Overlapping expectations and Hart's conditions for equilibrium in a securities model

Hart (J. Econ. Theory9 (1974), 293–311) gave conditions for equilibrium to exist in a securities model where each agent undertakes asset transactions to maximize expected utility of wealth. These conditions rule out agents wanting to undertake unbounded balanced transactions to reach a Pareto superior allocation given their expectations. With mild extra assumptions to make agents unwilling to risk incurring unbounded losses on their portfolios, Hart's conditions become equivalent to an assumption of “overlapping expectations,” which is comparable to a much weaker form of Green's “common expectations” (Econometrica41 (1973), 1103–1124).     

Markov rational expectations equilibria in an overlapping generations model

In this paper, we analyze rational expectations equilibrium paths in a stochastic overlapping generations model. The work presented here builds on results of S. E. Spear (J. Econ. Theory 35 (1985), 251–275), where is is shown that in a model with multiple goods and time non-separable preferences, a stochastic steady state equilibrium will generically fail to exist. A stochastic steady state is defined as an equilibrium in which the stochastic process of endogenously determined variables is measure isomorphic to the exogenous process driving the model. In this paper, we establish the existence of non-steady state equilibria and provide a characterization of their stochastic properties.     

Experts against adverse selection: A note on the existence of equilibrium with costly appropriable information

The existence of competitive equilibrium in Laffont's (J. Econ. Theory10 (1975)) model of adverse selection with costly information is studied. The existence of an equilibrium with finite prices is demonstrated without unusual restrictions on preferences or the technology of information production. This is made possible by changing the way in which the behaviour of information producing agents is modelled, and allowing for some public information.     

A Unifying Pair of Cournot-Nash Equilibrium Existence Results

For games with a measure space of players a tandem pair, consisting of a mixed and a pure Cournot-Nash equilibrium existence result, is presented. Their generality causes them to be completely mutually equivalent. This provides a unifying pair of Cournot-Nash existence results that goes considerably beyond the central result of E. J. Balder (1995, Int. J. Game Theory24, 79-94, Theorem 2.1). The versatility of this pair is demonstrated by the following new applications: (i) unification and generalization of the two equilibrium distribution existence results by K. P. Rath (1996, J. Math. Econ.26, 305-324) for anonymous games, (ii) generalization of the equilibrium existence result of T. Kim and N. C. Yannelis (1997, J. Econ. Theory77, 330-353) for Bayesian differential information games, (iii) inclusion of the Bayesian Nash equilibrium existence results of P. R. Milgrom and R. J. Weber (1985, Math. Oper. Res.10, 619-632) and E. J. Balder (1988, Math. Operations Res.13, 265-276) for games with private information in the sense of J. C. Harsanyi (1967, Manage. Sci.14, 159-182). Journal of Economic Literature Classification Number: C72.     

On the existence of equilibria in economies with infinitely many commodities and without ordered preferences

The present paper deals with the existence of equilibria in economies whose commodity space is L_∞(M, M, μ) and where the agents' preferences need not be complete or transitive. Applying a fixed point theorem of Browder, an equilibrium existence theorem for abstract economies (generalized qualitative games) is proven where each agent's choice set is contained in an arbitrary topological vector space. With the help of this theorem the existence of Walrasian general equilibrium for a suitably specified economic model is obtained. The final result is a generalization of T. F. Bewley's (J. Econ. Theory4 (1972), 514–540) equilibrium existence theorem to the case of non-ordered preferences.     

Stationary cardinal utility and optimal growth under uncertainty

In the literature on multiperiod planning under uncertainty, it is generally postulated that preferences may be represented by a von Neumann-Morgenstern utility index that is additive over time. This paper accomplishes two objectives: First, an axiomatic basis is provided for a more general class of non-additive utility indices defined over infinite consumption streams. Second, this class of utility functions is applied to extend existing results (J. Econ. Theory4 (1972), 479–513; J. Econ. Theory11 (1975), 329–339) on the nature of optimal growth under uncertainty. Of particular interest are the existence and stability of a stochastic steady state.     

