Undominated Nash Implementation with Collusion and Renegotiation

This article looks at implementation in economic environments when agents have perfect information about the state of the world, but cannot commit not to renegotiate bad outcomes or to collude against each other. If renegotiation satisfies a weak condition of disagreement point monotonicity, then any Pareto-efficient social choice function can be implemented if there are at least three agents who play undominated Nash equilibria. The mechanism does not use modulo or integer games, has no bad mixed strategy equilibria, and is “bounded.”Journal of Economic LiteratureClassification Number: D71.     

Implementation with partial provability

We extend implementation theory by allowing the social choice function to depend on more than just the preferences of the agents and allowing agents to support their statements with hard evidence. We show that a simple condition on evidence is necessary for the implementation of a social choice function f when the preferences of the agents are state independent and sufficient for implementation for any preferences (including state dependent) with at least three agents if the social planner can perform small monetary transfers beyond those called for by f. If transfers can be large, f can be implemented in a game with perfect information when there are at least two players under a boundedness assumption. For both results, transfers only occur out of equilibrium. The use of evidence enables implementation which is robust in the sense that the planner needs little information about agents? preferences or beliefs and agents need little information about each others? preferences. Our results are robust to evidence forgery at any strictly positive cost.     

POLITICALLY REALISTIC IMPLEMENTATION WITH INSPECTION: THE EQUITY-HONESTY-WELFARE TRADE-OFF

We study dominant strategy mechanisms where the planner knows the distribution of types and the agents are instructed to announce their types to the planner. It is assumed that the planner has access to a technology of inspection which is costly but perfect, and that he can penalize an agent who is inspected after announcements have been made if he is found to have lied about his type. It shall be shown that, in general, the welfare-maximizing mechanism that respects minimal equity will induce some agents to lie about their types.     

Negative Externalities and Evolutionary Implementation

We model externality abatement as an implementation problem. A social planner would like to ensure efficient behaviour among a group of agents whose actions are sources of externalities. However, the planner has limited information about the agents' preferences, and is unable to distinguish individual agents except through their action choices. We prove that if a concavity condition on aggregate payoffs is satisfied, the planner can guarantee that efficient behaviour is globally stable under a wide range of behaviour adjustment processes by administering a variable pricing scheme. Through a series of applications, we show that the concavity condition is naturally satisfied in settings involving negative externalities. We conclude by contrasting the performance of the pricing mechanism with that of a mechanism based on direct revelation and announcement dependent forcing contracts.     

Moral Hazard and Renegotiation with Multiple Agents

We investigate the effects of contract renegotiation in multi-agentsituations where risk-averse agents negotiate a contract offer to theprincipal after the agents observe a common, unverifiable perfect signalabout their actions. We show that renegotiation with multiple agentsreduces the cost of implementing any implementable action profile downto the first-best level, even though the principal cannot observe theagents' actions. Moreover, it is sufficient for the principal to use a"simple" initial contract, in the sense that it consists of nomore than a single sharing scheme for each agent and the total payments tothe agents are the same regardless of the realised state. An importantimplication is that decentralization, in the sense of delegated negotiationand proposals from the agents, can be as effective as centralized schemesthat utilize revelation mechanisms in unrestricted ways.     

Implementing efficient graphs in connection networks

We consider the problem of sharing the cost of a network that meets the connection demands of a set of agents. The agents simultaneously choose paths in the network connecting their demand nodes. A mechanism splits the total cost of the network formed among the participants. We introduce two new properties of implementation. The first property, Pareto Nash implementation (PNI), requires that the efficient outcome always be implemented in a Nash equilibrium and that the efficient outcome Pareto dominates any other Nash equilibrium. The average cost mechanism and other asymmetric variations are the only mechanisms that meet PNI. These mechanisms are also characterized under strong Nash implementation. The second property, weakly Pareto Nash implementation (WPNI), requires that the least inefficient equilibrium Pareto dominates any other equilibrium. The egalitarian mechanism (EG) and other asymmetric variations are the only mechanisms that meet WPNI and individual rationality. EG minimizes the price of stability across all individually rational mechanisms.     

Unforeseen Contingencies and Incomplete Contracts

We scrutinize the conceptual framework commonly used in the incomplete contract literature. This literature usually assumes that contractual incompleteness is due to the transaction costs of describing—or of even foreseeing—the possible states of nature in advance. We argue, however, that such transaction costs need not interfere with optimal contracting ( i.e. transaction costs need not be relevant ), provided that agents can probabilistically forecast their possible future payoffs (even if other aspects of the state of the nature cannot be forecast). In other words, all that is required for optimality is that agents be able to perform dynamic programming, an assumption always invoked by the incomplete contract literature. The foregoing optimality result holds very generally provided that parties can commit themselves not to renegotiate. Moreover, we point out that renegotiation may be hard to reconcile with a framework that otherwise presumes perfect rationality. However, even if renegotiation is allowed, the result still remains valid provided that parties are risk averse.     

