Dominant Strategy Implementation Research Articles

Ex-post implementation with interdependent values

We characterize ex-post implementable allocation rules for single object auctions under quasi-linear preferences with interdependent value functions. We show that requiring ex-post implementability is equivalent to requiring a weakening of monotonicity, which is a familiar condition used to characterize dominant strategy implementation. We illustrate that non-monotone rules may be necessary to achieve objectives such as efficiency and revenue maximizations, even in standard models such as the maximum signal model studied in Bulow and Klemperer (2002), and Bergemann et al. (2020).

Single-peaked domains with designer uncertainty

This paper studies single-peaked domains where the designer is uncertain about the underlying alignment according to which the domain is single-peaked. The underlying alignment is common knowledge amongst agents, but preferences are private knowledge. Thus, the state of the world has both a public and private element, with the designer uninformed of both. I first posit a relevant solution concept called implementation in mixed information equilibria, which requires Nash implementation in the public information and dominant strategy implementation in the private information given the public information. I then identify necessary and sufficient conditions for social choice rules (SCRs) to be implementable. The characterization is used to identify unanimous and anonymous implementable SCRs for different forms of designer uncertainty, which basically boils down to picking the right SCRs from the large class identified by Moulin (Public Choice 35(4):437–455, 1980), and hence this result can be seen as identifying which of Moulin’s SCRs are robust to designer uncertainty.

The broker-optimal bilateral trading mechanisms with linear contracts

We introduce a linear contract to the bilateral trading model with a broker in Myerson and Satterthwaite (Section 5, 1983). Among all the incentive-compatible and individually rational direct bilateral trading mechanisms, we provide a characterization of the broker-optimal direct bilateral trading mechanisms when the buyer makes a non-negative cash payment. In the optimal mechanism, the buyer makes zerocash payment, and shares equity with the seller. This mechanism enables the broker to gain higher profits than that in Myerson and Satterthwaite (1983). A dominant strategy implementation is also proposed. We also discuss the optimal mechanism when the buyer is allowed to be subsidized.

On incentive compatible, individually rational public good provision mechanisms

This paper characterizes mechanisms satisfying incentive compatibility and individual rationality in the classical public good provision problem. Many papers in the literature obtain the results in the so-called standard model of ex ante identical agents with a continuous, closed interval of types. The main contribution of this paper is the characterization of the budget-surplus maximizing mechanism satisfying incentive compatibility and individual rationality (Theorem 1 for Bayesian implementation and Theorem 3 for dominant strategy implementation) that applies to a finite discretization over the standard model. Making use of the proposed budget-surplus maximizing mechanisms, we show that some known results do not need the agents’ risk neutrality, whereas some others do rely on the agents’ risk neutrality in a subtle manner. Furthermore, we improve upon some known results and obtain new results which do not exist in the standard model.

Dominant strategy implementability and zero length cycles

Necessary conditions for dominant strategy implementability of an allocation function on a restricted type space are identified when utilities are quasilinear and the set of alternatives is finite. For any one-person mechanism obtained by fixing the other individuals’ types, the geometry of the partition of the type space into subsets that are allocated the same alternative is used to identify situations in which it is necessary for all of the cycle lengths in the corresponding allocation graph to be zero. When all cycle lengths are zero, it is shown that the allocation function can be implemented by setting the payment for an alternative equal to the average length of the arcs that terminate at its node in the allocation graph.

Dominant strategy implementation in a large population public goods game

We consider implementation of the efficient state in a large population public goods game. Agents are divided into a finite set of types. The planner asks agents to report types, which generates a reported type distribution. Based on reported types and distribution, the planner calculates the efficient strategy level and a Pigouvian transfer for each type of agent. We show that this direct mechanism satisfies incentive compatibility in strictly dominant strategies, strong budget balance and ex-post individual rationality.

Dominant strategy implementation of bargaining solutions

We consider the problem where agents bargain over their shares of a perfectly divisible commodity. The aim of this paper is to identify the class of bargaining solutions induced by dominant strategy implementable allocation rules. To this end, we characterize the class of dominant strategy implementable allocation rules and impose the property of welfarism, which makes it possible for any allocation rule to induce a bargaining solution. Our main result is that an allocation rule is dominant strategy implementable and satisfies welfarism and some mild requirements if and only if it induces a dictatorial solution.

