Bayesian Incentive Compatibility Research Articles

A general impossibility theorem on Pareto efficiency and Bayesian incentive compatibility

A general impossibility theorem on Pareto efficiency and Bayesian incentive compatibility

Mechanism design with belief-dependent preferences

This paper studies mechanism design when agents have belief-dependent preferences, in that utilities depend on the agents' hierarchical posterior beliefs about types. For instance, agents may be subject to temptation, shame, image concerns, or privacy concerns. In this setting, the textbook revelation principle does not hold, since mechanisms can provide agents with information that affects posterior beliefs. This paper uses a psychological game framework suited for mechanism design, and provides a novel version of the revelation principle for belief-dependent preferences. The new revelation principle makes use of extended direct mechanisms that map each reported type into material outcomes and private suggestions of what posterior beliefs the agents should have. The paper shows that it suffices to use extended direct mechanisms that satisfy three conditions: Bayesian incentive compatibility, individual rationality, and a new condition called believability. The new revelation principle is used to find revenue-maximizing auctions when bidders have different types of image concerns. Moreover, it provides an alternate tool—distinct from Myerson's communication revelation principle—to study mechanism design with after-games.

The vigor law as a kinematic invariant at work in perceptual-cognitive processes: Comment on "Motor invariants in action execution and perception" by Francesco Torricelli et al.

Cake-cutting is a metaphor for problems where a principal agent has to fairly allocate resources. Such problems cover various areas of operations research and management science, like, for instance, shift scheduling with employees' preferences. Recent work focuses on optimizing social efficiency while guaranteeing fairness, but ignore incentive-compatibility constraints, or vice versa. In this paper, we present a new approach to heuristic mechanism design with Bayesian incentive-compatibility. As opposed to other papers, we do not allow monetary transfer. Our approach relies on the revelation principle and the computation of Bayesian–Nash equilibria using the so-called return function. This computation consists in tracking a best-reply dynamics of return function, which are mappings of action to probability distribution on outcomes, instead of the more classical but harder-to-compute best-reply dynamics of strategies. In essence, our mechanism-design approach explores a parameterized class of revelation mechanisms, which we know by construction to be Bayesian incentive-compatible. We highlight the efficiency of this approach through numerical results on instances of respectively 2, 5 and 20 agents.

A planner-optimal matching mechanism and its incentive compatibility in a restricted domain

In many random assignment problems, the central planner pursues their own policy objective, such as matching size and minimum quota fulfillment. Several practically important policy objectives do not align with agents' preferences and are known to be incompatible with strategy-proofness. This paper demonstrates that such policy objectives can be attained using mechanisms that satisfy Bayesian incentive compatibility within a restricted domain of von Neumann Morgenstern utilities. We establish that a mechanism satisfies Bayesian incentive compatibility in an inverse-bounded-indifference domain if and only if the mechanism satisfies the three axioms of swap monotonicity, lower invariance, and interior upper variance. We apply this axiomatic characterization to analyze the incentive property of the constrained random serial dictatorship mechanism (CRSD). CRSD is designed to generate an individually rational assignment that optimizes the central planner's policy objective function. Since CRSD satisfies these axioms, it is Bayesian incentive compatible within an IBI domain.

Selecting a winner with external referees

We consider a problem of mechanism design without money, where a planner selects a winner among a set of agents with binary types and receives outside signals (like the report of external referees). We show that there is a gap between the optimal Dominant Strategy Incentive Compatible (DSIC) mechanism and the optimal Bayesian Incentive Compatible (BIC) mechanism. In the optimal BIC mechanism, the planner can leverage the outside signal to elicit information about agents' types. BIC mechanisms are lexicographic mechanisms, where the planner first shortlists agents who receive high reports from the referees and then uses agents' reports to break ties among agents in the shortlist. We compare the “self-evaluation” mechanism with a “peer evaluation” mechanism where agents evaluate other agents, and show that for the same signal precision, the self- evaluation mechanism outperforms the peer evaluation mechanism. We show that optimal Ex Post Incentive Compatible (EPIC) mechanisms give the planner an intermediate value between the optimal DSIC and BIC mechanisms

