A new necessary condition for implementation in iteratively undominated strategies

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.     

On efficient partnership dissolution under ex post individual rationality

This paper studies ex post individually rational, efficient partnership dissolution in a setting with interdependent valuations. We derive a sufficient condition that ensures the existence of an efficient dissolution mechanism that satisfies Bayesian incentive compatibility, ex post budget balancedness, and ex post individual rationality. For equal-share partnerships, we show that our sufficient condition is satisfied for any symmetric type distribution whenever the interdependence in valuations is non-positive. This result improves former existence results, demonstrating that the stronger requirement of ex post individual rationality does not always rule out efficiency. We also show that if we allow for two-stage revelation mechanisms, in which agents report their realized payoffs from the allocation, as well as imposing penalties off the equilibrium path, efficient dissolution is always possible even when the interdependence is positive. We further discuss the possibility of efficient dissolution with ex post quitting rights.     

Robust implementation in general mechanisms

A social choice function is robustly implemented if every equilibrium on every type space achieves outcomes consistent with it. We identify a robust monotonicity condition that is necessary and (with mild extra assumptions) sufficient for robust implementation.Robust monotonicity is strictly stronger than both Maskin monotonicity (necessary and almost sufficient for complete information implementation) and ex post monotonicity (necessary and almost sufficient for ex post implementation). It is equivalent to Bayesian monotonicity on all type spaces.     

Core and equilibria under ambiguity

This paper introduces new core and Walrasian equilibrium notions for an asymmetric information economy with non-expected utility preferences. We prove existence and incentive compatibility results for the notions we introduce. We also discuss a framework for ex ante, interim and ex post preferences.     

Ex post implementation

We analyze the problem of fully implementing a social choice set in ex post equilibrium. We identify an ex post monotonicity condition that is necessary and—in economic environments—sufficient for full implementation in ex post equilibrium. We also identify an ex post monotonicity no veto condition that is sufficient. Ex post monotonicity is satisfied in all single crossing environments with strict ex post incentive constraints.We show by means of two classic examples that ex post monotonicity does not imply nor is it implied by Maskin monotonicity. The single unit auction with interdependent valuations is shown to satisfy ex post monotonicity but not Maskin monotonicity. We further describe a Pareto correspondence that fails ex post monotonicity but satisfies Maskin monotonicity.     

The communication cost of selfishness

We consider how many bits need to be exchanged to implement a given decision rule when the mechanism must be ex post or Bayesian incentive compatible. For ex post incentive compatibility, the communication protocol must reveal enough information to calculate monetary transfers to the agents to motivate them to be truthful (agents' payoffs are assumed to be quasilinear in such transfers). For Bayesian incentive compatibility, the protocol may need to hide some information from the agents to prevent deviations contingent on the information. In both settings with selfish agents, the communication cost can be higher than in the case in which the agents are honest and can be relied upon to report truthfully. The increase is the “communication cost of selfishness.” We provide an exponential upper bound on the increase. We show that the bound is tight in the Bayesian setting, but we do not know this in the ex post setting. We describe some cases where the communication cost of selfishness proves to be very low.     

Implementation with partial provability

We extend implementation theory by allowing the social choice function to depend on more than just the preferences of the agents and allowing agents to support their statements with hard evidence. We show that a simple condition on evidence is necessary for the implementation of a social choice function f when the preferences of the agents are state independent and sufficient for implementation for any preferences (including state dependent) with at least three agents if the social planner can perform small monetary transfers beyond those called for by f. If transfers can be large, f can be implemented in a game with perfect information when there are at least two players under a boundedness assumption. For both results, transfers only occur out of equilibrium. The use of evidence enables implementation which is robust in the sense that the planner needs little information about agents? preferences or beliefs and agents need little information about each others? preferences. Our results are robust to evidence forgery at any strictly positive cost.     

A characterization of virtual Bayesian implementation

We provide a characterization of virtual Bayesian implementation in pure strategies for environments satisfying no-total-indifference. A social choice function in such environments is virtually Bayesian implementable if and only if it satisfies incentive compatibility and a condition we term virtual monotonicity. The latter is weaker than Bayesian monotonicity—known to be necessary for Bayesian implementation. Virtual monotonicity is weak in the sense that it is generically satisfied in environments with at least three alternatives. This implies that in most environments virtual Bayesian implementation is as successful as it can be (incentive compatibility is the only condition needed).     

