Mechanism design with partial state verifiability

We study implementation in environments where agents have limited ability to imitate others. Agents are randomly and privately endowed with type-dependent sets of messages. So sending a message becomes a partial proof regarding type. For environments where agents can send any combination of available messages, we develop an Extended Revelation Principle and characterize the incentive constraints which implementable allocations must satisfy. When not all message combinations are feasible, static mechanisms no longer suffice. If a ‘punishment’ allocation exists for each agent, then implementable allocations can be characterized as equilibria of a “Revelation Game,” in which agents first select from the menus of allocation rules, then the mediator requests each agent to send some verifying messages. When a punishment allocation fails to exist for some agent, dynamic games in which agents gradually reveal their evidence implement a larger set of outcomes. The latter result provides a foundation for a theory of debate.     

Comparing finite mechanisms

Summary. This paper obtains finite analogues to propositions that a previous literature obtained about the informational efficiency of mechanisms whose possible messages form a continuum. Upon reaching an equilibrium message, to which all persons “agree”, a mechanism obtains an action appropriate to the organization's environment. Each person's privately observed characteristic (a part of the organization's environment) enters her agreement rule. An example is the Walrasian mechanism in an exchange economy. There a message specifies a proposed trade vector for each trader as well as a price for each non-numeraire commodity. A trader agrees if the price of each non-numeraire commodity equals her marginal utility for that commodity (at the proposed trades) divided by her marginal utility for the numeraire. At an equilibrium message, the mechanism's action consists of the trades specified in that message, and (for classic economies) those trades are Pareto-optimal and individually rational. Even though the space of environments (characteristics) is a continuum, mechanisms with a continuum of possible messages are unrealistic, since transmitting every point of a continuum is impossible. In reality, messages have to be rounded off and the number of possible messages has to be finite. Moreover, reaching a continuum mechanism's equilibrium message typically requires infinite time and that difficulty is absent if the number of possible messages is finite. The question therefore arises whether results about continuum mechanisms have finite counterparts. If we measure a continuum mechanism's communication cost by its message-space dimension, then our corresponding cost measure for a finite mechanism is the (finite) number of possible equilibrium messages. We find that if two continuum mechanisms yield the same action but the first has higher message-space dimension, then a sufficiently fine finite approximation of the first has larger error than an approximation of the second if the cost of the first approximation is no higher than the cost of the second approximation. An approximation's “error” is the largest distance between the continuum mechanism's action and the approximation's action. We obtain bounds on error. We also study the performance of Direct Revelation (DR) mechanisms relative to “indirect” mechanisms, both yielding the same action, when the environment set grows. We find that as the environment-set dimension goes to infinity, so does the extra cost of the DR approximation, if the error of the DR approximation is at least as small as the error of the indirect approximation. While the paper deals with information-processing costs and not incentives, it is related to the incentive literature, since the Revelation Principle is central to much of that literature and one of our main results is the informational inefficiency of finite Direct Revelation mechanisms. Received: May 21, 2001; revised version: December 14, 2001 RID="*" ID="*" Earlier versions of this paper were presented at the Decentralization Conference, Washington University, St Louis, April 2000 and at the Eighth World Congress of the Econometric Society, August 2000. We are grateful for comments received on those occasions. The second author gratefully acknowledges support from National Science Foundation grant #IIS9712131. Correspondence to: T. Marschak     

Serial dictatorship and Pareto optimality

In a deterministic allocation problem in which each agent is entitled to receive exactly one object, an allocation is Pareto optimal if and only if it is the outcome of a serial dictatorship. We extend the definition of serial dictatorship to settings in which some agents may be entitled to receive more than one object, and study the efficiency and uniqueness properties of the equilibrium allocations. We prove that subgame perfect equilibrium allocations of serial dictatorship games are not necessarily Pareto optimal; and generally not all Pareto optima can be implemented as subgame perfect equilibrium allocations of serial dictatorship games, except in the 2-agent separable preference case. Moreover, serial dictatorship games do not necessarily have unique subgame perfect equilibrium allocations, except in the 2-agent case, hence their outcomes are indeterminate and manipulable.     

Duality theory for dynamic optimization models of economics: The continuous time case

This paper establishes that the competitive allocation process is the only informationally decentralized mechanism for exchange environments which (i) achieves Pareto optimal allocations; (ii) gives each consumer an allocation which is, according to his preferences, at least as good as his endowment; (iii) satisfies certain regularity conditions; and (iv) has a message space of the smallest dimension necessary to satisfy (i–iii).     

