Robustness of equilibria in anonymous local games

This paper studies the robustness of symmetric equilibria in anonymous local games to perturbations of prior beliefs. Two priors are strategically close on a class of games if players receive similar expected payoffs in equilibrium under the priors, for any game in that class. I show that if the structure of payoff interdependencies is sparse in a well-defined sense, the conditions for strategic proximity in anonymous local games are strictly weaker than the conditions for general Bayesian games of Kajii and Morris (1998) [11] when attention is restricted to symmetric equilibria. Hence, by exploiting the properties of anonymous local games, it is possible to obtain stronger robustness results for this class.     

EFFICIENT MIXED CLUBS: NONLINEAR-PRICING EQUILIBRIA WITH ENTREPRENEURIAL MANAGERS

Scotchmer and Wooders show that efficient clubs are homogeneous when consumers are divisible in Berglas's anonymous crowding model. However, if consumers are not divisible or if clubs have multiple facilities with economies of scope, mixed clubs are efficient. In such a model, we consider clubs with multiple membership policies for different types of consumers, and show the existence and efficiency of equilibrium with nonlinear policies. We employ entrepreneurial equilibrium, all equilibrium concept with profit-seeking entrepreneurs. Our theorem can be regarded as showing the existence of a core allocation that satisfies envy-free property in the absence of non-anonymous crowding effects.     

Risky arbitrage,asset prices,and externalities

We introduce a no-risky-arbitrage price condition (NRAP) for asset market models allowing both unbounded short sales and externalities such as trading volume. We then demonstrate that NRAP is sufficient for the existence of competitive equilibrium in the presence of externalities. Moreover, we show that if all risky arbitrages are utility increasing, then NRAP characterizes competitive equilibrium in the presence of externalities. We are indebted to an anonymous referee for helpful comments on an earlier version of this paper. Page and Wooders are especially grateful to CERMSEM and EUREQua for their support and hospitality which made possible our collaboration.     

A theory of commerce

The theory of commerce advanced here captures prominent features of retail trade: large employment, congestion effects, anonymous posted prices, and quantity discounts. This theory is built around a directed search model where buyers’ preferences are private information. The analytical solution is easily inserted in a Neoclassical growth framework. In this framework, the parameters of retail trade are calibrated using commercial margins and employment. Welfare properties depend on the sellers’ ability to charge two-tier prices. With two-tier prices, the directed search equilibrium is efficient. Otherwise, it is not. This contrasts with the full information benchmark, where directed search is always efficient.     

The acquisition of information in a dynamic market

Summary This paper models the information acquisition process in an intertemporal rational expectations framework. It demonstrates that equilibria do not generally exist in intertemporal economies in which agents are assumed to know the state-contingent price path and the information acquisition process is endogenous. In addition, an example of a fully revealing equilibrium in which agents pay a strictly positive amount for information is provided. Finally, we also show that it is possible for an equilibrium to exist in which agents choose to purchase information even if all agents, including the agents who purchased the information, are made strictly worse off by the purchase.The author would like to thank Kerry Back, Gerry Feltham Rich Kihlstrom, Vasant Naik, Bryan Routledge, Harald Uhlig and Josef Zechner for their comments and suggestions. A special note of thanks is due to the (anonymous) referee.     

Constitutional secession clauses

Taking the view that constitutions are devices whereby people coordinate to specific equilibria in circumstances that allow multiple equilibria, we show that a constitutional secession clause can serve as such a device and, therefore, that such a clause is more than an empty promise or an ineffectual threat. Employing a simple three-person recursive game, we establish that under certain conditions, this game possesses two equilibria—one in which a disadvantaged federal unit secedes and is not punished by the other units in the federation, and a second equilibrium in which this unit does not secede but is punished if it chooses to do so. This research was partially funded by a grant from the United States Institute of Peace at the California Institute of Technology. We wish to thank several anonymous referees who brought to our attention a number of things that we had not previously considered.     

Anonymous monotonic social welfare functions

This paper presents two results about preference domain conditions that deepen our understanding of anonymous and monotonic Arrovian social welfare functions (ASWFs). We characterize the class of anonymous and monotonic ASWFs on domains without Condorcet triples. This extends and generalizes an earlier characterization (as Generalized Majority Rules) by Moulin (Axioms of Cooperative Decision Making, Cambridge University Press, New York, 1988) for single-peaked domains. We also describe a domain where anonymous and monotonic ASWFs exist only when there are an odd number of agents. This is a counter-example to a claim by Muller (Int. Econ. Rev. 23 (1982) 609), who asserted that the existence of 3-person anonymous and monotonic ASWFs guaranteed the existence of n-person anonymous and monotonic ASWFs for any n>3. Both results build upon the integer programming approach to the study of ASWFs introduced in Sethuraman et al. (Math. Oper. Res. 28 (2003) 309).     

