抽樣均衡：選民出席投票之應用與一般理論

The notion of Nash equilibrium is the most important solution concept in the noncooperative game theory. However, there was a controversy over the interpretation of mixed-strategy Nash equilibria. Moreover, it is unsatisfactory to use Nash equilibrium to characterize the behavior of voter turnout. The aim of this work is to apply the concept of sampling equilibria to resolve the paradox of voting and propose that sampling equilibria can be used to justify mixed-strategy Nash equilibria. In Chapter 1 we contribute to the resolution of the paradox of voting by applying the concept of sampling equilibria. We develop a model of voter turnout where citizens are boundedly rational in a way that each citizen makes the statistical decision based on the sample that contains partial information about the other citizens' behaviors. Hence, given the sample and their prior beliefs, the citizens update their beliefs about the other citizens' behaviors and then make decisions whether or not to vote. By varying the sample size, this model synthesizes the decision theoretic model, the model of participation game with complete information or with incomplete information. If the election appears to be tied in equilibrium, we obtain the result, in the model with complete information, that the turnout rate approaches one when the sample size goes to infinity; while in the model with incomplete information we show that there is an equilibrium the voters with positive cost cast ballots. In general, when the sample size is finite, the turnout is substantial. In Chapter 2 we study the concept of sampling equilibrium in finite games and in games with incomplete information in which the extended games are finite. It is also assumed that each individual gets partial information (a sample) about the behaviors of the other players and makes decisions by the foundation of the statistical decision theory. We show that the sampling equilibrium approaches perfect equilibrium as the sample size tends to infinity. Moreover, as the sample size tends to infinity, every regular equilibrium is approximated by a sampling equilibrium and almost every individual's optimal statistical decision is a unique, pure strategy in this sampling equilibrium. Hence, the sampling equilibrium can be used to justify the mixed strategy (Bayesian) Nash equilibrium. Besides, the sampling equilibrium can be resolved by Newton iterates and thus can be used to calculate (Bayesian) Nash equilibrium.

並列關鍵字

sampling equilibria ； game theory ； paradox of voting ； voter turnout ； justifications of mixed-strategy equilibria

參考文獻

Beck, N. (1975). "The Paradox of Minimax Regret," American Political Science Review, 69, pp. 918.

Benaim, M. and Hirsch, M. (1999). "Mixed Equilibria and Dynamical Systems Arising from Fictitious Play in Perturbed Games," Games and Economic Behavior, 29, pp. 36n72.

Cox, G. W. and Munger, M. C. (1989). "Closeness, Expenditures, and Turnout in the 1982 U.S. House Elections," American Political Science Review, 83, pp. 217--231.

Dhillon, A. and Peralta, S. (2002). "Economic Theories of Voter Turnout," The Economic Journal, 112, pp. F332--F352.

Downs, A. (1957). An Economic Theory of Democracy. New York: Harper and Row.

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抽樣均衡：選民出席投票之應用與一般理論

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