Ex-post Incentive Compatibility Research Articles

Dynamic communication mechanism design

We consider dynamic communication mechanisms in a quasi-linear environment with single-dimensional types. The mechanism designer gradually identifies agents’ valuations by iteratively offering prices to agents at different stages. Agents pay the maximum price they accepted if their desirable decision is made. We show that within weakly tight mechanisms, if a communication mechanism is ex-post incentive compatible, then it is a monotone-price mechanism. English auctions are characterized as a class of mechanisms that satisfy ex-post incentive compatibility and efficiency.

An online cost allocation model for horizontal supply chains

Emerging technologies in cargo shipping delivery have provided a way to facilitate horizontal cooperation in the transportation of goods to reduce the shipping cost of the cooperating firms, but an open question in this cooperation is how to allocate the costs fairly among the participants. In this paper, we focus on routing in real time a fleet of capacitated vehicles to satisfy requests submitted by a set of customers with some of the requests unknown while assigning the service cost fairly among the requested customers. We propose a Hybrid Proportional Online Cost-Sharing (HPOCS) mechanism to tackle the cost-sharing problem and analyze its performance using simulation instances. Although HPOCS does satisfy the desirable properties, namely online fairness, budget balance, immediate response, individual rationality and ex-post incentive compatibility, it has a few drawbacks in certain scenarios. Therefore, we make two extensions to HPOCS: 1) we introduce the idea of discounts to encourage customers to request in advance to facilitate efficient vehicle routing; 2) we incorporate periodical re-optimization within the dynamic vehicle routing framework. Experimental analysis are made in both extensions to see the tradeoff between the performance and the loss of certain desirable properties.

Ex-post incentive compatible and individually rational assignments in housing markets with interdependent values

This paper presents a model for housing markets with interdependent values. We introduce private information on the quality of a house (i.e., high or low), which is known only to the initial owner. Interdependency means that the ex-post preference of an agent depends on the private information of the other agents with regard to the quality of houses. We prove that on a domain satisfying a richness condition, the no-trade rule is the only rule that satisfies ex-post incentive compatibility and ex-post individual rationality.

Robust implementation in weakly perfect Bayesian strategies

We examine a strong form of robust implementation in dynamic mechanisms that is both belief- and belief-revision-free. Specifically, we characterize robust wPBE-implementation, that is, full implementation in weak Perfect Bayesian equilibrium across all type spaces. We introduce a dynamic robust monotonicity condition that is weaker than Bergemann and Morris' (2011) robust monotonicity condition and show that under a conditional no total indifference condition, ex-post incentive compatibility and dynamic robust monotonicity characterize robust wPBE-implementation in general dynamic mechanisms. We also introduce a notion of weakly rationalizable implementation (wr-implementation) and prove that it is equivalent to robust wPBE-implementation. Applied to static mechanisms, wr-implementation exactly characterizes a version of static belief-free implementation.

Ex-Post Incentive Compatible and Individually Rational Assignments in Housing Markets with Interdependent Values

This paper presents a model of housing markets with interdependent values. Here, we introduce private information on the quality of a house (i.e., high or low), which is known only to the initial owner. Interdependency means that the ex-post preference of an agent depends on the private information of the other agents with regard to the quality of houses. We prove that the no-trade rule is the only one that satisfies ex-post incentive compatibility and ex-post individual rationality. This result differs significantly from that of the private values model in which there exist non-trivial strategy-proof and individually rational rules.

Maximizing Revenue with Limited Correlation: The Cost of Ex-Post Incentive Compatibility

In a landmark paper in the mechanism design literature, Cremer and McLean (1985) (CM for short) show that when a bidder’s valuation is correlated with an external signal, a monopolistic seller is able to extract the full social surplus as revenue. In the original paper and subsequent literature, the focus has been on ex-post incentive compatible (or IC) mechanisms, where truth telling is an ex-post Nash equilibrium. In this paper, we explore the implications of Bayesian versus ex-post IC in a correlated valuation setting. We generalize the full extraction result to settings that do not satisfy the assumptions of CM. In particular, we give necessary and sufficient conditions for full extraction that strictly relax the original conditions given in CM. These more general conditions characterize the situations under which requiring ex-post IC leads to a decrease in expected revenue relative to Bayesian IC. We also demonstrate that the expected revenue from the optimal ex-post IC mechanism guarantees at most a (|Θ| + 1)/4 approximation to that of a Bayesian IC mechanism, where |Θ| is the number of bidder types. Finally, using techniques from automated mechanism design, we show that, for randomly generated distributions, the average expected revenue achieved by Bayesian IC mechanisms is significantly larger than that for ex-post IC mechanisms.