Coalitional instability of the distributive Lindahl equilibrium

Summary Bergstrom [3] has showed that the Lindahlian approach to the analysis of public goods may also be used to analyze a model of wide-spread externalities in which agents have preferences defined on allocations rather than on individual commodity bundles. He has provided versions of the first and second welfare theorem for adistributive Lindahl equilibrium and also presented sufficient conditions for its existence. However, we shall show that, in contrast to Foley's [4] result on the core stability of a Lindahl equilibrium, a distributive Lindahl equilibrium need not satisfy coalitional stability. We will provide a robust example in which the unique, distributive Lindahl equilibrium does not belong to the -core defined either as in Scarf [11] or as in Yannelis [12].I would like to thank F. Canova, R. Serrano, M. Spagat, R. Vohra at Brown University, P. C. Padoan at University of Rome and an anonymous referee for their comments. I am also grateful to the participants at the Third Annual MeetingColloquia on Economic Research at I.G.I.E.R. in Milan, Italy, and to the participants at the Citibank Workshop in Economic Theory at Brown University.     

MARKET PRICE MECHANISMS AND STACKELBERG GENERAL EQUILIBRIA: AN EXAMPLE

This paper considers Stackelberg competition in a general equilibrium framework with a productive sector. The working of market power and the configurations of strategic interactions are complexified by the presence of a leader. Two market price mechanisms are studied: one is associated with the Stackelberg–Walras equilibrium and the other is linked to the Stackelberg–Cournot equilibrium. Throughout the example of a two commodity economy, several results are obtained about equilibria mergings and about welfare comparisons.     

Strongly robust equilibrium and competing-mechanism games

This paper formulates the notion of a strongly robust equilibrium relative to a set of mechanisms specified in any competing-mechanism game of complete information with multiple principals and multiple agents. It shows that when agents’ efforts are contractible, any strongly robust pure-strategy equilibrium relative to single-incentive contracts persists, regardless of the continuation equilibrium that agents play upon any principal's deviation to any complex mechanism.     

Endogenous business networks

Business networks are a feature of the organizational landscapeof many countries, though they vary in magnitude. This articledevelops a theory of business networks where they are endogenousto the reliability of the legal system. Networks are a substitutefor reliable institutional support that guarantees written contracts.The existence of networks exerts a negative effect on the functioningof the anonymous market. This is because the network absorbshonest individuals, raising the density of dishonest individualsengaged in anonymous market exchange. Since this lowers thepayoff from market exchange, larger networks may be easier toenforce. We find that networks are economically inefficientunless they are relatively large. This is consistent with theview that informal contract enforcement institutions may beinefficient in general equilibrium even though they enhanceefficiency in partial equilibrium.     

Collective choice under dichotomous preferences

Agents partition deterministic outcomes into good or bad. A mechanism selects a lottery over outcomes (time-shares). The probability of a good outcome is the canonical utility. The utilitarian mechanism averages over outcomes with largest “approval”. It is efficient, strategyproof, anonymous and neutral.We reach an impossibility if, in addition, each agent's utility is at least , where n is the number of agents; or is at least the fraction of good to feasible outcomes. We conjecture that no ex ante efficient and strategyproof mechanism guarantees a strictly positive utility to all agents, and prove a weaker statement.     

Strategic saving decisions in the infinite-horizon model

We study a mechanism that prevents the long-run distribution of wealth from becoming degenerate in the Ramsey–Cass–Koopmans model when households have different time-preference rates. This mechanism is based on the observation that price-taking behavior is no longer justified when all wealth is owned by a single household. Formalizing this observation, we obtain a model with a unique stationary equilibrium in which, depending on the parameter constellation, any number of households can own positive stocks of capital. We characterize this equilibrium and show for example that an increase in the dispersion of the time-preference rates across households unambiguously increases aggregate output. Whereas the main results are derived for a rather general class of production functions, we devote a separate section to the special case of the Cobb–Douglas technology for which the equilibrium conditions are particularly simple. The research reported in this paper forms part of the project “Economic Growth with Strategic Saving Decisions” supported by the Austrian Science Fund (FWF) under project number P17886. Comments from Robert Becker, Edward Green, Takashi Kamihigashi, David Levine, Fabrizio Zilibotti, anonymous referees, and participants at various conferences and seminars are gratefully acknowledged.     

