Economies with Multiple Public Projects

This paper discusses a general equilibrium model of an economy with multiple separately provided public projects. We assume an additively separable cost structure and consider valuation equilibria with separated finance systems, one for each collective good. Under non-Euclidean representation we show the decentralization of Pareto efficient allocations by valuation equilibria and the equivalence of the core and the set of nonnegative valuation equilibria. In the case of Euclidean representation, every Pareto efficient allocation is shown to be supported as an affine valuation equilibrium that is characterized by a personalized price per unit of each public good and a personalized lump sum tax or subsidy. These results complement and clarify already established insights into Lindahl pricing and its generalizations developed in the literature.     

Auctions of Heterogeneous Objects

Simultaneous sealed bid auctions of heterogeneous objects are analyzed. Each bidder's reservation value for an object depends upon the other objects he obtains. Bidders' reservation values are common knowledge. In simultaneous first-price auctions, the set of Walrasian equilibrium allocations contains the set of pure strategy Nash equilibrium allocations which in turn contains the set of strict Walrasian equilibrium allocations. Hence, pure strategy Nash equilibria (when they exist) are efficient. Mixed strategy Nash equilibria may be inefficient. In simultaneous second-price auctions, any efficient allocation can be implemented as a pure strategy Nash equilibrium outcome if a Walrasian equilibrium exists.Journal of Economic LiteratureClassification Numbers: D44, D51.     

Evolutionary Stability in the Investment-Opportunism-Retaliation Game

Can economically efficient outcomes be obtained and sustained in the absence of externally enforced property rights? We study the evolutionary properties of a game that exhibits two well-defined Nash equilibria: one generates an inefficient outcome while the other set generates an efficient outcome supported by the potential for retaliation. Although standard forward-looking refinements eliminate the efficient equilibrium, neither equilibrium type satisfies strict evolutionary stability criteria. However, both types of equilibrium define strategies that are neutrally stable, which makes them vulnerable to drift in dynamic environments. We conduct computer simulation experiments in which players learn adaptively via a tournament selection mechanism called sophisticated experimentation. Our simulations demonstrate that while the system spends a disproportionately high proportion of time in the inefficient equilibrium set, the efficient equilibrium is pervasive as the system drifts back and forth between the equilibrium sets, never settling on one or the other.     

Efficient Equilibria in the Voluntary Contributions Mechanism with Private Information

We characterize generally the Bayesian Nash equilibria of a voluntary contributions public goods game for two consumers with private information.The two consumers simultaneously make voluntary contributions to the public good, and the contributions are refunded if the total falls short of the cost of the public good. Several families of equilibria (step‐function, regular and semi‐regular) are studied. Necessary and sufficient conditions for regular and semi‐regular equilibrium allocations to be interim incentive efficient are derived. In the uniform distribution case we prove (i) the existence of an open set of incentive efficient regular equilibria when the cost of production is large enough and (ii) the existence of an open set of incentive efficient semi‐regular equilibria when the cost of production is low enough. Step‐function equilibra are proved to be interim incentive inefficient.     

Broadcasting Opinions with an Overconfident Sender*

We analyze a model where an altruistic, but possibly overconfident sender broadcasts one of a finite set of messages to rational receivers. If broadcasting is costless and the sender is rational, there is an informationally efficient equilibrium, but multiple equilibria may arise, and asymmetric equilibria might be more informative than the symmetric equilibrium even if the prior is symmetric. Although overconfidence on the part of the sender reduces informativeness in some cases, it may also eliminate less informative equilibria and lead to better information transmission. Overconfidence can also improve the informativeness of the message when broadcasting is costly.     

When Borch's Theorem Does Not Apply: Some Key Implications of Market Incompleteness,with Policy Relevance Today

Markets are incomplete when the assets available to the agents do not span the space of future contingencies. In that case, competitive equilibria on the markets for assets and commodities fail (generically) to be constrained efficient. Pareto‐superior allocations can be implemented through price/wage rigidities and quantity constraints. However, nominal rigidities are conducive to multiple equilibria, implying endogenous macroeconomic uncertainties that compound the primitive (exogenous) uncertainties. This paper defines a temporary general equilibrium for which there exists a set of equilibria defining an inflation – unemployment locus. Various policy implications are drawn, with relevance to the current crisis.     

Private provision of a discrete public good: efficient equilibria in the private-information contribution game

We study the voluntary provision of a discrete public good via the contribution game. Players independently and simultaneously make nonrefundable contributions to fund a discrete public good, which is provided if and only if contributions cover the cost of production. We characterize nonconstant continuous symmetric equilibria, giving sufficient conditions for their existence. We show the common normalization by which players’ values are distributed over [0, 1] is not without loss of generality: if the distribution over this interval has continuous density f with f(0) >  0, then no (nonconstant) continuous symmetric equilibrium exists. We study in detail the case in which players’ private values are uniformly distributed, showing that, generically, when one continuous equilibrium exists, a continuum of continuous equilibria exists. For any given cost of the good, multiple continuous equilibria cannot be Pareto ranked. Nevertheless, not all continuous equilibria are interim incentive efficient. The set of interim incentive efficient equilibria is exactly determined. The authors thank Manfred Dix, George Mailath, Andrew Postlewaite, and an anonymous referee for their comments.     

