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We prove—in the standard independent private-values model—that the outcome, in terms of interim expected probabilities of trade and interim expected transfers, of any Bayesian mechanism can also be obtained with a dominant-strategy mechanism.

We characterize dominant-strategy incentive compatibility with multidimensional types. A deterministic social choice function is dominant-strategy incentive compatible if and only if it is weakly monotone (W-Mon). The W-Mon requirement is the following: If changing one agent's type (while keeping the types of other agents fixed) changes the outcome under the social choice function, then the resulting difference in utilities of the new and original outcomes evaluated at the new type of this agent must be no less than this difference in utilities evaluated at the original type of this agent.

We consider a standard social choice environment with linear utilities and independent, one-dimensional, private types. We prove that for any Bayesian incentive compatible mechanism there exists an equivalent dominant strategy incentive compatible mechanism that delivers the same interim expected utilities for all agents and the same ex ante expected social surplus. The short proof is based on an extension of an elegant result due to Gutmann, Kemperman, Reeds, and Shepp (1991). We also show that the equivalence between Bayesian and dominant strategy implementation generally breaks down when the main assumptions underlying the social choice model are relaxed or when the equivalence concept is strengthened to apply to interim expected allocations.

We derive the incentive compatible and ex-ante welfare maximizing (i.e. utilitarian) mechanism for settings with an arbitrary number of agents and alternatives where the privately informed agents have single-crossing and single-peaked preferences. The optimal outcome can be implemented by modifying a sequential voting scheme that is used in many legislatures and committees. The modification uses a flexible majority threshold for each of several alternatives, and allows us to replicate, via a single sequential procedure, the entire class of anonymous, unanimous, and dominant strategy incentive compatible mechanisms. Our analysis relies on elegant characterizations of this class of mechanisms for single-peaked and single-crossing preferences.

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.

We extend the equivalence between Bayesian and dominant strategy implementation (Manelli and Vincent in Econometrica 78:1905-1938, 2010; Gershkov et al. in Econometrica 81: 197-220, 2013) to environments with nonlinear utilities satisfying a property of increasing differences over distributions and a convex-valued assumption. The new equivalence result produces novel implications to the literature on the principal-agent problem with allocative externalities, environmental mechanism design, and public good provision.

We consider deterministic dominant strategy implementation in multidimensional dichotomous domains in private values and quasi-linear utility setting. In such multidimensional domains, an agent’s type is characterized by a single number, the value of the agent, and a non-empty set of acceptable alternatives. Each acceptable alternative gives the agent utility equal to his value and other alternatives give him zero utility. We identity a new condition, which we call generation monotonicity, that is necessary and sufficient for implementability in any dichotomous domain. If such a domain satisfies a richness condition, then a weaker version of generation monotonicity, which we call 2-generation monotonicity (equivalent to 3-cycle monotonicity), is necessary and sufficient for implementation. We use this result to derive the optimal mechanism in a one-sided matching problem with agents having dichotomous types.

We consider deterministic dominant strategy implementation in multidimensional dichotomous domains in private values and quasi-linear utility setting. In such multidimensional domains, an agent’s type is characterized by a single number, the value of the agent, and a non-empty set of acceptable alternatives. Each acceptable alternative gives the agent utility equal to his value and other alternatives give him zero utility. We identity a new condition, which we call generation monotonicity, that is necessary and sufficient for implementability in any dichotomous domain. If such a domain satisfies a richness condition, then a weaker version of generation monotonicity, which we call 2-generation monotonicity (equivalent to 3-cycle monotonicity), is necessary and sufficient for implementation. We use this result to derive the optimal mechanism in a one-sided matching problem with agents having dichotomous types.

We introduce a perfect price discriminatingmechanismfor allocation problems with private information. A perfect price discriminating mechanism treats a seller, for example, as a perfect price discriminating monopolist who faces a price schedule that does not depend on her report. In any perfect price discriminating mechanism, every player has a dominant strategy to truthfully report her private information. We establish a characterization for dominant strategy implementation: Any outcome that can be dominant strategy implemented can also be dominant strategy implemented using a perfect price discriminating mechanism. We apply this characterization to derive the optimal, budget-balanced, dominant strategy mechanisms for public good provision and bilateral bargaining.

In a framework allowing infinitely many individuals, I prove that coalitionally strategyproof social choice functions satisfy \"tops only.\" That is, they depend only on which alternative each individual prefers the most, not on which alternative she prefers the second most, the third,..., or the least. The functions are defined on the domain of profiles measurable with respect to a Boolean algebra of coalitions. The unrestricted domain of profiles is an example of such a domain. I also prove an extension theorem.