Optimal Growth Models with Bounded or Unbounded Returns: A Unifying Approach

In this paper we propose a unifying approach to the study of optimal growth models with bounded or unbounded returns (above-below). Following our approach, we prove the existence of optimal solutions and show, without using the contraction method, that the value function is the unique solution to the Bellman equation for a particular class of functions. The value function can be obtained by the usual algorithm defined by the operator provided by the Bellman equation. Moreover, following our approach we obtain the recent results of F. Alvarez and N. Stokey (1998, J. Econ. Theory82, 167-189) as well as the well-known results. Journal of Economic Literature Classification numbers: C61, 041.     

On the generic nonexistence of pure strategy nash equilibria in continuous games

S. Srivastava (J. Econ. Theory 36 (1985), 26–35) states that in the space of continuous games an open and dense subset does not have a pure strategy. Nash equilibrium. The purpose of this note is twofold: first, to show that without a connectedness assumption on the strategy sets of the players this statement is false; second, to provide correct proofs of his main results.     

How Communication Improves Efficiency in Bargaining Games

We study a double auction with two-sided private information and preplay communication, for which Myerson and Satterthwaite (1983, J. Econ. Theory28, 265–281) showed that all equilibria are inefficient and the Chatterjee–Samuleson linear equilibrium is most efficient. Like several others, we find that players use communication to surpass equilibrium levels of efficiency, especially when the communication is face-to-face. Our main contribution is an analysis of how communication helps the parties achieve such high levels of efficiency. We find that when preplay communication is allowed, efficiency above equilibrium levels is a result of what we call “dyadic” strategies that allow the parties to coordinate on a single price that reflects both parties' valuations. Journal of Economic Literature Classification Numbers: C78, D82.     

Coalition-Proof Nash Equilibria II. Applications

In Bernheim, Peleg, and Whinston (“Coalition-Proof Equilibria. I. Concepts,” J. Econ. Theory 42 (1987), 1–12), we proposed the notion of Coalition-Proof Nash equilibrium and Perfectly Coalition-Proof Nash equilibrium as solution concepts for strategic environments in which players can freely discuss their strategies, but cannot make binding commitments. This paper undertakes applications to several economic problems, including the behavior of Cournot oligopolists, oligopolistic entry deterrence, cooperation in finite horizon games, and social choice rule implementation.     

Strategic behavior and competition: An overview

The eleven papers of the Journal of Economic Theory symposium issue, “Strategic Behavior and Competition,” are introduced. This symposium can be thought of as an outgrowth of the earlier symposium, “Noncooperative Approaches to the Theory of Perfect Competition,” which appeared in J. Econ. Theory 22 (1980).     

On Forward Induction and Evolutionary and Strategic Stability

We analyze which normal form solution concepts capture the notion of forward induction, as defined by E. van Damme (1989, J. Econ. Theory48, 476-496) in the class of generic two player normal form games preceded by an outside option. We find that none of the known strategic stability concepts (including Mertens stable sets and hyperstable sets) capture this form of forward induction. On the other hand, we show that the evolutionary concept of EES set (J. Swinkels, 1992, J. Econ. Theory57, 306-332) is always consistent with forward induction. Journal of Economic Literature Classification Number: C72.     

Free access vs private ownership: A comparison

Weitzman (J. Econ. Theory8 (1974), 225–234) has established that under free access properties of average or better quality will be overutilised relative to the efficient private property equilibrium. This leaves open the question of what happens to the low quality properties. It is shown here that there are conflicting considerations and the outcome is ambigous. Necessary and sufficient conditions are obtained for less of a variable input to be attracted to a site when access is free than when a private owner makes a charge for access.     

A characterisation of the perfect equilibria of infinite horizon games

This paper builds on the work of Fudenberg and Levine (J. Econ. Theory31 (1983), 251–268). It shows that the perfect equilibria of any game in which events become uniformly unimportant as their distance into the future increases can be characterised as limits of sequences of perfect approximate equilibrium points of finite horizon approximations to the game. The result holds both for a strong and for a weak topology. The topologies are tractable, and the nature of convergence relative to them is transparent. Finally, the weak topology is probably the weakest tractable topology in which the result holds.     

