Equilibrium theory with asymmetric information and with infinitely many commodities

The traditional deterministic general equilibrium theory with infinitely many commodities cannot cover economies with private information constraints on the consumption sets. We bring the level of asymmetric information equilibrium theory at par with that of the deterministic one. In particular, we establish results on equilibrium existence for exchange economies with asymmetric (differential) information and with an infinite dimensional commodity space. Our new equilibrium existence theorems include, as a special case, classical results, e.g. Bewley [Existence of equilibria in economies with infinitely many commodities, J. Econ. Theory 4 (1972) 514-540] or Mas-Colell [The price equilibrium existence problem in topological vector lattices, Econometrica 54 (1986) 1039-1053].     

The Debreu private ownership economy with complementary commodities and prices

Let E_p be a Debreu private ownership economy in which there are some complementary commodities. It means that all commodity bundles are contained in the proper subspace V   of commodity–space [R]l(l∈{1,2,…})${\mathfrak{[R]}}^l\left(l\in \left\{1,2,\dots \right\}\right)$. The production plans maximizing the producers' profits do not have to satisfy the dependency in the qualities of commodities seen in the consumers' plans. It may cause no-existence an equilibrium in economy E_p. The competitive leads, however, to adjustment the production plans to improve the consumers' satisfaction. The procedure of change the production system covering the consumers' requirements is presented. As a result, the model of the private ownership economy with complementary commodities and prices, being the simplification of the initial model, is elaborated. Consequently, the necessary condition for the existence of an equilibrium in the economy E_p is proved.     

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.     

Efficiency and consistency for locating multiple public facilities

In the problem of locating multiple public facilities studied by Barberà and Beviá [Self-selection consistent functions, J. Econ. Theory 105 (2002) 263-277; Locating public facilities by majority: stability, consistency and group formation, Games Econ. Behav. 56 (2006) 185-200], we offer simple necessary and sufficient conditions for efficiency, decentralizability of efficient decisions in a game of community division and local public goods provision, and a constructive algorithm for efficient and consistent decisions.     

Iterated potential and robustness of equilibria

For any given set-valued solution concept, it is possible to consider iterative elimination of actions outside the solution set. This paper applies such a procedure to define the concept of iterated monotone potential maximizer (iterated MP-maximizer). It is shown that under some monotonicity conditions, an iterated MP-maximizer is robust to incomplete information [A. Kajii, S. Morris, The robustness of equilibria to incomplete information, Econometrica 65 (1997) 1283-1309] and absorbing and globally accessible under perfect foresight dynamics for a small friction [A. Matsui, K. Matsuyama, An approach to equilibrium selection, J. Econ. Theory 65 (1995) 415-434]. Several simple sufficient conditions under which a game has an iterated MP-maximizer are also provided.     

Decentralizing lottery allocations in markets with indivisible commodities

Summary In economies with indivisible commodities, consumers tend to prefer lotteries in commodities. A potential mechanism for satisying these preferences is unrestricted purchasing and selling of lotteries in decentralized markets, as suggested in Prescott and Townsend [Int. Econ. Rev.25, 1–20]. However, this paper shows in several examples that such lottery equilibria do not always exist for economies with finitely many consumers. Other conditions are needed. In the examples, equilibrium and the associated welfare gains are realized if consumptions are bounded or if lotteries are based upon a common sunspot device as defined by Shell [mimeo, 1977] and Cass and Shell [J. Pol. Econ.91, 193–227]. The paper shows that any lottery equilibrium is either a Walrasian equilibrium or a sunspot equilibrium, but there are Walrasian and sunspot equilibria that are not lottery equilibria.This paper is based on Chapter 3 of my doctoral dissertation, written while I was a student at Cornell University. I thank Larry Blume, Yue Yun Chen, David Easley, Aditya Goenka, John Marshall, Bruce Smith, John Wooders and an anonymous referee. I am particularly grateful to Karl Shell and Cheng-Zhong Qin. I thank the Academic Senate at UCSB for financial support.     

Sustainable reputations with rating systems

In a product choice game played between a long lived seller and an infinite sequence of buyers, we assume that buyers cannot observe past signals. To facilitate the analysis of applications such as online auctions (e.g. eBay), online shopping search engines (e.g. BizRate.com) and consumer reports, we assume that a central mechanism observes all past signals, and makes public announcements every period. The set of announcements and the mapping from observed signals to the set of announcements is called a rating system. We show that, absent reputation effects, information censoring cannot improve attainable payoffs. However, if there is an initial probability that the seller is a commitment type that plays a particular strategy every period, then there exists a finite rating system and an equilibrium of the resulting game such that, the expected present discounted payoff of the seller is almost his Stackelberg payoff after every history. This is in contrast to Cripps, Mailath and Samuelson (2004) [5], where it is shown that reputation effects do not last forever in such games if buyers can observe all past signals. We also construct finite rating systems that increase payoffs of almost all buyers, while decreasing the seller?s payoff.     

