Incentive Compatible Allocation Research Articles

Group Incentive-Compatible Allocation of Discrete Resources When Ownership is Partitioned

Group Incentive-Compatible Allocation of Discrete Resources When Ownership is Partitioned

Optimal nonlinear taxation: a simpler approach

The typical method of solving for the optimal nonlinear tax schedule relies on deriving optimal incentive-compatible allocations. While this “primal approach” is mathematically rigorous, it lacks intuitive appeal. This paper considers a different method that relies on directly solving for the optimal tax system. This “dual approach” is much closer to actual tax policy as it centers around the welfare effects of tax reforms. I show that it can easily incorporate preference heterogeneity, as well as individual utility misoptimization. Beyond solving for the optimal tax system, the dual approach allows one to obtain insights into the welfare effects of small nonlinear tax reforms outside the optimum.

Persuasion in an asymmetric information economy: a justification of Wald’s maxmin preferences

To justify the use of Wald’s maxmin preferences in an asymmetric information economy, we introduce a mechanism designer who can convince/persuade agents to adopt Wald’s maxmin preferences. We show that more efficient and individually rational allocations become incentive compatible if the mechanism designer persuades agents to use Wald’s maxmin preferences instead of Bayesian preferences. Thus, we justify the Wald’s maxmin preferences by showing that agents can be persuaded to use them in order to enlarge the set of efficient, individually rational and incentive compatible allocations.

Monte Carlo sampling processes and incentive compatible allocations in large economies

Monte Carlo simulation is used in Hammond and Sun (Econ Theory 36:303–325, 2008. https://doi.org/10.1007/s00199-007-0279-7) to characterize a standard stochastic framework involving a continuum of random variables that are conditionally independent given macro shocks. This paper presents some general properties of such Monte Carlo sampling processes, including their one-way Fubini extension and regular conditional independence. In addition to the almost sure convergence of Monte Carlo simulation considered in Hammond and Sun (2008), here we also consider norm convergence when the random variables are square integrable. This leads to a necessary and sufficient condition for the classical law of large numbers to hold in a general Hilbert space. Applying this analysis to large economies with asymmetric information shows that the conflict between incentive compatibility and Pareto efficiency is resolved asymptotically for almost all sampling economies, following some similar results in McLean and Postlewaite (Econometrica 70:2421–2453, 2002) and Sun and Yannelis (J Econ Theory 134:175–194, 2007. https://doi.org/10.1016/j.jet.2006.03.001).

Bayesian implementation with verifiable information

This note studies the class of allocations that are fully Bayesian implementable in the presence of verifiable information. I identify a condition, termed evidence distinguishability, that together with incentive compatibility is both necessary and sufficient for full Bayesian implementation in direct mechanisms that elicit verifiable information. I show, however, that every evidence distinguishable allocation that is incentive compatible when verifiable information is not elicited is Bayesian monotonic at every verifiable deception; namely, at every verifiable joint report of information at which the direct mechanism delivers an undesirable outcome. To the extent that requiring Bayesian monotonicity to hold at every verifiable deception is a demanding condition, only indirect mechanisms can exploit the presence of verifiable information to fully implement incentive compatible allocations.

On the benefits of currency reform

Money allows agents to achieve allocations that are not possible without it. However, currency in most economies is a uniform object, and there may be incentive compatible allocations that cannot be implemented with a uniform currency. We show that currency reform, i.e., changing the monetary base by replacing one currency with another, is a powerful tool that can enable a monetary authority to achieve a desired allocation. Our monetary mechanism with currency reform is anonymous and features a nonlinear exchange rate between currencies and a monotone value of money. These results help interpret the characteristics of currency reforms observed in practice.

Contract withdrawals and equilibrium in competitive markets with adverse selection

In competitive common value adverse selection markets, existence of a pure strategy equilibrium is often justified by appealing to Wilson’s (J Econ Theory 16(2):167–207, 1977) concept of ‘anticipatory equilibrium.’ The anticipatory equilibrium is based on the notion that all market participants expect unprofitable contracts to be withdrawn. We present a model of individual contract withdrawals that captures the strategic process underlying the anticipatory equilibrium concept: We introduce an additional—endogenously ending—stage into the Rothschild and Stiglitz (Q J Econ 90(4):629–649, 1976) model in which initial contracts can be withdrawn repeatedly after observation of competitors’ contract offers and withdrawals. Individual contract withdrawal allows for a rich strategic interaction. We show that an equilibrium exists where consumers obtain their respective second-best efficient Miyazaki–Wilson–Spence (MWS) contracts. However, this equilibrium requires latent contracts on offer. Furthermore, any individually rational and incentive-compatible allocation that earns nonnegative profits on aggregate can be sustained as equilibrium allocation. We further allow for contract addition as in Riley’s (Econometrica 47(2):331–359, 1979) ‘reactive equilibrium.’ Allowing for contract addition does not change the set of possible outcomes.