A Generalization of the Clarke Mechanism to a Non-Quasi-Linear Utility Domain

A mechanism taxes and finances a public good under the assumption that each agent has a classical concave utility function. In the large limit of the economy with respect to the population, this mechanism asymptotically satisfies dominant strategy implementability and budget balancedness, and thus asymptotically achieves Pareto efficiency. If each agent has a quasi-linear utility function, then this mechanism reduces to the standard Clarke mechanism, which is known to achieve Pareto efficiency asymptotically only when each agent has a quasi-linear utility function.

Supermodularity and Complementarity in Economic Theory

This special issue brings together eight separate contributions reflecting recent advances in the methodology of supermodular optimization and games. Three of the papers fall in the main area of supermodular games. Balbus et al. (Econ Theory 67, 2019, https://doi.org/10.1007/s00199-017-1075-7 ) study supermodular games with a continuum of players. Jimenez-Martinez (Econ Theory 67, 2019, https://doi.org/10.1007/s00199-018-1107-y ) develops a model of versioning in social networks. Barthel and Hoffman (Econ Theory 67, 2019, https://doi.org/10.1007/s00199-017-1092-6 ) deal with a class of games with mixed-monotonic best responses (in both directions). The second group of papers falls in the related areas of mechanism design, principal agent, and matching. Johnson (Econ Theory 67, 2019, https://doi.org/10.1007/s00199-018-1127-7 ) considers synchronized Becker-style matching with incomplete information. Kushnir and Liu (Econ Theory 67, 2019, https://doi.org/10.1007/s00199-018-1124-x ) generalizes the equivalence between Bayesian and dominant strategy implementation to the case of nonlinear utilities. Zambrano (Econ Theory 2019, https://doi.org/10.1007/s00199-017-1087-3 ) studies a principal-agent model with choice between a risky and a safe projects. Christensen (Econ Theory 67, 2019, https://doi.org/10.1007/s00199-018-1116-x ) investigates the stability, existence, and uniqueness of equilibria, as solutions to systems of equations. Finally, Drugeon et al. (Econ Theory 67, 2019, https://doi.org/10.1007/s00199-018-1166-0 ) consider a class of dynamic programming problems with endogenous discount factor.

On the equivalence of Bayesian and dominant strategy implementation for environments with nonlinear utilities

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.

On the equivalence of Bayesian and deterministic dominant strategy implementation

In a symmetric single object allocation mechanism with n agents, we identify a necessary and sufficient condition for the existence of an equivalent deterministic dominant strategy incentive compatible mechanism for a given Bayesian incentive compatible mechanism.

Robust trading mechanisms over 0/1 polytopes

The problem of designing a trade mechanism (for an indivisible good) between a seller and a buyer is studied in the setting of discrete valuations of both parties using tools of finite-dimensional optimization. A robust trade design is defined as one which allows both traders a dominant strategy implementation independent of other traders’ valuations with participation incentive and no intermediary (i.e., under budget balance). The design problem which is initially formulated as a mixed-integer non-linear non-convex feasibility problem is transformed into a linear integer feasibility problem by duality arguments, and its explicit solution corresponding to posted price optimal mechanisms is derived along with full characterization of the convex hull of integer solutions. A further robustness concept is then introduced for a central planner unsure about the buyer or seller valuation distribution, a corresponding worst-case design problem over a set of possible distributions is formulated as an integer linear programming problem, and a polynomial solution procedure is given. When budget balance requirement is relaxed to feasibility only, i.e., when one allows an intermediary maximizing the expected surplus from trade, a characterization of the optimal robust trade as the solution of a simple linear program is given. A modified VCG mechanism turns out to be optimal.

Incentive Mechanisms for Fairness Among Strategic Agents

Mechanism design for incentivizing strategic agents to maximize their sum of utilities (SoU) is a well-studied problem in the context of resource allocation in networks. There are, however, a number of network resource allocation problems of interest where a designer may have a different objective than maximization of the SoU. The obvious reason for seeking a different objective is that this notion of efficiency does not account for fairness of allocation. A second, more subtle, reason for demanding fairer allocation is that it indirectly implies less variation in taxes paid by agents. This is desirable in a situation where implicit individual agent budgetary constraints make payment of large taxes unrealistic. In this paper, we study a family of social utilities that provide fair allocation (with SoU being subsumed as an extreme case) and derive conditions under which Bayesian and dominant strategy implementation is possible. Furthermore, it is shown how a modification of the above-mentioned mechanism by adding just one message per agent can guarantee full Bayesian implementation, i.e., no extraneous equilibria. We consider the problem of demand-side management in smart grids as a specific motivating application, and through numerical analysis, it is demonstrated that in this application, the proposed method can result in significant gains in fairness of allocation and a reduction in tax variation among agents.