Incentive-compatible and budget balanced AGV mechanism for peer-to-peer energy trading in smart grids

Peer-to-peer (P2P) energy trading refers to a type of decentralized transaction, where the energy from distributed energy resources is directly traded between peers. A key challenge in peer-to-peer energy trading is designing a safe, efficient, and transparent trading model and operating mechanism. In this study, we consider a P2P trading environment based on blockchain technology, where prosumers can submit bids or offers without knowing the reports of others. We propose an Arrow-d’Aspremont-Gerard-Varet (AGV)-based mechanism to encourage prosumers to submit their real reserve price and determine the P2P transaction price. We demonstrate that the AGV mechanism can achieve Bayesian incentive compatibility and budget balance. Kernel density estimation (KDE) is used to derive the prior distribution from the historical bid/offer information of the agents. Case studies are carried out to analyze and evaluate the proposed mechanism. Simulation results verify the effectiveness of the proposed mechanism in guiding agents to report the true reserve price while maximizing social welfare. Moreover, we discuss the advantages of budget balance for decentralized trading by comparing the Vickrey-Clarke-Groves (VCG) and AGV mechanisms.

Ordinal Bayesian incentive compatibility in random assignment model

We explore the consequences of weakening the notion of incentive compatibility from strategy-proofness to ordinal Bayesian incentive compatibility (OBIC) in the random assignment model. If the common prior of the agents is the uniform prior, then a large class of random mechanisms are OBIC with respect to this prior—this includes the probabilistic serial mechanism. We then introduce a robust version of OBIC: a mechanism is locally robust OBIC if it is OBIC with respect all independent and identical priors in some neighborhood of a given independent and identical prior. We show that every locally robust OBIC mechanism satisfying a mild property called elementary monotonicity is strategy-proof. This leads to a strengthening of the impossibility result in Bogomolnaia and Moulin (J Econ Theory 100:295–328, 2001): if there are at least four agents, there is no locally robust OBIC and ordinally efficient mechanism satisfying equal treatment of equals.

Optimal Mechanism Design With Approximate Bayesian Incentive Compatibility and Many Players

Optimal Mechanism Design With Approximate Bayesian Incentive Compatibility and Many Players

Optimal Mechanism Design With Approximate Bayesian Incentive Compatibility and Many Players

Optimal Mechanism Design With Approximate Bayesian Incentive Compatibility and Many Players

Bayesian Exploration: Incentivizing Exploration in Bayesian Games

In a wide range of recommendation systems, self-interested individuals (“agents”) make decisions over time, using information revealed by other agents in the past, and producing information that may help agents in the future. Each agent would like to exploit the best action given the current information but would prefer the previous agents to explore various alternatives to collect information. A social planner, by means of a well-designed recommendation policy, can incentivize the agents to balance exploration and exploitation in order to maximize social welfare or some other objective. The recommendation policy can be modeled as a multiarmed bandit algorithm under Bayesian incentivecompatibility (BIC) constraints. This line of work has received considerable attention in the “economics and computation” community. Although in prior work, the planner interacts with a single agent at a time, the present paper allows the agents to affect one another directly in a shared environment. The agents now face two sources of uncertainty: what is the environment, and what would the other agents do? We focus on “explorable” actions: those that can be recommended by some BIC policy. We show how the principal can identify and explore all such actions.

Epsilon-Efficiency in a Dynamic Partnership with Adverse Selection and Moral Hazard

Abstract For a dynamic partnership with adverse selection and moral hazard, we design a direct profit division mechanism that satisfies ϵ-efficiency, periodic Bayesian incentive compatibility, interim individual rationality, and ex-post budget balance. In addition, we design a voting mechanism that implements the profit division rule associated with this direct mechanism in perfect Bayesian equilibrium. For establishing these possibility results, we assume that the partnership exhibits intertemporal complementarities instead of contemporaneous complementarities; equivalently, an agent’s current effort affects other agents’ future optimal efforts instead of current optimal efforts. This modelling assumption fits a wide range of economic settings.

