in the unfair contests.