The efficiency of competitive mechanisms under private information

We consider the efficiency properties of exchange economies where privately informed traders behave strategically. Specifically, a competitive mechanism is any mapping of traders’ reports about their types to an equilibrium price vector and allocation of the reported economy. In our model, some traders may have non-vanishing impact on prices and allocations regardless of the size of the economy. Although truthful reporting by all traders cannot be achieved, we show that, given any desired level of approximation, there is such that any Bayesian-Nash equilibrium of any competitive mechanism of any private information economy with or more traders leads, with high probability, to prices and allocations that are close to a competitive equilibrium of the true economy. In particular, allocations are approximately efficient. A key assumption is that there is small probability that traders behave non-strategically.     

Perfect competition in asymmetric information economies: compatibility of efficiency and incentives

The idea of perfect competition for an economy with asymmetric information is formalized via an idiosyncratic signal process in which the private signals of almost every individual agent can influence only a negligible group of agents, and the individual agents’ relevant signals are essentially pairwise independent conditioned on the true states of nature. Thus, there is no incentive for an individual agent to manipulate her private information. The existence of incentive compatible, ex post Walrasian allocations is shown for such a perfectly competitive asymmetric information economy with or without “common values”. Consequently, the conflict between incentive compatibility and Pareto efficiency is resolved exactly, and its asymptotic version is derived for a sequence of large, but finite private information economies.     

A complete characterization of Pareto optimality for general OLG economies

In the context of general pure exchange OLG economies where agents can have heterogeneous longevities, we provide both sufficient and necessary conditions for Pareto optimality of competitive equilibria. For the case in which all agents live for the same number of periods, we find that these conditions are equivalent. We also find this equivalence when agents can have different lifetimes, but in this case we need to impose particular restrictions on relative equilibrium prices. Moreover, we show that without these conditions on prices the equivalence, and hence a full characterization, is not necessarily obtained.     

Global stability condition on the plane: A general law of demand

It is well known that global stability of competitive equilibrium obtains only under quite stringent restrictions. This paper identifies a set of restrictions which may be interpreted as a very weak form of the so-called Law of Demand and shows how this may imply global stability for motion on the plane. It is also of some interest that this condition is satisfied by a perturbed version of the celebrated Scarf example which does not satisfy existing conditions for global stability.     

The role of boundary solutions in principal-agent problems of the Holmström-Milgrom type

The paper extends the Holmström-Milgrom [B. Holmström, P. Milgrom, Aggregation and linearity in the provision of intertemporal incentives, Econometrica 55 (1987) 303-328] analysis of intertemporal incentive provision to allow for the implementation of actions on the boundary of the feasible set. Boundary actions provide the principal with some freedom in choosing incentive schemes. This can be used to reduce premia. The paper characterizes optimal incentive schemes for the continuous-time Brownian-motion model and its discrete-time approximations. Linearity of incentive schemes in “accounts” is confirmed. However, for models with effort costs depending only on mean returns, the availability of boundary actions destroys the linearity of optimal incentive schemes in profits.     

A limit characterization of belief-free equilibrium payoffs in repeated games

The present paper studies repeated games with private monitoring, and characterizes the set of belief-free equilibrium payoffs in the limit as the discount factor approaches one and the noise on private information vanishes. Contrary to the conjecture by Ely et al. [J.C. Ely, J. Hörner, W. Olszewski, Belief-free equilibria in repeated games, Econometrica 73 (2005) 377-415], the equilibrium payoff set is computed by the same formula, no matter how many players there are. As an application of this result, a version of the folk theorem is established for N-player prisoner's dilemma games.     

THE SECOND‐PRICE AUCTION SOLVES KING SOLOMON'S DILEMMA*

The planner wants to give k identical, indivisible objects to the top k valuation agents at zero costs. Each agent knows her own valuation of the object and whether it is among the top k. Modify the (k+ 1)st‐price sealed‐bid auction by introducing a small participation fee and the option not to participate in it. This simple mechanism implements the desired outcome in iteratively undominated strategies. Moreover, no pair of agents can profitably deviate from the equilibrium by coordinating their strategies or bribing each other.     