Ordinally Bayesian incentive compatible probabilistic voting rules

We study probabilistic voting rules in a two-voter model. The notion of incentive compatibility we consider is ordinal Bayesian incentive compatibility (OBIC) as introduced in d’Aspremont and Peleg (1988). We show that there exist anonymous and ex-post efficient probabilistic voting rules that are not random dictatorships and at the same time are OBIC with respect to an independently distributed generic prior. This contrasts with the results obtained for deterministic voting mechanisms obtained in Majumdar and Sen (2004) and in Mishra (2016). In case of neutral and efficient rules, there are two kinds of results. First we show that imposing OBIC with respect to some generic prior leads to random dictatorship when there are three alternatives. Second, we show that the result is no longer true when there are four or more alternatives and consequently we provide sufficient conditions on the priors for the result to be true.

The Complexity of Black-Box Mechanism Design with Priors

We study black-box reductions from mechanism design to algorithm design for welfare maximization in settings of incomplete information. Given oracle access to an algorithm for an underlying optimization problem, the goal is to simulate an incentive compatible mechanism. The mechanism will be evaluated on its expected welfare, relative to the algorithm provided, and its complexity is measured by the time (and queries) needed to simulate the mechanism on any input. While it is known that black-box reductions are not possible in many prior-free settings, settings with priors appear more promising: there are known reductions for Bayesian incentive compatible (BIC) mechanism design for general classes of welfare maximization problems. This dichotomy begs the question: which mechanism design problems admit black-box reductions, and which do not? Our main result is that black-box mechanism design is impossible under two of the simplest settings not captured by known positive results. First, for the problem of allocating n goods to a single buyer whose valuation is additive and independent across the goods, subject to a downward-closed constraint on feasible allocations, we show that there is no polytime (in n ) BIC black-box reduction for expected welfare maximization. Second, for the setting of multiple single-parameter agents—where polytime BIC reductions are known—we show that no polytime reductions exist when the incentive requirement is tightened to Max-In-Distributional-Range. In each case, we show that achieving a sub-polynomial approximation to the expected welfare requires exponentially many queries, even when the set of feasible allocations is known to be downward-closed.

Ordinal Bayesian Incentive Compatibility in Random Assignment Model

We explore the consequences of weakening the notion of incentive compatibility from strategy-proofness to ordinal Bayesian incentive compatibility (OBIC) in the random assignment model. If the common prior of the agents is a uniform prior, then a large class of random mechanisms are OBIC with respect to this prior - this includes the probabilistic serial mechanism. We then introduce a robust version of OBIC: a mechanism is locally robust OBIC if it is OBIC with respect all independent priors in some neighborhood of a given independent prior. We show that every locally robust OBIC mechanism satisfying a mild property called elementary monotonicity is strategy-proof. This leads to a strengthening of the impossibility result in Bogomolnaia and Moulin (2001): if there are at least four agents, there is no locally robust OBIC and ordinally efficient mechanism satisfying equal treatment of equals.

A Planner-Optimal Matching Mechanism and Its Incentive Compatibility in a Restricted Domain

In many random assignment problems, the central planner has their own policy objective, such as matching size and minimum quota fulfillment. A number of practically important policy objectives are not aligned with agents' preferences and known to be incompatible with strategy-proofness. This paper proves that such policy objectives can be achieved by mechanisms that satisfy Bayesian incentive compatibility in a restricted domain of von Neumann Morgenstern utilities. We prove that if a mechanism satisfies the three axioms of swap monotonicity, lower invariance, and interior upper invariance, then the mechanism satisfies Bayesian incentive compatibility in an inverse-bounded-indifference (IBI) domain. We apply this axiomatic characterization to analyze the incentive property of a novel mechanism, the constrained serial dictatorship mechanism (CRSD). CRSD is designed to generate an individually rational assignment that maximizes the central planner's policy objective function. As CRSD satisfies these axioms, CRSD is Bayesian incentive compatible in an IBI domain.

