Dominant Strategy Incentive Compatible Mechanism Research Articles

Rank‐optimal assignments in uniform markets

We prove that in a market where agents rank objects independently and uniformly at random, there exists an assignment of objects to agents with a constant average rank (i.e., an average rank independent of the market size). The proof builds on techniques from random graph theory and the FKG inequality (Fortuin et al. (1971)). When the agents' rankings are their private information, no Dominant Strategy Incentive Compatible mechanism can implement the assignment with the smallest average rank; however, we show that there exists a Bayesian Incentive Compatible mechanism that does so. Together with the fact that the average rank under the Random Serial Dictatorship (RSD) mechanism grows infinitely large with the market size, our findings indicate that the average rank under RSD can take a heavy toll compared to the first‐best, and highlight the possibility of using other assignment methods in scenarios where average rank is a relevant objective.

(Almost) efficient mechanisms for bilateral trading

We study the bilateral trade problem: one seller, one buyer and a single, indivisible item for sale. It is well known that there is no fully-efficient and incentive compatible mechanism for this problem that maintains a balanced budget. We design simple and robust mechanisms that obtain approximate efficiency with these properties. We show that even minimal use of statistical data can yield good approximation results. We then demonstrate how a mechanism for this simple bilateral-trade problem can be used as a “black-box” for constructing mechanisms in more general environments. Finally, we show that dominant-strategy incentive-compatible mechanisms cannot guarantee any constant-factor approximation to the optimal gains from trade.

Limitations of Incentive Compatibility on Discrete Type Spaces

In the design of incentive compatible mechanisms, a common approach is to enforce incentive compatibility as constraints in programs that optimize over feasible mechanisms. Such constraints are often imposed on sparsified representations of the type spaces, such as their discretizations or samples, in order for the program to be manageable. In this work, we explore limitations of this approach, by studying whether all dominant strategy incentive compatible mechanisms on a set T of discrete types can be extended to the convex hull of T.Dobzinski, Fu and Kleinberg (2015) answered the question affirmatively for all settings where types are single dimensional. It is not difficult to show that the same holds when the set of feasible outcomes is downward closed. In this work we show that the question has a negative answer for certain non-downward-closed settings with multi-dimensional types. This result should call for caution in the use of the said approach to enforcing incentive compatibility beyond single-dimensional preferences and downward closed feasible outcomes.

Mechanism design without quasilinearity

This paper studies a model of mechanism design with transfers where agents' preferences need not be quasilinear. In such a model, (i) we characterize dominant strategy incentive compatible mechanisms using a monotonicity property, (ii) we establish a revenueuniquenessresult (for every dominant strategy implementable allocation rule, there is a unique payment rule that can implement it), and (iii) we show that every dominant strategy incentive compatible, individually rational, and revenue‐maximizing mechanism must charge zero payment for theworstalternative (outside option). These results are applicable in a wide variety of problems (single object auction, multiple object auction, public good provision, etc.) under suitable richness of type space. In particular, our results are applicable to two important type spaces: (a) type space containing an arbitrarily small perturbation of quasilinear type space and (b) type space containing all positive income effect preferences.

Dominant-strategy and Bayesian incentive compatibility in multi-object trading environments

When a single-object is to be traded, Bayesian and dominant-strategy incentive compatible mechanisms are interim-utility equivalent in independent, private-values environments; in the same environments, the equivalence breaks down when there are many distinct, indivisible objects to trade. We show that the fixed supply of each type of good imposes strong restrictions on the mechanisms that can be implemented. These restrictions can then be used to determine whether a given Bayesian mechanism has an equivalent dominant-strategy mechanism in a multi-unit model.

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.

Mechanism Design Without Quasilinearity

This paper studies a model of mechanism design with transfers where agents' preferences need not be quasilinear. In such a model: (1) we characterize dominant strategy incentive compatible mechanisms using a monotonicity property; (2) we establish a revenue uniqueness result: for every dominant strategy implementable allocation rule, there is a unique payment rule that can implement it; and (3) we show that every dominant strategy incentive compatible, individually rational, and revenue-maximizing mechanism must charge zero transfer for the worst alternative (outside option). These results are applicable in a wide variety of problems (single object auction, multiple object auction, public good provision etc.) under suitable richness of type space. In particular, our results can be applied to models where preferences of agents are arbitrarily small perturbations of quasilinear preferences and illustrate the (non)-robustness of some of the classic results in mechanism design with quasilinearity. We show various applications of our results.