Structural estimation of congestion costs

We estimate a structural model of congestion costs using a Bayesian Nash equilibrium approach: The individual's preference for traveling depends on the anticipated level of congestion, which in turn is determined by travelers’ decisions of mobility. The model is estimated using a French transportation household survey. Results confirm the presence of incomplete information and show that aversion to congestion is 6.6% lower during peak times than during off-peak times. A traveler's willingness-to-pay to save 1 min in traffic is estimated at 0.73 euros during peak times and 0.25 euros during off-peak times.     

Bargaining and inequity aversion: On the efficiency of the double auction

In a bargaining setting with asymmetrically informed, inequity-averse parties, a fully efficient mechanism (i.e., the double auction) exists if and only if compassion is strong. Less compassionate parties do not trade in the double auction in the limit of strong envy.     

A note on optimal procurement contracts with limited direct cost inflation

Laffont and Tirole's [Using cost observation to regulate firms, J. Polit. Econ. 94 (1986) 614-641] pioneering analysis identifies the optimal procurement contract when the supplier can readily inflate his innate production cost without detection. When the buyer has some ability to limit such cost inflation, an alternative contract can outperform the contract identified by Laffont and Tirole. The alternative contract induces substantial pooling, discontinuous production costs and effort supply, and rent that varies non-monotonically with innate cost.     

On the informational efficiency of simple scoring rules

We study information aggregation in large elections. With two candidates, efficient information aggregation is possible (e.g., Feddersen and Pesendorfer [5], [6] and [7]). We show that this result does not extend to elections with more than two candidates. We study a class of simple scoring rules in voting games with Poisson population uncertainty and three candidates. No simple scoring rule aggregates information efficiently, even if preferences are dichotomous and a Condorcet winner always exists. We introduce a weaker criterion of informational efficiency that requires a voting rule to have at least one efficient equilibrium. Only approval voting satisfies this criterion.     

Pareto optima and equilibria when preferences are incompletely known

An exchange economy in which agents have convex incomplete preferences defined by families of concave utility functions is considered. Sufficient conditions for the set of efficient allocations and equilibria to coincide with the set of efficient allocations and equilibria that result when each agent has a utility in her family are provided. Welfare theorems in an incomplete preferences framework therefore hold under these conditions and efficient allocations and equilibria are characterized by first order conditions.     

On the first-order approach in principal-agent models with hidden borrowing and lending

We provide sufficient conditions for the validity of the first-order approach for two-period dynamic moral hazard problems where the agent can save and borrow secretly. The first-order approach is valid if the following conditions hold: (i) the agent has non-increasing absolute risk aversion utility (NIARA), (ii) the output technology has monotone likelihood ratios (MLR), and (iii) the distribution function of output is log-convex in effort (LCDF). Moreover, under these three conditions, the optimal contract is monotone in output. We also investigate a few possibilities of relaxing these requirements.     

Intertemporal pricing in markets with differential information

Summary This paper provides a theory of intertemporal pricing in a small market with differential information about the realizations of a stochastic process which determines demand. We study the sequential equilibria in stationary strategies of the stochastic game between a seller and buyer. The seller has zero cost of producing one unit of a non-durable good in all market periods. The buyer's value for the good is a random variable governed by a simple Markov process. At the beginning of each period the unit's value is determined by nature and is privately revealed to the buyer. The seller posts a single price offer each period, which the buyer either accepts or rejects. Only two types of price paths emerge in equilibrium: either prices are constant, or they have persistent cycles between a low and a high value. In both cases, however, prices are sticky in the sense that changes in price are less frequent than changes in the economy's fundamentals.We thank John Rust and Asher Wolinsky for helpful comments. We also gratefully acknowledge financial support from NSF grant SES 89-09242.     

Subgame perfect implementation: A full characterization

Moore and Repullo [Subgame perfect implementation, Econometrica 56 (1988) 1191-1220], and Abreu and Sen [Subgame perfect implementation: a necessary and almost sufficient condition, J. Econ. Theory 50 (1990) 285-299] introduce distinct necessary and sufficient conditions for SPE implementation, when the number of players is at least three. This paper closes the gap between the conditions—a complete characterization of the SPE implementable choice rules is provided. The characterization consists of α^*, which strengthens α of Abreu-Sen by adding it a restricted veto-power condition, and the unanimity condition. Under strict preferences α^* is equal to α.     