Efficient and stable collective choices under gregarious preferences

We consider collective choice problems where a set of agents have to choose an alternative from a finite set and agents may or may not become users of the chosen alternative. An allocation is a pair given by the chosen alternative and the set of its users. Agents have gregarious preferences over allocations: given an allocation, they prefer that the set of users becomes larger. We require that the final allocation be efficient and stable (no agent can be forced to be a user and no agent who wants to be a user can be excluded). We propose a two-stage sequential mechanism whose unique subgame perfect equilibrium outcome is an efficient and stable allocation which also satisfies a maximal participation property.     

A Revelation Mechanism for Soft Information under Moral Hazard

This paper constructs a revelation mechanism to address a problem of moral hazard under soft information. The agent alone observes the stochastic outcome of her action, which she reports to the principal. Therefore the principal also faces a problem of ex post adverse selection. Economically relevant restrictions induce constraints on the principal's choice of mechanism and the Revelation Principle fails to apply. Specifically, a direct mechanism induces some pooling, which does not replicate the allocation obtained using a larger message space. Pooling also weakens the ex ante incentives. The Revelation Principle is extended to obtain type separation. A better audit relaxes frictions.     

Efficient and stable collective choices under gregarious preferences

We consider collective choice problems where a set of agents have to choose an alternative from a finite set and agents may or may not become users of the chosen alternative. An allocation is a pair given by the chosen alternative and the set of its users. Agents have gregarious preferences over allocations: given an allocation, they prefer that the set of users becomes larger. We require that the final allocation be efficient and stable (no agent can be forced to be a user and no agent who wants to be a user can be excluded). We propose a two-stage sequential mechanism whose unique subgame perfect equilibrium outcome is an efficient and stable allocation which also satisfies a maximal participation property.     

The (sub-)optimality of the majority rule

We consider collective choice from two alternatives. Ex-ante, each agent is uncertain about which alternative she prefers, and may be uncertain about the intensity of her preferences. An environment is given by a probability distribution over utility vectors that is symmetric across agents and neutral across alternatives. In many environments, the majority voting rule maximizes agents? ex-ante expected utilities among all anonymous and dominant-strategy implementable choice rules. But in some environments where the agents? utilities are stochastically correlated, other dominant-strategy choice rules are better for all agents. If utilities are stochastically independent across agents, majority voting is ex-ante optimal among all anonymous and incentive-compatible rules. We also compare rules from an interim-viewpoint.     

Single Object Auctions With Externalities: A Tractable Model

We consider the single object auction model with allocative externalities in a private valuation and quasi‐linear setting. We model externalities by assuming that every agent has a private valuation (for the object) and a strict ranking of other agents. The utility for an agent when another agent receives the object is the product of his own valuation and a real number that depends on the rank of this agent in his ranking. When the only private information is the valuation of the agents, we characterise the implementable allocation rules and use these to derive the optimal auction. The optimal auction collects payments from agents who do not receive the object.     

Group incentive compatibility in a market with indivisible goods

In a market where each trader has one unit of an indivisible good, there are procedures for exchanging goods which result in competitive allocations. One of these procedures, the top trading cycle, has the property that it is in each trader's best interest to report his true preferences over the set of goods. This note shows that no subset of traders can misrepresent their preferences and improve the allocation for all members of the subset. Additionally, if there are no indifferences in the preferences, then some traders in a subset that misrepresents preferences do worse.     

Outside versus inside bonds: A Modigliani–Miller type result for liquidity constrained economies

When agents are liquidity constrained, two options exist – sell assets or borrow. We compare the allocations arising in two economies: in one, agents can sell government (outside) bonds and in the other they can borrow by issuing (inside) bonds. All transactions are voluntary, implying no taxation or forced redemption of private debt. We show that any allocation in the economy with inside bonds can be replicated in the economy with outside bonds but that the converse is not true. However, the optimal policy in each economy makes the allocations equivalent.     

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.     

On Ramsey's conjecture: efficient allocations in the neoclassical growth model with private information

In his seminal paper of 1928, Ramsey conjectured that if agents discounted the future differently, in the long run all agents except the most patient would live at the subsistence level. The validity of this conjecture was investigated in different environments. In particular, it has been confirmed in the neoclassical growth model with dynamically complete markets. This paper studies this conjecture in a version of this model that includes private information and heterogeneous agents. A version of Bayesian implementation is introduced and a recursive formulation of the original allocation problem is established. Efficient allocations are renegotiation-proof and the expected utility of any agent cannot go to zero with positive probability if the economy does not collapse. If the economy collapses all agents will get zero consumption forever. Thus, including any degree of private information in the neoclassical growth model will deny Ramsey's conjecture, if efficient allocations are considered.     