On the informational efficiency of the competitive resource allocation process

The purpose of this paper is to formalize the competitive process as a parametric process, and then prove the minimality of its message space among the message spaces for a broad class of parametric processes that includes the class of processes considered by Hurwicz (in “Studies in Resource Allocation Processes” (K. J. Arrow and L. Hurwicz, Eds.), pp. 413–423, Cambridge Univ. Press, Cambridge, 1977), Mount and Reiter (J. Econ. Theory6 (1974), 161–192), and Osana (J. Econ. Theory17 (1978), 66–78). The proof of this result turns crucially on the “asymmetry property” (which is stronger than the well-known “uniqueness property” of Hurwicz) and on an injectiveness lemma which is applicable to parametric processes.     

Starting Small and Commitment

I study a model of a long-term partnership with two-sided incomplete information. The partners jointly determine the stakes of their relationship and individually decide whether to cooperate with or betray each other over time. I characterize the extremal—interim incentive efficient—equilibria. In these equilibria, the partners generally “start small,” and the level of interaction grows over time. The types of players separate quickly. Further, cooperation between “good” types is viable regardless of how pessimistic the players are about each other initially. The quick nature of separation in an extremal equilibrium contrasts with the outcome selected by a strong renegotiation criterion (as studied in Watson (1999, J. Econ. Theory85, 52–90). Journal of Economic Literature Classification Numbers: C72, C73, D74.     

Capital as a commitment: Strategic investment to deter mobility

This paper analyzes how an early entrant in a market can exploit its head start by strategic investment. The analysis is based on Spence's paper, Investment strategy and growth in a new market, (Bell J. Econ., 10 (1979), 1–19). We frist study the investment game in the no-discounting case, which embodies the key features of mobility deterrence. We establish the existence of a set of perfect equilibria and suggest that one particular equilibrium is most reasonable. This equilibrium, also valid with discounting, involves the follower firm being forever deterred from investing to its steady-state reaction curve, in contrast to Spence's proposed solution.     

On Fixed-Path Rationing Methods

Moulin (J. Econ. Theory84 (1999), 41-72) characterizes the fixed-path rationing methods by efficiency, strategy-proofness, consistency, and resource-monotonicity. In this note we give a straightforward proof of his result. Journal of Economics Literature Classification Numbers: D63, D70.     

Aggregation and the existence of a social utility function

In a well-known paper Gorman (Econometrica21 (1953)) established that the necessary and sufficient condition for the existence of an aggregate, or social, utility function, independent of the distribution of income, is that all individuals' income consumption paths be parallel straight lines. Recently Chipman (J. Econ. Theory8 (1974)), building on the paper of Hurwicz and Uzawa (in “Preference Utility and Demand”) has shown that if the distribution of income is proportional and individual preferences are homothetic, aggregate consumption behavior obeys the necessary integrability conditions. It is shown here that the consistency of aggregate behavior can be derived from more general conditions than the ones used by Chipman and Gorman. Examples of demand systems from which aggregate behavior implies a social utility function are provided. It is then shown that if individual demand functions are linear in income—a form employed by both Gorman and Chipman—it is not necessary that the distribution of income be fixed.     

Generic 4 × 4 Two Person Games Have at Most 15 Nash Equilibria

The maximal generic number of Nash equilibria for two person games in which the two agents each have four pure strategies is shown to be 15. In contrast to Keiding (1997),Games Econ. Behav.21, 148–160, who arrives at this result by referring to the enumeration of Grünbaum and Sreedharan (1967),J. Combin. Theory2, 437–465, our argument is based on a collection of lemmas that constrain the set of equilibria. Several of these pertain to any common numberdof pure strategies for the two agents.Journal of Economic LiteratureClassification Number: C72.