A characterization of inefficiency in stochastic overlapping generations economies

In this paper, we provide a characterization of interim inefficiency in stochastic economies of overlapping generations. With respect to the established body of results in the literature, we allow for sequentially incomplete markets and we remove the hypothesis of two-period horizons, by considering longer, though uniformly bounded, horizons for generations. The characterization exploits a suitably Modified Cass Criterion, based entirely on observable prices and independent of the length of the horizons of generations. For sequentially incomplete markets, we introduce a notion of unambiguous inefficiency, separating the inefficient intertemporal allocation of resources from incomplete risk-sharing. Unambiguous inefficiency reduces to inefficiency when markets are sequentially complete. Furthermore, our analysis shows that the hypothesis of two-period horizons is purely heuristic in establishing a criterion for inefficiency.     

Efficiency and information aggregation in large uniform-price auctions

We prove that the equilibria of a large interdependent-value, uniform-price auction model where bidders have arbitrary preferences for multiple units can be approximated by a nonatomic exchange economy. We show that the uniform-price auction is approximately efficient with a large number of participants and asymptotically aggregates idiosyncratic bidder information into the market price. More generally our analysis framework provides conditions justifying the use of nonatomic limit model approximations to analyze the large-market behavior of game-theoretic models. We demonstrate continuity requirements on the economic primitives sufficient for the equilibrium strategies of the two models to converge as the number of participants in the finite game approaches infinity.     

An efficiency theorem for incompletely known preferences

There are n agents who have von Neumann-Morgenstern utility functions on a finite set of alternatives A. Each agent i's utility function is known to lie in the nonempty, convex, relatively open set Ui. Suppose L is a lottery on A that is undominated, meaning that there is no other lottery that is guaranteed to Pareto dominate L no matter what the true utility functions are. Then, there exist utility functions ui∈Ui for which L is Pareto efficient. This result includes the ordinal efficiency welfare theorem as a special case.     

When is multidimensional screening a convex program?

A principal wishes to transact business with a multidimensional distribution of agents whose preferences are known only in the aggregate. Assuming a twist (= generalized Spence-Mirrlees single-crossing) hypothesis, quasi-linear utilities, and that agents can choose only pure strategies, we identify a structural condition on the value b(x,y) of product type y to agent type x — and on the principal?s costs c(y) — which is necessary and sufficient for reducing the profit maximization problem faced by the principal to a convex program. This is a key step toward making the principal?s problem theoretically and computationally tractable; in particular, it allows us to derive uniqueness and stability of the principal?s optimal strategy — and similarly of the strategy maximizing the expected welfare of the agents when the principal?s profitability is constrained. We call this condition non-negative cross-curvature: it is also (i) necessary and sufficient to guarantee convexity of the set of b-convex functions, (ii) invariant under reparametrization of agent and/or product types by diffeomorphisms, and (iii) a strengthening of Ma, Trudinger and Wang?s necessary and sufficient condition (A3w) for continuity of the correspondence between an exogenously prescribed distribution of agents and of products. We derive the persistence of economic effects such as the desirability for a monopoly to establish prices so high they effectively exclude a positive fraction of its potential customers, in nearly the full range of non-negatively cross-curved models.     

A ‘technically level playing-field’ profit efficiency analysis of enforced competition between publicly funded institutions

The study demonstrates how recent advances in the data envelopment analysis (DEA) of profit efficiency, and in combining DEA and stochastic frontier analysis (SFA) to measure producer performance, can be used to obtain a ‘technically level playing-field’ profit efficiency performance measure. A three-stage analysis is used to provide an empirical investigation of public-sector universities facing regulatory pressures to attain both profit efficiency and output quality. Stage one employs directional distance function analysis to decompose DEA profit efficiency measures into technical and allocative components. As these performance measures incorporate the impacts of managerial inefficiency, the operating environment and luck (statistical noise), stage two applies SFA to total (radial and non-radial) slacks to obtain a degree of disentanglement from the latter two impacts. The stage-two results are used to define a common environment and common luck scenario, thus permitting university producers’ inputs to be adjusted so as to reflect operation within this more level playing-field scenario. Stage three recomputes the first-stage DEA for this scenario, to yield an (input-focused) ‘technically level playing-field’ measure of profit efficiency that unifies the regulatory financial audit and output-quality indicators in a single, best-practice-benchmarked, performance measure.