Mechanism design with side payments: Individual rationality and iterative dominance

We investigate the collective decision with incomplete information and side payments. We show that a direct mechanism associated with the social choice function that satisfies budget balancing, incentive compatibility, and interim individual rationality exists for generic prior distributions. We consider the possibility that a risk-averse principal extracts full surplus in agency problems with adverse selection. With regard to generic prior distributions, we show that there exists a modified direct mechanism associated with the virtual social choice function, which satisfies budget balancing and interim individual rationality, such that truth telling is the unique three times iteratively undominated message rule profile.     

Implementation without incentive compatibility: Two stories with partially informed planners

We consider two stories, Typhoon by Conrad and Traveler's Dilemma by Basu, 1994, Basu, 2007, as implementation problems under incomplete information without incentive compatibility, but where the planner has some private information regarding the state. If social choice functions do not satisfy incentive compatibility, full implementation is unattainable via existing approaches. For each story, we construct a direct mechanism that relies on the planner's private information. We provide a sufficient condition on players' beliefs regarding the state under which every player has a unique rationalizable action, namely, telling the truth. Thus, in these stories, the planner's information can bypass the lack of incentive compatibility.     

Fully sincere voting

In a general social choice framework where the requirement of strategy-proofness may not be sensible, we call a social choice rule fully sincere if it never gives any individual an incentive to vote for a less-preferred alternative over a more-preferred one and provides an incentive to vote for an alternative if and only if it is preferred to the default option that would result from abstaining. If the social choice rule can depend only on the number of votes that each alternative receives, those rules satisfying full sincerity are convex combinations of the rule that chooses each alternative with probability equal to the proportion of the vote it receives and an arbitrary rule that ignores voters' preferences. We note a sense in which the natural probabilistic analog of approval voting is the fully sincere rule that allows voters maximal flexibility in expressing their preferences and gives these preferences maximal weight.     

Fully sincere voting

In a general social choice framework where the requirement of strategy-proofness may not be sensible, we call a social choice rule fully sincere if it never gives any individual an incentive to vote for a less-preferred alternative over a more-preferred one and provides an incentive to vote for an alternative if and only if it is preferred to the default option that would result from abstaining. If the social choice rule can depend only on the number of votes that each alternative receives, those rules satisfying full sincerity are convex combinations of the rule that chooses each alternative with probability equal to the proportion of the vote it receives and an arbitrary rule that ignores voters' preferences. We note a sense in which the natural probabilistic analog of approval voting is the fully sincere rule that allows voters maximal flexibility in expressing their preferences and gives these preferences maximal weight.     

Optimal democratic mechanisms for taxation and public good provision

We study the interdependence of optimal tax and expenditure policies. An optimal policy requires that information on preferences is made available. We first study this problem from a general mechanism design perspective and show that efficiency is possible only if the individuals who decide on public good provision face an own incentive scheme that differs from the tax system. We then study democratic mechanisms with the property that tax payers vote over public goods. Under such a mechanism, efficiency cannot be reached and welfare from public good provision declines as the inequality between rich and poor individuals increases.     

Incentive Regulation and The Cost Structure of The Local Telephone Exchange Network

This paper combines an engineering process model of the cost of local exchange telecommunications firms with an analytical model of optimal incentive regulation (with ex post cost observability), to study empirically the properties of the optimal regulatory mechanism. Relying on detailed properties of the cost function, we examine three issues: (i) the extent of natural monopoly when informational rents associated with regulation are taken into account; (ii) the extent of incentive correction, which expresses the divergence of pricing under the optimal mechanism from optimal pricing under complete information; (iii) the implementation of optimal regulation through a menu of linear contracts. Our findings are that, for fixed territory, strong economies of scale allow local exchange telecommunications to retain monopoly characteristics even when the (informational) costs of regulation are properly accounted for, the incentive correction term is small in magnitude, and that optimal regulation can be well approximated through relatively simple linear contracts.     

Weak monotonicity and Bayes–Nash incentive compatibility

An allocation rule is called Bayes–Nash incentive compatible, if there exists a payment rule, such that truthful reports of agents' types form a Bayes–Nash equilibrium in the direct revelation mechanism consisting of the allocation rule and the payment rule. This paper provides a characterization of Bayes–Nash incentive compatible allocation rules in social choice settings where agents have multi-dimensional types, quasi-linear utility functions and interdependent valuations. The characterization is derived by constructing complete directed graphs on agents' type spaces with cost of manipulation as lengths of edges. Weak monotonicity of the allocation rule corresponds to the condition that all 2-cycles in these graphs have non-negative length. For the case that type spaces are convex and the valuation for each outcome is a linear function in the agent's type, we show that weak monotonicity of the allocation rule together with an integrability condition is a necessary and sufficient condition for Bayes–Nash incentive compatibility.     

