Ex-post Individual Rationality Research Articles

Multidimensional bargaining and posted prices

A seller and a buyer bargain over the quantities and prices of multiple goods. Both agents have private information about their preferences. Utility is quasilinear in money. We show that a deterministic mechanism satisfies (i) dominant-strategy incentive compatibility, (ii) ex-post individual rationality and (iii) ex-post budget balance if and only if it is a posted-price mechanism. A similar, more general result holds if (iii) is replaced by ex-post collusion-proofness and a no-free lunch condition. We provide a unified proof of both findings via the property of non-bossiness.

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.

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.

Strategy-proof multi-object mechanism design: Ex-post revenue maximization with non-quasilinear preferences

A seller is selling multiple objects to a set of agents, who can buy at most one object. Each agent's preference over (object, payment) pairs need not be quasilinear. The seller considers the following desiderata for her mechanism, which she terms desirable: (1) strategy-proofness, (2) ex-post individual rationality, (3) equal treatment of equals, (4) no wastage (every object is allocated to some agent). The minimum Walrasian equilibrium price (MWEP) mechanism is desirable. We show that at each preference profile, the MWEP mechanism generates more revenue for the seller than any desirable mechanism satisfying no subsidy. Our result works for the quasilinear domain, where the MWEP mechanism is the VCG mechanism, and for various non-quasilinear domains, some of which incorporate positive income effect of agents. We can relax no subsidy to no bankruptcy in our result for certain domains with positive income effect.

Non-optimality of state by state monopoly pricing with demand uncertainty: An example

This paper considers a monopoly’s profit maximizing problem, where there is a continuum of consumers with unit demand, and valuations are given by one of two possible demand distributions/states. The firm’s problem is to maximize profits by choosing an optimal mechanism among direct revelation mechanisms that satisfy interim incentive compatibility and ex-post individual rationality. We show that setting the monopoly price in each demand state may not be optimal.

Constrained Dynamic Mechanism Design with Public Correlation

We design a non-clairvoyant dynamic mechanism under budget and ex-post individual rationality constraints that is dynamic incentive-compatible and achieves non-trivial revenue performance, even without any knowledge about the future. In particular, our dynamic mechanism obtains a constant approximation to the optimal dynamic mechanism having access to all information in advance. To the best of our knowledge, this is the first dynamic mechanism that achieves a constant approximation and strictly respects dynamic incentive-compatibility and budget constraints without relying on any forecasts of the future. Our dynamic mechanism is enabled by a general design framework for dynamic mechanisms under complex environments, coined Lossless History Compression (LHC) mechanisms. LHC mechanisms compress the history into a state carrying the least historical information without losing any generality in terms of either revenue or welfare. In particular, the characterization works for i) almost arbitrary constraints on the outcomes, ii) private type distributions that are publicly correlated, and iii) any objective function defined on the historical reports, allocations, and the cumulative payments. We further prove that a non-clairvoyant dynamic mechanism is dynamic incentive-compatible if and only if it is equivalent to a stage-wise incentive compatible and state-utility independent mechanism, in which the latter means that the buyer's expected utility at each stage is independent of the state.

Robust bilateral trade with discrete types

Bilateral trade problem is the most common market interaction in which a seller and a buyer bargain over an indivisible object, and the valuation of each agent about the object is private information. We investigate the cases where mechanisms satisfying Dominant Strategy Incentive Compatibility (DIC) and Ex-post Individual Rationality (EIR) properties can exhibit robust performance in the face of imprecision in prior structure. We start with the general mathematical formulation for the bilateral trade problem with DIC, EIR properties. We derive necessary and sufficient conditions for DIC, EIR mechanisms to be Ex-post efficient at the same time. Then, we define a new property—Allocation Maximality—and prove that the Posted Price mechanisms are the only mechanisms that satisfy DIC, EIR and Allocation Maximal properties. We also show that Posted Price mechanism is not the only mechanism that satisfies DIC and EIR properties. The last part of the paper introduces different sets of priors for agents’ types and consequently allows ambiguity in the problem framework. We derive robust counterparts and solve them numerically for the proposed objective function under box and ϕ -divergence ambiguity specifications. Results suggest that restricting the feasible set to Posted Price mechanisms can decrease the objective value to different extents depending on the uncertainty set.