Non-myopic learning in differential information economies: the core

Summary. We study the process of learning in a differential information economy, with a continuum of states of nature that follow a Markov process. The economy extends over an infinite number of periods and we assume that the agents behave non-myopically, i.e., they discount the future. We adopt a new equilibrium concept, the non-myopic core. A realized agreement in each period generates information that changes the underlying structure in the economy. The results we obtain serve as an extension to the results in Koutsougeras and Yannelis (1999) in a setting where agents behave non-myopically. In particular, we examine the following two questions: 1) If we have a sequence of allocations that are in an approximate non-myopic core (we allow for bounded rationality), is it possible to find a subsequence that converges to a non-myopic core allocation in a limit full information economy? 2) Given a non-myopic core allocation in a limit full information economy can we find a sequence of approximate non-myopic core allocations that converges to that allocation? Received: May 25, 1999; revised version: August 9, 1999     

Existence and fairness of value allocation without convex preferences

Shafer (Econometrica, 48 (1980), 467–476) proved that in a finite exchange economy value allocations exist, provided that each agent has convex, complete, transitive, compact and monotone preferences. However, if preferences are not convex, then value allocations may not exist. To remedy this difficulty we enlarge the set of value allocations by introducing the concept of approximate value allocations, and show that in a finite exchange economy approximate value allocations exist, even if preferences are not convex, or compact, or monotone. This value existence result can be used to provide a very general value existence theorem for a sequence of finite economies. Further, we show that value allocations may discriminate in favor of or against a coalition of agents.     

Equity in exchange economies

Let ψ be a “fair” choice correspondence, i.e., ψ associates to every economy in some initial position a set of final allocations at which the gains from trade have been fairly distributed. We propose to declare equitable any final allocation which is invariant under arbitrary permutations among the agents of the components of the initial allocation, followed by the operation of ψ. We also formulate a series of other criteria patterned on this model, and we investigate the existence of allocations satisfying these criteria for several natural choices of ψ.     

A Core‐Equilibrium Convergence in a Public Goods Economy

This paper shows a core‐equilibrium convergence in a public goods economy where consumers' preferences display warm glow effects. We demonstrate that if each consumer becomes satiated to other consumers' provision, then as the economy grows large the core shrinks to the set of Edgeworth allocations. Moreover, we show that an Edgeworth allocation can be decentralized as a warm glow equilibrium.     

Role of linking mechanisms in multitask agency with hidden information

We investigate the adverse selection problem where a principal delegates multiple tasks to an agent. We characterize the virtually implementable social choice functions by using the linking mechanism proposed by Jackson and Sonnenschein (2007) [20] that restricts the message spaces. The principal does not require any incentive wage schemes and can therefore avoid any information rent and welfare loss. We show the resemblance between the functioning of this message space restriction and that of incentive wage schemes. We also extend the results of the single-agent model to the multi-agent model.     

Building and rebuilding trust with promises and apologies

Using trust games, we study how promises and messages are used to build new trust where it did not previously exist and to rebuild damaged trust. In these games, trustees made non-binding promises of investment-contingent returns, then investors decided whether to invest, and finally trustees decided how much to return. After an unexpected second game was announced, but before it commenced, trustees could send a one-way message. This design allowed us to observe the endogenous emergence and natural distribution of trust-relevant behaviors and focus on naturally occurring remedial strategies used by promise-breakers and distrusted trustees, their effects on investors, and subsequent outcomes. In the first game 16.6% of trustees were distrusted and 18.8% of trusted trustees broke promises. Trustees distrusted in the first game used long messages and promises closer to equal splits to encourage trust in the second game. To restore damaged trust, promise-breakers used apologies and upgraded promises. On average, investments in each game paid off for investors and trustees, suggesting that effective use of cheap signals fosters profitable trust-based exchange in these economies.     

Fair allocations of a renewable resource

In an economy with finitely many agents, one renewable resource, and an infinite horizon, it is shown that there is exactly one maximal allocation corresponding to given limiting shares of consumption and this allocation converges monotonically. Therefore, if there is no discounting, at most one fair maximal program exists—that which gives an equal amount to each individual in the limit. In this allocation, envy is always finite. However, only in special cases is it envyfree. This is in contrast to the case of finite economies where envy-free and Pareto efficient allocations may not exist or, if they exist, may not be unique.