CREDIBILITY AND RENEGOTIATION OF OUTCOME FUNCTIONS IN IMPLEMENTATION*

Recent research has been motivated by the fact that the outcome function in implementation may not be “credible”. On the one hand, the players may try to renegotiate the final outcome, if there is another outcome which they prefer. On the other hand, the “social planner” may have an incentive not to implement the finaloutcome, if there is another outcome which he prefers. I show that in the exchange economy, the first problem is not serious. a planner with unlimited commitment power can design a “collusion-proof” mechanism, which is stable against all sorts of group devciation, including the ex post trade of goods among the agents. I will, However, argue tha hte second problem (the planner's commitment problem) can be very serious.     

Double implementation in economies with production technologies unknown to the designer

Summary. This paper considers double implementation of Walrasian allocations and Lindahl allocations in Nash and strong Nash equilibria for both private and public goods economies when preferences, initial endowments, production technologies, and coalition patterns are all unknown to the designer. It will be noted that the mechanisms presented here are feasible and continuous. In addition, unlike most mechanisms proposed in the literature, our mechanism works not only for three or more agents, but also for two-agent economies, and thus it is a unified mechanism which is irrespective of the number of agents. Received: March 12, 1998; revised version: March 12, 1998     

Retrading in market games

When agents are not price takers, they typically cannot obtain an efficient real location of resources in one round of trade. This paper presents a non-cooperative model of imperfect competition where agents can retrade allocations, consistent with Edgeworth's idea of recontracting. We show (a) there are Pareto optimal allocations, including competitive equilibrium allocations, that can be approximated arbitrarily closely when trade is myopic, i.e., when agents play a static Nash equilibrium at every round of retrading; (b) any converging sequence of allocations generated by myopic retrading can be supported along some retrade-proof subgame perfect equilibrium path when traders anticipate future rounds of trading.     

Achieving efficiency with manipulative bargainers

Two agents bargain over the allocation of a bundle of divisible commodities. After strategically reporting utility functions to a neutral arbitrator, the outcome is decided by using a bargaining solution concept chosen from a family that includes the Nash and the Raiffa–Kalai–Smorodinsky solutions. When reports are restricted to be continuous, strictly increasing and concave, it has been shown that this kind of “distortion game” leads to inefficient outcomes. We study the distortion game originated when agents are also allowed to claim non-concave utility functions. Contrasting with the previous literature, any interior equilibrium outcome is efficient and any efficient allocation can be supported as an equilibrium outcome of the distortion game. In a similar fashion to the Nash demand game we consider some uncertainty about the opponent's features to virtually implement the Nash bargaining solution.     

Socially optimal procurement with tight budgets and rationing

We investigate the behaviour of a social planner that secures the supply of a good, e.g. an environmental benefit, through contracting with private agents. While the social planner seeks to maximise net social benefits, she is also controlled with a fixed budget. Private agents are profit maximising and hold private information concerning their variable costs of production. They also have known fixed costs of contracting. We find that budget constraints and fixed costs change the optimal contract design in more than one way: the social planner minimises costs, rations high-cost contracts to reduce fixed costs and information rents, and distorts contracts for all agent types, including low-cost agents. We find that rationing improves social welfare. Also, even though social costs – including tax distortion – are explicitly taken into consideration, they do not affect the design of optimal contracts when budgets are tight. In those cases the budget constraint dominates the solution.     

The erosion of personal norms and cognitive dissonance

In this article, we study how personal norms and behaviour interact and evolve when agents try to reduce cognitive dissonance, and how this dynamic relates to Nash equilibrium. We find that in long run, agents play, and norms prescribe, Nash equilibrium in material payoffs (in the absence of norms). Our model captures two main facts: (i) norms erode along the play of the game; (ii) the erosion of norms depends on the set of possible economic choices, so that the policy maker can potentially influence them.     

Learning to alternate

The Individual Evolutionary Learning (IEL) model explains human subjects’ behavior in a wide range of repeated games which have unique Nash equilibria. Using a variation of ‘better response’ strategies, IEL agents quickly learn to play Nash equilibrium strategies and their dynamic behavior is like that of humans subjects. In this paper we study whether IEL can also explain behavior in games with gains from coordination. We focus on the simplest such game: the 2 person repeated Battle of Sexes game. In laboratory experiments, two patterns of behavior often emerge: players either converge rapidly to one of the stage game Nash equilibria and stay there or learn to coordinate their actions and alternate between the two Nash equilibria every other round. We show that IEL explains this behavior if the human subjects are truly in the dark and do not know or believe they know their opponent’s payoffs. To explain the behavior when agents are not in the dark, we need to modify the basic IEL model and allow some agents to begin with a good idea about how to play. We show that if the proportion of inspired agents with good ideas is chosen judiciously, the behavior of IEL agents looks remarkably similar to that of human subjects in laboratory experiments.     

