Strategy-Proof Mechanism Design with Boundedly Rational Agents: Theory and Experiment

In a strategy-proof mechanism, implementation theory mostly assumes that each agent is rational in the sense that the agent reveals its true preference to induce its most preferred outcome. This assumption is sufficient to guarantee that the agent seeks such an outcome, but not necessary because the agent might be able to induce the outcome by revealing its other preference. On the basis of such an understanding, this paper considers an implementation problem with the bounded rationality of agents. The bounded rationality presented in this paper means that the agent might choose its best response which is different from its dominant strategy. To describe such behavior, this paper introduces a new notion of equilibrium, called ( n − k ) -dominant strategy Nash equilibrium at 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 is collectively chosen under the existence of boundedly rational agents, this paper introduces a new notion of implementation, called k -secure implementation, which is a 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 satisfies k -secure implementability, but not secure implementability which is equivalent to n -secure implementability. In addition, this paper shows that majority rule realized the socially optimal outcome in the environments in laboratory experiments.