Dominant Strategy Implementability and Zero Length Cycles

Necessary conditions for dominant strategy implementability of an allocation function on a restricted type space are identified when utilities are quasilinear and the set of alternatives is finite. For any one-person mechanism obtained by fixing the other individuals’ types, the geometry of the partition of the type space into subsets that are allocated the same alternative is used to identify situations in which it is necessary for all of the cycle lengths in the corresponding allocation graph to be zero. When all cycle lengths are zero, it is shown that the allocation function can be implemented by setting the payment for an alternative equal to the average length of the arcs that terminate at its node in the allocation graph.

An externality-robust auction: Theory and experimental evidence

Behavioral robustness is essential in mechanism design. Existing papers focus on robustness as captured by dominant strategies. This paper studies the novel concept of externality-robustness, which addresses players' motives to affect other players' monetary payoffs. One example is externalities due to spite, which has been used to explain overbidding in second-price auctions. We show theoretically and experimentally that a trade-off exists between dominant-strategy implementation and externality-robust implementation. In particular, we derive the externality-robust counterpart of the second-price auction. Our experiments replicate the earlier finding of overbidding in the second-price auction, but we find that average bids equal value in the externality-robust auction. Our data also reveal that both auctions produce the same level of efficiency, suggesting that both dimensions of robustness are equally important. Our results are relevant for mechanism design in general, because the concept of externality-robustness is applicable to arbitrary mechanism design problems.

The Theory of Implementation. What Did We Learn?

In this survey we review the most important aspects of Implementation theory. We present the notions of a mechanism, a social choice correspondence and that of implementation. We first review the main contributions to implementation under dominant strategies namely the impossibility theorems that show the impossibility to implement efficient allocations when the preference domain is sufficiently large. Then we review Nash implementation and we show that a Maskin monotonic social choice correspondence satisfying no veto power can be implemented. Finally we review the case of Bayesian equilibrium, a kind of intermediate case between Nash and Dominant strategy implementation.

On the Equivalence of Bayesian and Dominant Strategy Implementation: The Case of Non-Linear Utilities

We extend the equivalence between Bayesian and dominant strategy implementation established by Gershkov et al. (Econometrica, 2013) to environments with non-linear utilities satisfying the property of increasing differences over distributions and the 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.

On sufficiency of dominant strategy implementation in environments with correlated types

We show that for any mechanism there exists an equivalent dominant strategy incentive compatible mechanism for social choice environments with correlated types when agent’s matrix of conditional probabilities satisfies the full rank condition.

An Externality-Robust Auction: Theory and Experimental Evidence

Behavioral robustness is essential in mechanism design. Existing papers focus on robustness as captured by dominant strategies. This paper studies the novel concept of externality-robustness, which addresses players’ motives to affect other players’ monetary payoffs. One example is externalities due to spite, which has been used to explain overbidding in second-price auctions. We show theoretically and experimentally that a trade-off exists between dominant-strategy implementation and externality-robust implementation. In particular, we derive the externality-robust counterpart of the second-price auction. Our experiments replicate the earlier finding of overbidding in the second-price auction, but we find that average bids equal value in the externality-robust auction. Our data also reveal that both auctions produce the same level of efficiency, suggesting that both dimensions of robustness are equally important. Our results are relevant for mechanism design in general, because the concept of externality-robustness is applicable to arbitrary mechanism design problems.

Surplus extraction with rich type spaces

We characterize revenue maximizing mechanisms in auction settings with ‘rich’ type spaces, where bidders obtain information from sources other than their own valuation. By considering a relaxed problem, we provide an upper bound on revenue extraction that explicitly builds on the richness of the information structure. We provide a condition under which this upper bound is achieved and describe an optimal mechanism. Under this condition, we also show that the optimal revenue can be achieved through dominant strategy implementation. The optimal revenue result generalizes the full surplus extraction result of Cremer and McLean (1988) [5] as well as the standard independent private values revenue maximizing auction presented in Myerson (1981) [10] , providing a unified treatment for two sets of results irreconcilable so far.