A game theory-based design of incentive schemes for social cloud services

This paper presents the design of incentive schemes that encourage the contribution of resources to the opportunistic cloud services (OCS) social cloud platform as well as the efficient usage of such resources. A game theoretic approach has been employed to model and design the incentive schemes with two game models presented. The existence of a pure strategy Nash equilibrium for both the cooperative and non-cooperative games has been proven. Three base incentive schemes have also been presented. These schemes are the dominant strategy scheme, equi-profit scheme, and dominant equi-profit scheme. Evaluation of the incentive schemes are performed and conclusion made that the schemes meet the desired properties of budget-balance, ex-post individual rationality, incentive compatibility, allocative efficiency, robustness, and flexibility to accommodate changing user behaviour on the OCS social cloud services platform.

A game theory-based design of incentive schemes for social cloud services

This paper presents the design of incentive schemes that encourage the contribution of resources to the opportunistic cloud services (OCS) social cloud platform as well as the efficient usage of such resources. A game theoretic approach has been employed to model and design the incentive schemes with two game models presented. The existence of a pure strategy Nash equilibrium for both the cooperative and non-cooperative games has been proven. Three base incentive schemes have also been presented. These schemes are the dominant strategy scheme, equi-profit scheme, and dominant equi-profit scheme. Evaluation of the incentive schemes are performed and conclusion made that the schemes meet the desired properties of budget-balance, ex-post individual rationality, incentive compatibility, allocative efficiency, robustness, and flexibility to accommodate changing user behaviour on the OCS social cloud services platform.

A simple budget-balanced mechanism

In the private values single object auction model, we construct a satisfactory mechanism—a dominant strategy incentive compatible and budget-balanced mechanism satisfying equal treatment of equals. Our mechanism allocates the object with positive probability to only those agents who have the highest value and satisfies ex-post individual rationality. This probability is at least $$(1-\frac{2}{n})$$ , where n is the number of agents. Hence, our mechanism converges to efficiency at a linear rate as the number of agents grow. Our mechanism has a simple interpretation: a fixed allocation probability is allocated using a second-price Vickrey auction whose revenue is redistributed among all the agents in a simple way. We show that our mechanism maximizes utilitarian welfare among all satisfactory mechanisms that allocate the object only to the highest-valued agents.

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.

Strategy-Proof Multi-Object Auction Design: Ex-Post Revenue Maximization with No Wastage

A seller is selling multiple objects to a set of agents, who can buy at most one object. Each agent's preference over (object, payment) pairs need not be quasilinear. The seller considers the following desiderata for her mechanism, which she terms desirable: (1) strategy-proofness, (2) ex-post individual rationality, (3) equal treatment of equals, (4) no wastage (every object is allocated to some agent). The minimum Walrasian equilibrium price (MWEP) mechanism is desirable. We show that at each preference profile, the MWEP mechanism generates more revenue for the seller than any desirable mechanism satisfying no subsidy. Our result works for the quasilinear domain, where the MWEP mechanism is the VCG mechanism, and for various non-quasilinear domains, some of which incorporate positive income effect of agents. We can relax no subsidy to no bankruptcy in our result for certain domains with positive income effect.

Distributed Caching Algorithms for Interconnected Operator CDNs

Fixed and mobile network operators increasingly deploy managed content distribution networks (CDNs) with the objective of reducing the traffic on their transit links and to improve their customers’ quality of experience. As network operator managed CDNs (nCDNs) become commonplace, operators will likely provide common interfaces to interconnect their nCDNs for mutual benefit, as they do with peering today. In this paper, we consider the problem of using distributed algorithms for computing a cache allocation for nCDNs. We show that if every network operator aims to minimize its cost and bilateral payments are not allowed, then it may be impossible to compute a cache allocation. For the case when bilateral payments are possible, we propose two distributed algorithms, the aggregate value compensation and the object value compensation algorithms, which differ in terms of the level of parallelism they allow and in terms of the amount of information exchanged between nCDNs. We prove that the algorithms converge, and we propose a scheme to ensure ex-post individual rationality. Simulations performed on a real autonomous system-level network topology and synthetic topologies show that the algorithms have geometric rate of convergence, and scale well with the graphs’ density and the nCDN capacity.

