VIRTUAL IMPLEMENTATION IN ITERATIVELY UNDOMINATED STRATEGIES - COMPLETE INFORMATION

被引:117
作者
ABREU, D [1 ]
MATSUSHIMA, H [1 ]
机构
[1] UNIV TSUKUBA,INST SOCIO ECON PLANNING,TSUKUBA,IBARAKI 305,JAPAN
关键词
IMPLEMENTATION; ITERATIVELY UNDOMINATED STRATEGIES; FINITE MECHANISMS; MIXED STRATEGIES; VIRTUAL;
D O I
10.2307/2951536
中图分类号
F [经济];
学科分类号
02 ;
摘要
We investigate the implementation of social choice functions in complete information environments. We consider social choice functions (scf's) which map from a finite set of preference profiles to lotteries over alternatives, and require virtual implementation in iteratively undominated strategies. An scf x is virtually implementable in iteratively undominated strategies if for all epsilon > 0, there exists an scf y which is epsilon-close to x (that is, for all preference profiles, x and y map to lotteries which are within epsilon of one another) and which is (exactly) implementable in iteratively undominated strategies. Under very weak domain restrictions we show that if there are three or more players, any scf is virtually implementable in iteratively undominated strategies. A noteworthy feature of our constructions is that we only employ finite mechanisms. As a corollary, we obtain virtual implementation in (pure and) mixed strategy Nash equilibrium using well-behaved (in particular, finite) mechanisms. The literature on implementation in Nash equilibrium and its refinements is compromised by its reliance on game forms with unnatural features (for example, "integer" games), or "modulo" constructions with mixed strategies arbitrarily excluded. In contrast, our results allow for mixed strategies and do not rely on mechanisms with obviously suspicious features.
引用
收藏
页码:993 / 1008
页数:16
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