An algorithm for verifying double implementability in Nash and strong Nash equilibria

Abstract Suh (Suh, S., 1997. Double implementation in Nash and strong Nash. Social Choice and Welfare 14, 439−447.) considered a decision making problem where there are a set of alternatives and a finite number of agents with preferences defined over the set of alternatives, and provided a necessary and sufficient condition for double implementation in Nash and strong Nash equilibria. One problem we encounter in Suh’s paper is that it is difficult to apply the condition directly to a given (social choice) correspondence. Here we provide an algorithm which helps us to verify whether a correspondence satisfies the condition or not.

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