On the robustness of laissez-faire

This paper considers a model economy in which agents are privately informed about their type: their endowments of various goods and their preferences over these goods. While preference orderings over observable choices are allowed to be correlated with an agent's private type, we assume that the planner/government is both uncertain about the nature of this joint distribution and unable to choose among multiple equilibria of any given social mechanism. We model the planner/government as having a maxmin objective in the face of this uncertainty.Our main theorem is as follows: Once we allow for this kind of uncertainty and assume no wealth effects in preferences, the uniquely optimal social contract is laissez-faire, in which agents trade in unfettered markets with no government intervention of any kind.     

Credibility and endogenous societal discounting

We consider a dynamic moral hazard economy inhabited by a planner and a population of privately informed agents. We assume that the planner and the agents share the same discount factor, but that the planner cannot commit. We show that optimal allocations in such settings solve the problems of committed planners who discount the future less heavily than agents. Thus, we provide micro-foundations for dynamic moral hazard models that assume a societal discount factor in excess of the private one. We extend the analysis to allocations that are reconsideration-proof in the sense of Kocherlakota [Kocherlakota, N., 1996. Reconsideration-proofness: A refinement for infinite horizon time inconsistency. Games and Economic Behavior 15, 33–54]. We show that these allocations solve the choice problem of a committed planner with a unit discount factor.     

On the welfare effects of allowing unlimited renegotiation in agency relationships

We study renegotiation in an agency setting where the number of offers and accept/reject decisions parties can make is potentially unlimited. Thus any contract, either on or off the equilibrium path, may be subject to possible renegotiation. We first show that the principal will not be able to gain complete access to the agent’s private information with unlimited renegotiation, unlike when the potential number of renegotiations is finite. Rather the agent either employ a randomized reporting strategy or do not to report at all. We then identify conditions under which expected allocations are most efficient with the contract that induces no agent communication. More significantly, by doing so we also identify conditions under which the parties are made strictly worse off by committing to end renegotiation after a fixed number of rounds. We thank workshop participants at University of California, Irvine, University of Chicago, Duke University, Hong Kong University of Science and Technology, University of Houston, London School of Economics, University of Minnesota, Ohio State University, the Carnegie Mellon Accounting Research Conference, the editor, and an anonymous referee for their helpful comments and suggestions.     

Wage bargaining and turnover costs with heterogenous labor and perfect history screening

We study effects of mobility costs in a model of (Nash) wage bargaining between workers and firms, with instantaneous matching, heterogeneous workers, identical firms and free firm entry, and where firms can screen workers perfectly according to their previous work history but not their actual productivity. We derive the employment level and the minimum worker quality standard, in the market solution, and in the efficient solution established by a social planner. When workers have positive bargaining power, there is always some inefficient unemployment among desired workers in the market solution. The lowest hiring standard chosen by firms is higher than the planner's standard when firing costs are high relative to hiring costs, but may be lower in the opposite case. We show that any higher established hiring standard corresponds to a market equilibrium. The model explains a tendency for a high initial unemployment rate to remain high, particularly for low-skilled workers.     

Double moral hazard and renegotiation

We examine renegotiation in a double moral hazard model with an ex ante budget balancing constraint when both the principal and the agent are allowed to make a renegotiation offer even though the principal proposes an initial contract. Under a belief restriction, any perfect-Bayesian equilibrium leads to an allocation that is superior to the second-best allocation of the standard double moral hazard model without renegotiation. The result of this paper gives some reasons for the existence of intermediary organizations such as holding companies, law houses, consulting firms, investment banks or venture capital. The result can also provide the rationalization for a fund set up by a group of firms of the industry in which their product is legally required to be recyclable.     

Can contracts solve the hold-up problem? Experimental evidence

In the contract-theoretic literature, there is a vital debate about whether contracts can mitigate the hold-up problem, in particular when renegotiation cannot be prevented. Ultimately, this question has to be answered empirically. As a first step, we have conducted a laboratory experiment with 960 participants. We consider investments that directly benefit the non-investing party. While according to standard theory, contracting would be useless if renegotiation cannot be ruled out, we find that option contracts significantly improve investment incentives compared to a no-contract treatment. This finding might be attributed to Hart and Moore?s (2008) recent idea that contracts can serve as reference points.