Strategy-Proof Mechanism Design with Boundedly Rational Agents

This paper considers an implementation problem with bounded rationality of the agents. Bounded rationality presented here means that the agent might choose the agent's best response which is different from the agent's dominant strategy. To describe such a behavior, this paper introduces a new notion of equilibrium, called (n-k)-dominant strategy Nash equilibrium, in which at most k∈{0,1,⋯,n} boundedly rational agents might choose their best responses which are different from their dominant strategies and at least (n-k) rational agents choose their dominant strategies. In addition, to show what a socially optimal outcome collectively chosen under the existence of boundedly rational agents, this paper introduces a new notion of implementation, called k-secure implementation, which is double implementation in dominant strategy equilibria and (n-k)-dominant strategy Nash equilibria. In specific environments with k≤(n+1)/2, this paper shows that majority rule and the median voter rule satisfy k-secure implementability, but not secure implementability (Saijo, T., T. Sjöström, and T. Yamato (2007) “Secure Implementation,” Theoretical Economics 2, pp.203-229) which is equivalent to n-secure implementability respectively