Robust dynamic implementation

This paper extends the belief-free approach to robust mechanism design to dynamic environments, in which agents obtain information over time. A social choice function (SCF) is robustly partially implemented if it is perfect Bayesian incentive compatible for all possible beliefs. It is shown that this is possible if and only if the SCF is ex-post incentive compatible. Robust full implementation imposes the stronger condition that, for all possible beliefs, all Perfect Bayesian Equilibria induce outcomes consistent with the SCF. Characterizing the set of such equilibria is a key difficulty in studying this problem. This paper shows that, for a weaker notion of equilibrium, the set of all such equilibria can be computed by means of a recursive procedure which combines the logic of rationalizability and backward induction reasoning. These results are then used to show that, in environments with single-crossing preferences and well-behaved intertemporal effects, strict ex-post incentive compatibility and a condition which limits the strength of preference interdependencies are sufficient to guarantee robust full implementation.

On budget balance of the dynamic pivot mechanism

We modify the dynamic pivot mechanism of Bergemann and Välimäki (Econometrica, 2010) in such a way that lump-sum fees are collected from the players. We show that the modified mechanism satisfies ex-ante budget balance as well as ex-post efficiency, periodic ex-post incentive compatibility, and periodic ex-post individual rationality, as long as the Markov chain representing the evolution of players' private information is irreducible and aperiodic and players are sufficiently patient. We also show that the diverse preference assumption of Bergemann and Välimäki may preclude budget balance.

Efficient assignment with interdependent values

We study the “house allocation” problem in which n agents are assigned n objects, one for each agent, when the agents have interdependent values. We show that there exists no mechanism that is Pareto efficient and ex-post incentive compatible, and the only mechanism that is ex-post group incentive compatible is constant across states. By contrast, we demonstrate that a Pareto efficient and Bayesian incentive compatible mechanism exists in the two agent house-allocation problem, given sufficient congruence of preferences and the standard single crossing property. We also show that (approximate) Pareto efficiency can be achieved once we relax the incentive compatibility requirements to approximate ex-post incentive compatibility or Bayesian incentive compatibility.

A Model of Housing Markets with Interdependent Values

This paper offers a simple model of housing markets with interdependent values. Here, we introduce private information on the quality of a house, which is known only to the initial owner. An ex-post preference of an agent is assumed to depend on such information. We prove that ex-post incentive compatibility together with another axiom leads to an impossibility: (i) a rule satisfies ex-post individual rationality and ex-post incentive compatibility if and only if it is the no-trade rule; (ii) there exists no rule that satisfies ex-post efficiency and ex-post incentive compatibility; and (iii) a rule satisfies non-bossiness and ex-post incentive compatibility if and only if it is agent-wise constant. Our results differ significantly from those of the private values model in which there exist non-trivial strategy-proof rules that satisfy desirable axioms.

A sufficient condition for two-person ex post implementation in a general environment

This paper establishes sufficient conditions for two-person ex post implementation of a social choice set in a general environment. A single social choice function is ex post implementable if it satisfies ex post incentive compatibility (EPIC) and ex post monotonicity no veto (EMNV) conditions. A general social choice set is ex post implementable if it satisfies another condition, intersection property (IP), in addition to the above.

Online Cost-Sharing Mechanism Design for Demand-Responsive Transport Systems

Demand-responsive transport (DRT) systems provide flexible transport services for passengers who request door-to-door rides in shared-ride mode without fixed routes and schedules. DRT systems face interesting coordination challenges. For example, one has to design cost-sharing mechanisms for offering fare quotes to potential passengers so that all passengers are treated fairly. The main issue is how the operating costs of the DRT system should be shared among the passengers (given that different passengers cause different amounts of inconvenience to the other passengers), taking into account that DRT systems should provide fare quotes instantaneously without knowing future ride request submissions. We determine properties of cost-sharing mechanisms that make DRT systems attractive to both the transport providers and passengers, namely online fairness, immediate response, individual rationality, budget balance, and ex-post incentive compatibility. We propose a novel cost-sharing mechanism, which is called Proportional Online Cost Sharing (POCS), which provides passengers with upper bounds on their fares immediately after their ride request submissions despite missing knowledge of future ride request submissions, allowing them to accept their fare quotes or drop out. We examine how POCS satisfies these properties in theory and computational experiments.

Two-person ex post implementation

This paper investigates the ex post implementation of a social choice set with two agents. A social choice set F is ex post implementable with two agents if F satisfies the conditions of ex post incentive compatibility (EPIC) and ex post monotonicity (EM) in an environment that is economic and has a bad outcome. Furthermore, if F is a social choice function, (EPIC), (EM), and an economic environment are sufficient.

Optimal Dynamic Mechanism Design and the Virtual Pivot Mechanism

We consider the problem of designing optimal mechanisms for settings where agents have dynamic private information. We present the Virtual-Pivot Mechanism, that is optimal in a large class of environments that satisfy a separability condition. The mechanism satisfies a rather strong equilibrium notion (it is periodic ex-post incentive compatible and individually rational). We provide both necessary and sufficient conditions for immediate incentive compatibility for mechanisms that satisfy periodic ex-post incentive compatibility in future periods. The result also yields a strikingly simple mechanism for selling a sequence of items to a single buyer. We also show the allocation rule of the Virtual-Pivot Mechanism has a very simple structure (a Virtual Index) in multi-armed bandit settings. Finally, we show through examples that the relaxation technique we use does not produce optimal dynamic mechanisms in general non-separable environments.