Implementation in dominant strategy equilibrium

A social choice rule is any proposed solution to the problem of collective decision making and it embeds the normative features that can be attached to the mentioned problem. Implementation of social choice rules in dominant strategy equilibrium is the decentralization of the decision power among the agents such that the outcome that is a priori recommended by the social choice rule can be obtained as a dominant strategy equilibrium outcome of the game form which is endowed with the preferences of the individuals. This work has two features. First, it is a survey on the literature on implementation in dominant strategy and its link with the economic theory. Second, it constructs some new relationships among the key terms of the literature. In this framework, it states and proves a slightly generalized version of the Gibbard-Satterthwaite impossibility theorem. Moreover, it states and proves that the cardinality of a singlepeaked domain converges to zero as the number of alternatives increase to infinity.