Weak monotonicity and Bayes–Nash incentive compatibility

An allocation rule is called Bayes–Nash incentive compatible, if there exists a payment rule, such that truthful reports of agents' types form a Bayes–Nash equilibrium in the direct revelation mechanism consisting of the allocation rule and the payment rule. This paper provides a characterization of Bayes–Nash incentive compatible allocation rules in social choice settings where agents have multi-dimensional types, quasi-linear utility functions and interdependent valuations. The characterization is derived by constructing complete directed graphs on agents' type spaces with cost of manipulation as lengths of edges. Weak monotonicity of the allocation rule corresponds to the condition that all 2-cycles in these graphs have non-negative length. For the case that type spaces are convex and the valuation for each outcome is a linear function in the agent's type, we show that weak monotonicity of the allocation rule together with an integrability condition is a necessary and sufficient condition for Bayes–Nash incentive compatibility.     

Efficiency and incentive compatibility in differential information economies

Summary. We introduce several efficiency notions depending on what kind of expected utility is used (ex ante, interim, ex post) and on how agents share their private information, i.e., whether they redistribute their initial endowments based on their own private information, or common knowledge information, or pooled information. Moreover, we introduce several Bayesian incentive compatibility notions and identify several efficiency concepts which maintain (coalitional) Bayesian incentive compatibility. Received: March 25, 1996; revised September 5, 1996     

The ABC mechanism: an incentive compatible payoff mechanism for elicitation of outcome and probability transformations

When it comes to experiments with multiple-round decisions under risk, the current payoff mechanisms are incentive compatible with either outcome weighting theories or probability weighting theories, but not both. In this paper, I introduce a new payoff mechanism, the Accumulative Best Choice (“ABC”) mechanism that is incentive compatible for all rational risk preferences. I also identify three necessary and sufficient conditions for a payoff mechanism to be incentive compatible for all models of decision under risk with complete and transitive preferences. I show that ABC is the unique incentive compatible mechanism for rational risk preferences in a multiple-task setting. In addition, I test empirical validity of the ABC mechanism in the lab. The results from both a choice pattern experiment and a preference (structural) estimation experiment show that individual choices under the ABC mechanism are statistically not different from those observed with the one-round task experimental design. The ABC mechanism supports unbiased elicitation of both outcome and probability transformations as well as testing alternative decision models that do or do not include the independence axiom.

     

Optimal tax treatment of private contributions for public goods with and without warm glow preferences

Tax-favored contributions for financing some public goods may be a useful part of optimal nonlinear income tax and expenditure policy. There are two sides to the potential gain from subsidized donations. First, for a given level of public good provision, higher private donations from high earners than low earners eases the incentive compatibility constraint for donors and so can raise social welfare. This follows since considering a lower-paid job includes a perception of a drop in public good provision. Second, private donation reduces consumption, easing the resource constraint. This paper explores optimal policy, using first a model with standard preferences and then a model with a warm glow of giving. In addition to showing the conditions for the level of public goods, the paper considers the pattern of optimal subsidization across earnings levels. Analysis of optimal taxation with warm glow preferences is sensitive to the choice of preferences that are relevant for a social welfare evaluation. After considering optimal rules with formulations of social welfare which do and do not include warm glow utility, the paper considers the choice of normative criterion. Like the earlier literature, this paper assumes that organizing private donations is costless while tax collection has a deadweight burden. Since private charitable fundraising is very far from costless, the paper is an exploration of economic mechanisms, not a direct guide to policy.     

Anticipated regret as an explanation of uncertainty aversion

The paper provides a psychological explanation of uncertainty aversion based on the fear of regret. We capture an agent’s regret using a reference-dependent utility function in which the agent’s utility depends on the performance of his chosen option relative to the performance of the option that would have been best ex post. An uncertain option is represented as a compound lottery. The basic idea is that selecting a compound lottery reveals information, which alters the ex post assessment of what the best choice would have been, inducing regret. We provide sufficient conditions under which regret implies uncertainty aversion in the sense of quasi-concave preferences over compound lotteries.