Simple mechanisms for subadditive buyers via duality

A central problem in mechanism design is how to design simple and approximately revenue-optimal auctions in multi-item multi-buyer settings. Prior to our work, all results only apply to cases where the buyers' valuations are linear over the items. We unify and improve all previous results, as well as generalize the results to accommodate non-linear valuations [Cai and Zhao 2017]. In particular, we prove that a simple, deterministic and Dominant Strategy Incentive Compatible (DSIC) mechanism, namely, the sequential posted price with entry fee mechanism, achieves a constant fraction of the optimal revenue among all randomized, Bayesian Incentive Compatible (BIC) mechanisms, when buyers' valuations are XOS (a superclass of submodular valuations) over independent items. If the buyers' valuations are subadditive over independent items, the approximation factor degrades to O (log m ), where m is the number of items. We obtain our results by first extending the Cai-Devanur-Weinberg duality framework to derive an effective benchmark of the optimal revenue for subadditive buyers, and then developing new analytic tools that combine concentration inequality of subadditive functions, prophet-inequality type of arguments, and a novel decomposition of the benchmark.

Efficient Division When Preferences are Private: Using the Expected Externality Mechanism

We study the problem of allocating multiple items to two agents whose cardinal preferences are private information. If money is available, Bayesian incentive compatibility and ex-ante Pareto efficiency can be achieved using the Expected Externality Mechanism (EEM). Absent money, under certain reasonable conditions, Bayesian incentive compatibility and ex-post Pareto efficiency remain achievable with a modified EEM that uses one good as a numeraire in lieu of money. We study this modified EEM’s properties and compare it with other allocation procedures.

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.

A Fair and Budget-Balanced Incentive Mechanism for Energy Management in Buildings

We propose a mechanism design based approach for the temperature setting in shared spaces (such as meeting rooms, library, and open office areas) in buildings. The proposed mechanism asks each occupant to report her willingness-to-pay for three possible outcomes: keeping the current temperature, lowering the temperature for one degree, and raising the temperature for one degree. Collecting the occupants’ preferences, the proposed mechanism chooses the outcome that maximizes the social welfare, i.e., the sum of all occupants’ willingness-to-pay (the overall thermal comfort of all occupants) minus the energy cost. The (normalized) energy cost is shared among occupants in a fair manner, according to a generalized Arrow-d’Aspremont-Gerard-Varet (AGV) mechanism. The proposed generalized AGV mechanism ensures that all occupants obtain the same (ex-ante) net payoff, while maintaining Bayesian incentive compatibility, ex-post efficiency, and ex-post budget balance of the standard AGV mechanism. We implement the proposed mechanism in an experiment with 30 students. Numerical results (based on the true temperature preferences reported by participating students) demonstrate that the proposed mechanism can lead to Pareto-better performance (in terms of energy cost and thermal comfort) than existing approaches, and fairer payment distributions than the standard AGV mechanism.

Setting lower bounds on truthfulness

This paper presents inapproximability results for paradigmatic multi-dimensional truthful mechanism design problems.We first show a lower bound of 2−1n for the scheduling problem with n unrelated machines (formulated as a mechanism design problem in the seminal paper of Nisan and Ronen on Algorithmic Mechanism Design). Our lower bound applies to universally-truthful randomized mechanisms, regardless of any computational assumptions on the running time of these mechanisms. Moreover, it holds even for the wider class of truthfulness-in-expectation mechanisms.We then turn to Bayesian settings and show a lower bound of 1.2 for Bayesian Incentive-Compatible (BIC) mechanisms. No lower bounds for truthful mechanisms in multi-dimensional settings which incorporate randomness were previously known.Next, we define the workload-minimization problem in networks. We prove lower bounds for the inter-domain routing setting presented by Feigenbaum, Papadimitriou, Sami, and Shenker.Finally, we prove lower bounds for Max–Min fairness, Min–Max fairness, and envy minimization.