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.

Novel Mechanisms for Online Crowdsourcing with Unreliable, Strategic Agents

Motivated by current day crowdsourcing platforms and emergence of online labor markets, this work addresses the problem of task allocation and payment decisions when unreliable and strategic workers arrive over time to work on tasks which must be completed within a deadline. We consider the following scenario: a requester has a set of tasks that must be completed before a deadline; agents (aka crowd workers) arrive over time and it is required to make sequential decisions regarding task allocation and pricing. Agents may have different costs for providing service and these costs are private information of the agents. We assume that agents are not strategic about their arrival times but could be strategic about their costs of service. In addition, agents could be unreliable in the sense of not being able to complete the assigned tasks within the allocated time; these tasks must then be reallocated to other agents to ensure ontime completion of the set of tasks by the deadline. For this setting, we propose two mechanisms: a DPM (DynamicPrice Mechanism) and an ABM (Auction Based Mechanism). Both mechanisms are dominant strategy incentive compatible, budget feasible, and also satisfy ex-post individual rationality for agents who complete the allocated tasks. These mechanisms can be implemented in current day crowdsourcing platforms with minimal changes to the current interaction model.

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.

Imperfect Monitoring May Be Perfectly Fine: Differential Game Theory and an Application to Climate Change

We study a class of finite-horizon differential games with control-state separable objective functionals and state equations. In this context, we introduce simple mechanisms that give a dynamic payoff to agents that only depends on the current value of the state variable. Thus, in many applications their implementation requires moderate monitoring capability. We are able to show that these mechanisms induce, in Markov-perfect equilibrium, any economically meaningful control path that is continuously differentiable and satisfies certain mild regularity assumptions. Moreover, if the target control-state path represents a Pareto improvement over an inefficient unregulated outcome, a suitably chosen ex-ante cost-sharing scheme ensures ex-post individual rationality, in addition to budget balance. At the same time, if the differential game has pre-existing linear cost structure no such agreement is necessary. Our results extend to an infinite time horizon and a multi-dimensional state space. We apply our analysis to a simple differential-game model of global climate change and exhibit a mechanism, which induces the globally optimal emissions path in Markov-perfect equilibrium.

Minimizing Regret When Dissolving a Partnership

We study the problem of dissolving an equal-entitlement partnership when the objective is to minimize maximum regret. We initially focus on the family of linear-pricing mechanisms and derive regret-optimizing strategies. We also demonstrate that there exist linear-pricing mechanisms satisfying ex-post efficiency. Next, we analyze a binary-search mechanism which is ex-post individually rational. We discuss connections with the standard Bayesian-Nash framework for both linear and binary-search mechanisms. On a more general level, we show that if entitlements are unequal, ex-post efficiency and ex-post individual rationality impose significant restrictions on permissible mechanisms. In particular, they rule out both linear and binary-search mechanisms.

Design of an Optimal Bayesian Incentive Compatible Broadcast Protocol for Ad Hoc Networks with Rational Nodes

Nodes in an ad hoc wireless network incur certain costs for forwarding packets since packet forwarding consumes the resources of the nodes. If the nodes are rational, free packet forwarding by the nodes cannot be taken for granted and incentive based protocols are required to stimulate cooperation among the nodes. Existing incentive based approaches are based on the VCG (Vickrey-Clarke-Groves) mechanism which leads to high levels of incentive budgets and restricted applicability to only certain topologies of networks. Moreover, the existing approaches have only focused on unicast and multicast. Motivated by this, we propose an incentive based broadcast protocol that satisfies Bayesian incentive compatibility and minimizes the incentive budgets required by the individual nodes. The proposed protocol, which we call BIC-B (Bayesian incentive compatible broadcast) protocol, also satisfies budget balance. We also derive a necessary and sufficient condition for the ex-post individual rationality of the BIC-B protocol. The BIC-B protocol exhibits superior performance in comparison to a dominant strategy incentive compatible broadcast protocol.