Incentive compatible allocation and exchange of discrete resources

The allocation and exchange of discrete resources, such as transplant organs, public housing, dormitory rooms, and many other resources for which agents have single-unit demand, is often conducted via direct mechanisms without monetary transfers. Incentive compatibility and efficiency are primary concerns when designing such mechanisms. We construct the full class of group strategy-proof and Pareto-efficient mechanisms and show that each of them can be implemented by endowing agents with control rights over resources. This new class, which we call trading cycles, contains new mechanisms as well as known mechanisms such as top trading cycles, serial dictatorships, and hierarchical exchange. We illustrate how one can use our construction to show what can and what cannot be achieved in a variety of allocation and exchange problems, and we provide an example in which the new trading-cycles mechanisms are more Lorenz equitable than all previously known mechanisms.

Price Discrimination by a Two-Sided Platform: With Applications to Advertising and Privacy Design

We study price discrimination by a monopoly two-sided platform who mediates interactions between two different groups of agents. We adapt a canonical model of second degree price discrimination a la Mussa and Rosen (1978) to a two-sided platform by focusing on non-responsiveness, a clash between the allocation the platform wants to achieve and the incentive compatible allocations. In this framework we address the key question of when a price discrimination on one side complements or substitutes a price discrimination on the other side. We offer two applications on advertising platforms and also highlight the role of commitment in eliciting personal information for targeted advertising.

Incentive compatible allocation without money

Mechanism design typically involves the use of monetary payments to incentivize truthful reporting of private information. But what if payments are impossible? This letter summarizes recent work on how lotteries and the threat of non-allocation can be leveraged to similar ends in single-item allocation settings with a secondary good that can serve a limited numéraire role.

When a Price is Enough: Implementation in Optimal Tax Design

This paper studies the design of tax systems that implement a planner's second-best allocation in a market economy. An example shows that the widely used Mirrleesian (1976) tax system cannot implement all incentive-compatible allocations. Hammond's (1979) principle of taxation proves that any incentive-compatible allocation can be implemented through at least one tax system. However, this tax system is often undesirable since it severely restricts the choice space of agents in the economy. In this paper we derive necessary and sufficient conditions to verify whether a given tax system can implement a given incentive-compatible allocation. We show that when an incentive-compatible allocation is on the Pareto frontier, and/or surjective onto the choice space, a tax system that equates the marginal tax rates to the optimal wedges can implement the second best, without restricting the choice space of the agents. It follows that the Mirrleesian tax system can successfully implement the second best in the identified classes. Since the second-best allocation of welfarist planners is always on the Pareto frontier, our results (ex post) validate most tax systems proposed in the literature. Outside of the identified classes, the planner may need to restrict the choice space of agents to implement its second best in the market. This sheds new light on rules, quotas and prohibitions used in real-world tax and benefit systems.

Auctions with dynamic populations: Efficiency and revenue maximization

We examine an environment where goods and privately informed buyers arrive stochastically to a market. A seller in this setting faces a sequential allocation problem with a changing population. We characterize the set of incentive compatible allocation rules and provide a generalized revenue equivalence result. In contrast to a static setting where incentive compatibility implies that higher-valued buyers have a greater likelihood of receiving an object, in this dynamic setting, incentive compatibility implies that higher-valued buyers have a greater likelihood of receiving an object sooner. We also characterize the set of efficient allocation rules and show that a dynamic Vickrey-Clarke-Groves mechanism is efficient and dominant strategy incentive compatible. We then derive an optimal direct mechanism. We show that the revenue-maximizing direct mechanism is a pivot mechanism with a reserve price. Finally, we consider sequential ascending auctions in this setting, both with and without a reserve price. We construct memoryless equilibrium bidding strategies in this indirect mechanism. Bidders reveal their private information in every period, yielding the same outcomes as the direct mechanisms. Thus, the sequential ascending auction is a natural institution for achieving either efficient or optimal outcomes. Interestingly, this is not the case for sequential second-price auctions, as the bids in a second-price auction do not reveal sufficient information to realize either the efficient or optimal allocation.