On industry equilibrium under uncertainty

The paper considers an industry consisting of numerous firms that produce a homogeneous output, the demand for which is a random variable. Each firm belongs to one of K possible types, and each type is characterized by a U-shaped average cost curve. It is shown that: (i) the first-order necessary conditions for efficient investment and output are sufficient; accordingly, the set of competitive equilibria is non-empty and coincides with the set of efficient allocations; (ii) a dynamic process of free entry and exit of firms, guided by expected profits, is quasistable and every limit point is a competitive equilibrium. The paper also defines a sufficient condition for uniqueness of the competitive equilibrium, in which case it is stable.     

WELFARE GAINS AND LOSSES IN SUNSPOT EQUILIBRIA*

We study a standard two period exchange economy with one nominal asset. As is well known, there is a continuum of sunspot equilibria around each efficient equilibrium. A sunspot equilibrium is inefficient but some households may gain in sunspot equilibria relative to the efficient equilibrium. We show that a household's equilibrium utility level is either locally maximized or locally minimized at the efficient equilibrium, and derive a condition which identifies whether or not a household's utility is locally minimized or maximized.     

General equilibrium without utility functions: how far to go?

How far can we go in weakening the assumptions of the general equilibrium model? Existence of equilibrium, structural stability and finiteness of equilibria of regular economies, genericity of regular economies and an index formula for the equilibria of regular economies have been known not to require transitivity and completeness of consumers’ preferences. We show in this paper that if consumers’ non-ordered preferences satisfy a mild version of convexity already considered in the literature, then the following properties are also satisfied: (1) the smooth manifold structure and the diffeomorphism of the equilibrium manifold with a Euclidean space; (2) the diffeomorphism of the set of no-trade equilibria with a Euclidean space; (3) the openness and genericity of the set of regular equilibria as a subset of the equilibrium manifold; (4) for small trade vectors, the uniqueness, regularity and stability of equilibrium for two version of tatonnement; (5) the pathconnectedness of the sets of stable equilibria.     

On Renegotiation-Proof Equilibria in Finitely Repeated Games

This paper studies renegotiation-proof equilibria of Beno?̂t and Krishna (1993) in finitely repeated games with more than two players. We provide a simple characterization of the set of average payoffs from renegotiation-proof equilibria: the limiting set of average equilibrium payoffs is either efficient or dimensionally small as the horizon of the repeated game goes to infinity. Two sufficient conditions for the former to occur are provided. An example shows that those conditions cannot be weakened.Journal of Economic LiteratureClassification Numbers: C72, C73.     

Growth in economies with non convexities: sunspots and lottery equilibria

Summary. We investigate the relation between lotteries and sunspot allocations in a dynamic economy where the utility functions are not concave. In an intertemporal competitive economy, the household consumption set is identified with the set of lotteries, while in the intertemporal sunspot economy it is the set of measurable allocations in the given probability space of sunspots. Sunspot intertemporal equilibria whenever they exist are efficient, independently of the sunspot space specification. If feasibility is, at each point in time, a restriction over the average value of the lotteries, competitive equilibrium prices are linear in basic commodities and intertemporal sunspot and competitive equilibria are equivalent. Two models have this feature: Large economies and economies with semi-linear technologies. We provide examples showing that in general, intertemporal competitive equilibrium prices are non-linear in basic commodities and, hence, intertemporal sunspot equilibria do not exist. The competitive static equilibrium allocations are stationary, intertemporal equilibrium allocations, but the static sunspot equilibria need not to be stationary, intertemporal sunspot equilibria. We construct examples of non-convex economies with indeterminate and Pareto ranked static sunspot equilibrium allocations associated to distinct specifications of the sunspot probability space.Received: 25 August 2003, Revised: 16 March 2004, JEL Classification Numbers: D84, D90.Correspondence to: Paolo SiconolfiWe thank Herakles Polemarchakis for helpful conversations on the topic. The research of Aldo Rustichini was supported by the NSF grant NSF/SES-0136556.     

Generalized potentials and robust sets of equilibria

This paper introduces generalized potential functions of complete information games and studies the robustness of sets of equilibria to incomplete information. A set of equilibria of a complete information game is robust if every incomplete information game where payoffs are almost always given by the complete information game has an equilibrium which generates behavior close to some equilibrium in the set. This paper provides sufficient conditions for the robustness of sets of equilibria in terms of argmax sets of generalized potential functions. These sufficient conditions unify and generalize existing sufficient conditions. Our generalization of potential games is useful in other game theoretic problems where potential methods have been applied.     