On two competing mechanisms for priority-based allocation problems

We consider the priority-based allocation problem: there is a set of indivisible objects with multiple supplies (e.g., schools with seats) and a set of agents (e.g., students) with priorities over objects (e.g., proximity of residence area). We study two well-known and competing mechanisms. The agent-optimal stable mechanism (AOSM) allots objects via the deferred acceptance algorithm. The top trading cycles mechanism (TTCM) allots objects via Gale's top trading cycles algorithm. We show that the two mechanisms are equivalent, or TTCM is fair (i.e., respects agents’ priorities), or resource monotonic, or population monotonic, if and only if the priority structure is acyclic. Furthermore, if AOSM fails to be efficient (consistent) for a problem, TTCM also fails to be fair (consistent) for it. However, the converse is not necessarily true.     

A unified treatment of finite and infinite economies: limited arbitrage is necessary and sufficient for the existence of equilibrium and the core

Summary. A single condition, limited arbitrage, is shown to be necessary and sufficient for the existence of a competitive equilibrium and the core in economies with any number of markets, finite or infinite, with or without short sales. This extends earlier results of Chichilnisky [8] for finite economies. This unification of finite and infinite economies is achieved by proving that in Hilbert spaces limited arbitrage is necessary and sufficient for the compactness of the Pareto frontier. Limited arbitrage has also been shown to be necessary and sufficient for a resolution of the social choice paradox [9], [10], [12], [13], [14]. Received: August 4, 1995; revised version: April 11, 1997     

An empirical comparison of implied tree models for KOSPI 200 index options

This paper compares implied tree models for KOSPI 200 index options with regards to the pricing and hedging performance. With Cox, Ross, and Rubinstein's [Cox, J., Ross, S., & Rubinsteinm, M., 1979. Option pricing: A simplified approach. Journal of Financial Economics, 7, 229–263] standard binomial tree (SBT) model as a benchmark, we analyzed three models: Rubinstein's [Rubinstein, M., 1994. Implied binomial trees. Journal of Finance, 49, 771–818] implied binomial tree (IBT), Jackwerth's [Jackwerth, J. C., 1997. Generalized binomial trees. Journal of Derivatives, 5, 7–17] generalized binomial tree (GBT), and Derman and Kani's [Derman, E., & Kani, I., 1994. Riding on a smile. Risk, 7, 32–39] implied volatility tree (IVT) models. The SBT model, the simplest, shows the best performance. Moreover, the delta-hedged strategy in all of the binomial models generates, on average, negative gains. This finding, consistent with the findings by Bakshi and Kapadia [Bakshi, G., & Kapadia, N., 2003. Delta-hedged gains and the negative market volatility risk premium. Review of Financial Studies, 16, 527–566], indicates the existence of a negative market volatility risk premium.     

Sealed bid auctions with uncertainty averse bidders

Summary. Traditional analysis of auctions assumes that each bidder's beliefs about opponents' valuations are represented by a probability measure. Motivated by experimental findings such as the Ellsberg Paradox, this paper examines the consequences of relaxing this assumption in the first and second price sealed bid auctions with independent private values. The multiple priors model of Gilboa and Schmeidler [Journal of Mathematical Economics, 18 (1989), 141–153] is adopted specifically to represent the bidders' (and the auctioneer's) preferences. The unique equilibrium bidding strategy in the first price auction is derived. Moreover, under an interesting parametric specialization of the model, it is shown that the first price auction Pareto dominates the second price auction. Received: December 15, 1995; revised version: February 19, 1997     

Tiebout equilibria in local public good economies with spillovers

This paper analyzes the effects of spillovers on the equilibrium population distribution across jurisdictions in a local public good economy with free mobility. Spillovers are parametrized by a matrix [α_ij] where α_ij ∈ [0, 1]. When spillovers are symmetric and close to 0 or 1 (pure local public goods and pure public goods), all equilibrium jurisdiction structures are symmetric. However, any population distribution can be sustained in equilibrium for some value of the spillover parameter α. In the class of utility functions with additive externalities, we identify the unique family of utility functions for which equilibria are symmetric except for an isolated value of α. This is a class of utility functions which are linear in the public good and a power function of the private good, u(c, γ) = − A(1 − c)^β + γ. With this specification of utility, we show that an increase in α results in a more fragmented equilibrium population distribution, and that when spillovers are asymmetric and large, a jurisdiction which is more centrally located (i.e. benefits more from the public goods provided in other jurisdictions) has a larger population in equilibrium.     