Sorting versus screening: Search frictions and competing mechanisms

In a market where sellers compete by posting trading mechanisms, we allow for a general search technology and show that its features crucially affect the equilibrium mechanism. Price posting prevails when meetings are rival, i.e., when a meeting by one buyer reduces another buyer's meeting probability. Under price posting buyers reveal their type by sorting ex-ante. Only if the meeting technology is sufficiently non-rival, price posting is not an equilibrium. Multiple buyer types then visit the same sellers who screen ex-post through auctions.     

On the theory of effective demand under stochastic rationing

The concept of effective demand under stochastic manipulable quantity rationing is shown to be compatible with the existence of nontrivial equilibrium. It is argued that stochastic rationing is unavoidable for any satisfactory definition of effective demand. Moreover, manipulability of the rationing mechanism is necessary for reasons of logical consistency, at least if the distribution over realisations for each agent depends on his own action and on the aggregate values of demand and supply only. In that case, anonymous stochastic rationing schemes reduce to those random functions, the mean value function of which is the uniform proportional rationing mechanism.     

An efficient solution to the informed principal problem

In this paper I study mechanism design by an informed principal. I show that generically this problem has an ex-post efficient solution. In the equilibrium mechanism, the informed principal appropriates all expected social surplus, with each type of her getting all expected social surplus conditional on that type. This outcome is supported as a perfect sequential equilibrium of the informed principal game when the joint probability distribution from which the agents’ types are drawn satisfies two conditions: the well-known condition of Cremer and McLean and Identifiability condition introduced by Kosenok and Severinov [Individually rational, budget-balanced mechanisms and allocation of surplus, J. Econ. Theory (2002), forthcoming]. Conversely, these conditions are necessary for an ex-post efficient outcome to be attainable in an equilibrium of the informed principal game. Under these conditions only our equilibrium outcome constitutes a neutral optimum, i.e. cannot be eliminated by any reasonable concept of blocking [R. Myerson, Mechanism design by an informed principal, Econometrica 51 (1983) 1767-1797]. Identifiability and Cremer-McLean conditions are generic when there are at least three agents, and none of them has more types than the number of type profiles of the other agents.     

A differential game between government and firms: Comments

It is argued here that the Nash equilibrium calculated by Gradus (1989) is not the Nash equilibrium found when applying the definition generally employed in differential game theory. The model presented by Gradus would call for a modified Nash equilibrium concept as outlined in this note.The author is indebted to Jan van Geldrop and an anonymous referee.     

Ordering infinite utility streams

We reconsider the problem of ordering infinite utility streams. As has been established in earlier contributions, if no representability condition is imposed, there exist strongly Paretian and finitely anonymous orderings of intertemporal utility streams. We examine the possibility of adding suitably formulated versions of classical equity conditions. First, we provide a characterization of all ordering extensions of the generalized Lorenz criterion as the only strongly Paretian and finitely anonymous rankings satisfying the strict transfer principle. Second, we offer a characterization of an infinite-horizon extension of leximin obtained by adding an equity-preference axiom to strong Pareto and finite anonymity.     

The taxation of trades in assets

When the asset market is incomplete, there typically exist taxes on trades in assets that are Pareto improving. This fiscal policy is anonymous, it is fully and correctly anticipated by traders, and it results in ex post Pareto optimal allocations; as such, it improves over previously proposed constrained interventions.     

SUNSPOT EQUILIBRIA IN A PRODUCTION ECONOMY: DO RATIONAL ANIMAL SPIRITS CAUSE OVERPRODUCTION?*

We study a standard two‐period economy with one nominal bond and one firm. The firm finances the input with the nominal bond in the first period and its profits are distributed to the shareholders in the second period. We show that in the neighbourhood of each efficient equilibrium, a sunspot equilibrium also exists. It is shown that the equilibrium interest rate is lower than the efficient level and that there is overproduction in the sunspot equilibrium, under some conditions. However, there is no sunspot equilibrium if the profit share of the firm can be traded as well as the bond.