On some alternative criteria for justice between generations

This paper is concerned with Rawls' principle of just savings. Both the intergenerational maxi–min solution and the Nash equilibrium are analyzed in the context of a simple growth model and a specific preference structure. The results are compared to the Utilitarian solution. The maxi–min solution is intertemporally inconsistent and all the Nash equilibria are Pareto inefficient. The latter part of the paper analyzes intergenarational strong equilibria, the α-core and the β-core. It is shown that for the model in question the set of strong equilibria is empty, and that both the α- and β-cores are roughly speaking equal to the set of all Pareto efficient programmes of accumulation.     

Menu theorems for bilateral contracting

This paper studies bilateral contracting where multiple principals negotiate contracts with multiple agents independently. It is shown that pure-strategy equilibrium allocations relative to any ad hoc set of feasible mechanisms are supported by pure-strategy perfect Bayesian equilibria relative to the set of menus. This paper also shows that all equilibrium allocations to any ad hoc set of feasible mechanisms are supported by correlated equilibria relative to the set of menus, where a state is a probability distribution function over payoff-relevant variables. Furthermore, all equilibrium allocations relative to the set of menus persist even if principals use more complex mechanisms.     

Equilibrium Selection and Stability for the Groves Ledyard Mechanism

In their seminal paper Groves and Ledyard (1976) construct a balanced incentive compatible mechanism that solves the free rider problem. In subsequent research, Bergstrom, Simon, and Titus (1983) prove that there exist numerous asymmetric equilibria in addition to the symmetric equilibrium. In the present paper, we explicitly solve for the additional equilibria and use computational experiments to examine the structure and stability of the set of equilibria of the Groves Ledyard Mechanism. We find that all of the equilibria found by Berstrom, Simon, and Titus are unstable and that for a high level of the punishment parameter these equilibria do not exist. Further, we find that there exists an additional boundary equilibrium for each of the equilibria found by Bergstrom, Simon, and Titus. The boundary equilibria are all stable.     

Inefficient lobbying,populism and oligarchy

This paper analyzes the efficiency consequences of lobbying in a production economy with imperfect commitment. We first show that the Pareto efficiency result found for truthful equilibria of common agency games in static exchange economies no longer holds under these more general conditions. We construct a model of pressure groups where the set of efficient truthful common agency equilibria has measure zero. Second, we show that, under fairly general assumptions, the equilibrium will be biased against the group with the highest productivity of private capital, reflecting the fact that, on the margin, less productive groups find lobbying relatively more rewarding. Finally, as an application, if lobbies representing the “poor” and the “rich” have identical organizational capacities, we show that the equilibrium is biased towards the poor, who have a comparative advantage in politics, rather than in production. If the pressure groups differ in their organizational capacity, both pro-rich (oligarchic) and pro-poor (populist) equilibria may arise, all of which are inefficient with respect to the constrained optimum.     

Imperfect monitoring in communication networks

Individuals in many social networks imperfectly monitor other individuals’ network relationships. This paper shows that, in a model of a communication network, imperfect monitoring leads to the existence of many inefficient equilibria. Reasonable restrictions on actions or on beliefs about others’ actions can, however, eliminate many of these inefficient equilibria even with imperfect monitoring. Star networks, known to be efficient in many settings, are shown to have desirable monitoring characteristics. More generally, this paper provides a formal framework in which to study incorrect perceptions as an equilibrium phenomenon in social networks.     

Competition Among Universities and the Emergence of the Élite Institution

We consider an environment where two education institutions compete by selecting the proportion of their funding devoted to teaching and research and the criteria for admission for their students, and where students choose whether and where to attend university. We study the relationship between the cost incurred by students for attending a university located away from their home town and the equilibrium configuration that emerges in the game played by the universities. Symmetric equilibria, where universities choose the same admission standard, only exist when the mobility cost is high; when the mobility cost is very low, there is no pure strategy equilibrium. For intermediate values of the mobility cost, only asymmetric equilibria may exist; the final section of the paper provides an example where asymmetric equilibria do indeed exist for a plausible and robust set of parameters.     

Restricted feedback in long term relationships

This paper studies long term relationships, modeled as repeated games, with restricted feedback. Players condition current play on summary statistics of past play rather than the entire history, as may be the case in online markets. Our state strategy equilibrium framework allows for arbitrary restrictions on strategies. We derive a recursive characterization for the set of equilibrium payoffs similar to that of Abreu, Pearce, and Stacchetti (1986, 1990) [2], [3] for perfect public equilibria and show that the set of equilibrium payoffs is the largest fixed point of a monotone operator. We use our characterization to derive necessary and sufficient conditions for efficient trade in a repeated product choice game where costumers condition their purchase decisions only on the last performance signal.