A new necessary condition for implementation in iteratively undominated strategies

• Published in: Journal of economic theory Vol. 146; no. 6; pp. 2583 - 2595
• Main Authors: Kunimoto, Takashi, Serrano, Roberto
• Format: Journal Article
• Language: English
• Published: New York Elsevier Inc 01.11.2011; Elsevier Science Publishing Company, Inc
• Subjects: Agency theory; Approximation; Conditioning; Deceit; Deception; Documents; Economic incentives; Economic theory; Economics; Exact and approximate implementation; Incentive compatibility; Incentives; Iterative methods; Iteratively undominated strategies; Mathematical analysis; Mathematical functions; Measurability; Measurement; Mechanism design; Pay-off; Policy implementation; Restricted deception-proofness; Restrictive business practices; Strategy; Studies; Measurability; Iteratively undominated strategies; D78; Mechanism design; Restricted deception-proofness; Incentive compatibility; Exact and approximate implementation; C72; D82
• ISSN: 0022-0531; 1095-7235
• DOI: 10.1016/j.jet.2011.02.005

We uncover a new necessary condition for implementation in iteratively undominated strategies by mechanisms that satisfy the “best element property” where for each agent, there exists a strategy profile that gives him the highest payoff in the mechanism. This class includes finite and regular mechanisms. We conclude that either the quasilinearity-like assumptions of available sufficiency results cannot be completely dispensed with or some mechanisms that do not satisfy the best element property must be employed. We term the condition “restricted deception-proofness.” It requires that, in environments with identical preferences, the social choice function be immune to all deceptions, making it then stronger than incentive compatibility. In some environments the conditions for (exact or approximate) implementation by mechanisms satisfying the best element property are more restrictive than previously thought.