Rates of information aggregation in common value auctions

We study the rates at which transaction prices aggregate information in common value auctions under the different information structures in Wilson (Rev. Econ. Stud. 44 (1977) 511) and Pesendorfer and Swinkels (Econometrica 65 (1997) 1247). We consider uniform-price auctions in which k identical objects of unknown value are auctioned to n bidders, where both n and k are allowed to diverge to infinity, and k/n converges to a number in [0,1). The Wilson assumptions lead to information aggregation at a rate proportional to , but the price aggregates information at a rate proportional to in the PS setting. We also consider English auctions, and investigate whether the extra information revealed in equilibrium improves convergence rates in these auctions.     

Correlated Nash equilibrium

We modify the epistemic conditions for Nash equilibrium only to accommodate Gilboa and Schmeidler's [I. Gilboa, D. Schmeidler, Maxmin expected utility with nonunique prior, J. Math. Econ. 18 (1989) 141-153] maxmin expected utility preferences, and identify the equilibrium concept in n-player strategic games that characterizes the modified epistemic conditions. The epistemic characterization supports the equilibrium concept as a minimal generalization of Nash equilibrium, in the sense that it deviates from Nash equilibrium only in terms of players' attitude towards ambiguity. Consequently, comparing it with Nash equilibrium constitutes a ceteris paribus study of the effects of ambiguity on how a game is played. For example, with ambiguity, (beliefs about) action choices are in general correlated.     

On efficiency of the English auction

We study efficiency properties of the irrevocable exit English auction in a setting with interdependent values. Maskin (1992) [1] shows that the pairwise single-crossing condition is sufficient for efficiency of the English auction with two bidders and suggests that it is also a necessary condition. This paper clarifies and extends Maskin?s results to the case of N bidders. We introduce the generalized single-crossing condition—a fairly intuitive extension of the pairwise single-crossing condition—and prove that it is essentially a necessary and sufficient condition for the existence of an efficient equilibrium of the N-bidder English auction.     

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.     

Allocation rules for land division

This paper studies the classical land division problem formalized by Steinhaus (Econometrica 16 (1948) 101-104) in a multi-profile context. We propose a notion of an allocation rule for this setting.  We discuss several examples of rules and properties they may satisfy. Central among these properties is division independence: a parcel may be partitioned into smaller parcels, these smaller parcels allocated according to the rule, leaving a recommended allocation for the original parcel. In conjunction with two other normative properties, division independence is shown to imply the principle of utilitarianism.     

Too much of a good thing? Why altruism can harm the environment?

Success of eco-labeling schemes, broadly defined, varies among products and across countries. Based on a simple theoretical framework, we show that the nature of environmental attributes among products (i.e., private versus public) and the consumer type (i.e., egoist versus altruist) shape the overall performance of such schemes. In addition, we demonstrate that altruistic consumers exhibiting a too high willingness to pay for the eco-labeled product can inadvertently prevent egoistic consumers from purchasing it, leading to a sub-optimal outcome in terms of environmental performance. Several policy and managerial implications are drawn.     

Coalitions, agreements and efficiency

If agents negotiate openly and form coalitions, can they reach efficient agreements? We address this issue within a class of coalition formation games with externalities where agents’ preferences depend solely on the coalition structure they are associated with. We derive Ray and Vohra's [Equilibrium binding agreements, J. Econ. Theory 73 (1997) 30-78] notion of equilibrium binding agreements using von Neumann and Morgenstern [Theory of Games and Economic Behavior, Princeton University Press, Princeton, 1944] abstract stable set and then extend it to allow for arbitrary coalitional deviations (as opposed to nested deviations assumed originally). We show that, while the extended notion facilitates the attainment of efficient agreements, inefficient agreements can nevertheless arise, even if utility transfers are possible.     

Insider trading with public and shared information

We study the impact of public information and shared information on traders' trading behavior in the context of Kyle's (1985) speculative market. We suppose that there are four types of traders in our model: one insider, M outsiders, liquidity traders, and market makers. We explicitly describe the unique linear Nash equilibrium and find that public information harms the insider but benefits the outsiders and noise traders. Also, the market is more efficient because of the existence of public information.