General distributed economic framework for dynamic spectrum allocation

The emergence of novel radio techniques enables the application of advantageous revolutionary spectrum policies. An important body of research has appeared about possible frequency management schemes, but none of them proposes solutions that meet every related criteria. In this paper we present our work on dynamic spectrum allocation and pricing that offers a distributed mechanism design, well-suited to practical employment issues. Our model handles interference effects without any restricting assumptions, provides universal scalable and incentive-compatible allocation and pricing mechanisms. We provide both analytical and numerical evaluation of the proposed framework, and in either case we prove this latter to be a suitable approach to efficient and flexible spectrum utilization.

The Price of Admission: Who Gets into Private School and How Much Do They Pay?

This paper uses mechanism design theory to analyze how elementary and secondary private schools decide which students to admit from their applicant pool when wealth is private information. The problem for an individual private school of who to admit and how much to charge in tuition, is complicated by the existence of peer-effects: the value students place on attending school is increasing with the average ability of the entire class at that school. This feature, coupled with the fact that students can always attend public school for free, places constraints on the types of classes the private school can admit. An incentive compatible allocation rule which admits only high ability students violates the private school's operating constraint, while an allocation rule which admits only on the basis of wealth violates student participation constraints. Recognizing the costs associated with verifying wealth type can assist in explaining the structure of tuition contracts between students and private schools.This article has been accepted for publication in the Economics of Education Review.

Incentive Compatible Allocation and Exchange of Discrete Resources

Allocation and exchange of discrete resources such as kidneys, school seats, and many other resources for which agents have single-unit demand is conducted via direct mechanisms without monetary transfers. Incentive compatibility and efficiency are primary concerns in designing such mechanisms. We construct the full class of group strategy-proof and Pareto efficient mechanisms and show that each of them can be implemented by endowing agents with control rights over resources. This new class, which we call trading cycles, contains new mechanisms as well as known mechanisms such as top trading cycles, serial dictatorships, and hierarchical exchange. We illustrate how one can use our construction to show what can and what cannot be achieved in a variety of allocation and exchange problems, and we provide an example in which the new trading-cycles mechanisms are more equitable than all previously known mechanisms.

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.

Sequential communication with ex post participation constraints

This paper examines an informed principal–agent game with ex post participation constraints for the agent. It shows that the players do not lose by communicating in turn among themselves rather than simultaneously if and only if the principal communicates first. It then considers every Bayesian incentive compatible allocation rules that assign non-negative payoffs for one player in a bilateral asymmetric information framework. It provides necessary and sufficient conditions for sequential communication to be as efficient as simultaneous communication in implementing these allocation rules when the player with unbounded payoffs moves first.

Optimal Taxation with Private Government Information

The Ramsey model of fiscal policy implies that taxes should be smooth in the sense of having small variances. In contrast, empirical labour tax processes are smooth in the sense of being random walks; they provide prima facie evidence for incomplete government insurance. This paper considers whether private government information might lie behind such incomplete insurance. It shows that optimal incentive compatible policies exhibit limited use of state contingent debt and greater persistence in taxes and debt, and it argues that they are better approximations to empirical fiscal policies than those implied by the Ramsey model. The paper also establishes that optimal incentive compatible allocations converge to allocations such that the government's incentive compatibility constraint no longer binds. Generally, these limiting allocations are ones in which the government is maximally indebted. Their credibility and the interaction of incentive compatibility and credibility is briefly discussed.

Optimal Taxation with Private Government Information

The Ramsey model of fiscal policy implies that taxes should be smooth in the sense of having small variances. In contrast, empirical labour tax processes are smooth in the sense of being random walks; they provide prima facie evidence for incomplete government insurance. This paper considers whether private government information might lie behind such incomplete insurance. It shows that optimal incentive compatible policies exhibit limited use of state contingent debt and greater persistence in taxes and debt, and it argues that they are better approximations to empirical fiscal policies than those implied by the Ramsey model. The paper also establishes that optimal incentive compatible allocations converge to allocations such that the government's incentive compatibility constraint no longer binds. Generally, these limiting allocations are ones in which the government is maximally indebted. Their credibility and the interaction of incentive compatibility and credibility is briefly discussed.

Purification of incentive compatible allocations

In implementation theory it is common to consider social choice functions that map to lotteries over outcomes. For example, virtual implementation has been used widely with social choice functions that involve randomization. This paper investigates (in incomplete information environments) the possibility of purification of such social choice functions, where purification means that the “replacement” social choice function maps to outcomes rather than distributions over outcomes, is incentive compatible and generates the same distribution over payoffs and outcomes as the original social choice function.