Spanning tree auctions: A complete characterization

We consider a mechanism design problem over a connected graph in private value environment where the type of an agent is a single number. The preference over transfers is quasi-linear for every agent. We give a complete characterization of dominant strategy incentive compatible mechanisms for this problem. Further, by imposing a suitable version of anonymity and non-bossiness along with dominant strategy incentive compatibility, we find that the only mechanisms satisfying all these conditions are the Groves mechanisms.

Optimal Voting Rules

We study dominant strategy incentive compatible (DIC) and deterministic mechanisms in a social choice setting with several alternatives. The agents are privately informed about their preferences, and have single-crossing utility functions. Monetary transfers are not feasible. We use an equivalence between deterministic, DIC mechanisms and generalized median voter schemes to construct the constrained-efficient, optimal mechanism for an utilitarian planner. Optimal schemes for other welfare criteria such as, say, a Rawlsian maximin can be analogously obtained.

Ordinal Bayesian incentive compatibility in restricted domains

We study deterministic voting mechanisms by considering an ordinal notion of Bayesian incentive compatibility (OBIC). If the beliefs of agents are independent and generic, we show that a mechanism is OBIC and satisfies an additional condition called elementary monotonicity if and only if it is a dominant strategy incentive compatible mechanism. Our result works in a large class of preference domains (that include the unrestricted domain, the single-peaked domain, the single-dipped domain, and some single-crossing domains). We can significantly weaken elementary monotonicity in our result in the single-peaked domain if we assume unanimity and in a large class of domains if we assume unanimity and tops-onlyness.

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.

On the Equivalence between Bayesian and Dominant Strategy Implementation: The Case of Correlated Types

We consider general social choice environments with private values and correlated types. Each agent's matrix of conditional probabilities satisfies the full rank condition. We show that for any Bayesian incentive compatible mechanism there exists a dominant strategy incentive compatible mechanism that delivers the same interim expected utilities to all agents and generates at least the same social surplus. In addition, if there is a social alternative that is inferior to the other alternatives for all agents the dominant strategy incentive compatible mechanism matches exactly the social surplus. These results extend to environments with interdependent values satisfying the single crossing condition.

On the Equivalence of Bayesian and Dominant Strategy Implementation

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.

On the Equivalence of Bayesian and Dominant Strategy Implementation in a General Class of Social Choice Problems

We consider a standard social choice environment with linear utilities and independent, one-dimensional, private values. We provide a short and constructive proof 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. We demonstrate the usefulness and applicability of our approach with several examples. Finally, we show that the equivalence between Bayesian and dominant strategy implementation breaks down when utilities are non-linear or when values are interdependent, multi-dimensional, or correlated.

Dominant strategy mechanisms for contract auctions with risk aversion and moral hazard

Within the class dominant strategy incentive compatible mechanisms, we show that there exists an optimal contracting mechanism for the principal for a version of the incomplete information principal-agent problem in which several agents compete for a contract and the principal selects an agent via a contract auction. In our auction model, we assume that the principal and the agents are risk averse, and we allow for uncountably many agent types. We also assume that the principal's probability measure over type profiles in such that correlation between agent's types is possible. Thus, we do not require that agents' types be independently distributed. Finally, we impose limited liability constraints upon the set of contracts. Due to the nature of the individual rationality and incentive compatibility constraints, the existence problem is nonstandard and novel existence arguments are required. We prove existence using a measurable selection result and a new notion of compactness called K-compactness.

On the robustness of strategy proof mechanisms

Following the Gibbard-Satterthwaite impossibility theorem, the incentives literature has explored restrictions on the domains of unknown characteristics which enable the implementation of some social choice rules by dominant strategy incentive compatible mechanisms. This paper makes precise the intuitive idea that, even when restrictions on preferences take the extreme form of finite- dimensional parametrizations, implementable social choice rules display a lack of robustness and in a sense made explicit are rare.