Existence and stability of overconsumption equilibria

Growth models with endogenous mortality assume generally that life expectancy is increasing with output per capita and, thus, with individual consumption, whatever its level is. However, empirical evidence supports a U-shaped relationship between consumption and mortality, implying that the monotonicity of that relation is local but not global. This paper develops a two-period OLG model where life expectancy is a non-monotone function of consumption, and where agents form myopic anticipations about life expectancy. The existence, uniqueness and stability of steady-state equilibria are studied. It is shown that overconsumption equilibria — i.e. equilibria at which consumption exceeds the level maximizing life expectancy — exist in highly productive economies with a low impatience. We identify also conditions under which there exist long-run cycles in output and longevity around overconsumption equilibria.     

Rich language and refinements of cheap-talk equilibria

I formalize the notion of equilibrium language, define the relation of having a richer language, and show the existence of equilibria with maximally rich language. I also study the stability of equilibria with respect to inflows of messages that can enrich their language, and provide examples of implausible cheap-talk equilibria, not refined away by the existing refinements, which can be refined away on the grounds of stability properties.     

Multiple equilibria in dynamic rational expectations models: A critical review

Multiple equilibria are a ubiquitous feature of dynamic rational expectations models. Researchers have been divided on the implications of this phenomenon. Some have viewed this as a reflection of reality and a possible explanation of a wide range of economic phenomena. Others have suggested various selection criteria for choosing one among the many equilibria. This paper reviews the major selection criteria that have been proposed, and through application to three well-known models shows under what circumstances one might expect them to choose the same or different equilibria. In addition, this paper proposes a new criteria based on the limit of finite-horizon equilibria and investigates its relation to the other criteria.     

A Note on Best Response Dynamics

We investigate the relationship between the continuous time best response dynamic, its perturbed version, and evolutionary dynamics in relation to mixed strategy equilibria. We find that as the level of noise approaches zero, the perturbed best response dynamic has the same qualitative properties as a broad class of evolutionary dynamics. That is, stability properties of equilibria are robust across learning dynamics of quite different origins and motivations. Journal of Economic Literature Classification Numbers: C72, D83.     

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.     

Competitive screening in insurance markets with endogenous wealth heterogeneity

We examine equilibria in competitive insurance markets with adverse selection when wealth differences arise endogenously from unobservable savings or labor supply decisions. The endogeneity of wealth implies that high-risk individuals may ceteris paribus exhibit the lower marginal willingness to pay for insurance than low risks, a phenomenon that we refer to as irregular-crossing preferences. In our model, both risk and patience (or productivity) are privately observable. In contrast to the models in the existing literature, where wealth heterogeneity is exogenously assumed, equilibria in our model no longer exhibit a monotone relation between risk and coverage. Individuals who purchase larger coverage are no longer higher risks, a phenomenon frequently observed in empirical studies.     

Indeterminacy with environmental and labor dynamics

We study the joint dynamics of labor reallocation and environmental change when workers have rational expectations and incur migration costs. We emphasize the relation between parameter values and the area of state space in which indeterminacy of equilibria can occur. Unlike the one-dimensional model in which the wage differential adjusts instantaneously, here the measure of the region of indeterminacy is not monotonic in the cost of adjustment.     

More strategies, more Nash equilibria

We show in this paper that for the class of two-player games with compact real intervals as strategy spaces and continuous and strictly quasi-concave payoff functions there exists a monotone relation between the size of strategy spaces and the number of Nash equilibria. These sufficient conditions for our theorem to hold are shown to be tight.     

Sunspot equilibria and the transfer paradox

Summary. We show that for international economies with two countries, in which agents have additively separable utility functions, the existence of sunspot equilibria is equivalent to the occurrence of the transfer paradox. This equivalence enables us to provide some new insights on the relation of the existence of sunspot equilibria and the multiplicity of spot market equilibria.Received: 1 October 2003, Revised: 1 April 2004, JEL Classification Numbers: C62, D52, F3, F20, 012.Correspondence to: Thorsten HensWe would like to thank Anke Gerber for carefully checking and improving our arguments. Moreover, we are grateful to Piero Gottardi for his encouragement and his comments, to Andreu Mas-Colell and Mike Jerison for very fruitful discussions and to Klaus Schenk-Hoppé for his support in using . All remaining errors are ours.     

Consistent planning under quasi-geometric discounting

We study properties of stationary Markov-perfect equilibria in a general model of intertemporal choice under quasi-geometric discounting. The dynamics generated by stationary Markov-perfect equilibria can be very complicated, even if the model satisfies strict convexity and smoothness properties and the decision maker is arbitrarily patient. If there exist multiple stationary Markov-perfect equilibria, then it is in general possible to construct infinitely many non-degenerate stationary sunspot equilibria as well.     

On ‘Informationally Robust Equilibria’ for Bimatrix Games

Informationally robust equilibria (IRE) are introduced in Robson (Games Econ Behav 7: 233–245, 1994) as a refinement of Nash equilibria for strategic games. Such equilibria are limits of a sequence of (subgame perfect) Nash equilibria in perturbed games where with small probability information about the strategic behavior is revealed to other players (information leakage). Focusing on bimatrix games, we consider a type of informationally robust equilibria and derive a number of properties they form a non-empty and closed subset of the Nash equilibria. Moreover, IRE is a strict concept in the sense that the IRE are independent of the exact sequence of probabilities with which information is leaked. The set of IRE, like the set of Nash equilibria, is the finite union of polytopes. In potential games, there is an IRE in pure strategies. In zero-sum games, the set of IRE has a product structure and its elements can be computed efficiently by using linear programming. We also discuss extensions to games with infinite strategy spaces and more than two players. The authors would like to thank Marieke Quant for her helpful comments.     

A theory of stopping time games with applications to product innovations and asset sales

Summary In this paper, the pure strategy subgame perfect equilibria of a general class of stopping time games are studied. It is shown that there always exists a natural class of Markov Perfect Equilibria, called stopping equilibria. Such equilibria can be computed as a solution of a single agent stopping time problem, rather than of a fixed point problem. A complete characterization of stopping equilibria is presented. Conditions are given under which the outcomes of such equilibria span the set of all possible outcomes from perfect equilibria. Two economic applications of the theory, product innovations and the timing of asset sales, are discussed.Parts of this paper were presented at seminars at Chicago, Rochester and Rutgers and we acknowledge helpful comments. We are also indebted to a referee for his detailed and thoughtful comments. The usual disclaimer applies.     

Verifying gross substitutability

Summary. In labor market models as well as in exchange economies with indivisible goods gross substitutability is used as a property to guarantee the existence of competitive equilibria. This paper develops an easy way to check gross substitutability for utility functions concerning a finite set of indivisible goods (or employees) and money. Concavity is one of the conditions that has to be satisfied. Only one other, but similar, type of relation must be checked to guarantee gross substitutability. Received: 21 August 2000; revised version: 28 November 2001     

The computation of quantity-constrained equilibria by virtual taxes

A method to compute Drèze equilibria is derived by defining virtual-tax equilibria, giving a constructional proof of the existence of such equilibria and showing the equivalence with Drèze equilibria. Some numerical examples conclude the paper.     

Dynamics of International Debt Overhang with Two Lender Banks

This paper presents a dynamic formalization of the behaviour of creditor banks on the secondary market for debts. I formulate the problem as an infinite-horizon game with two banks as players where each bank decides in every period either to sell its loan exposure to the debtor country at the present secondary market price, or to wait and keep its exposure to the next period. There exist three types of subgame-perfect equilibria with the property called the time continuation. I consider the relation ship between our equilibria and those of the Kaneko–Prokop (1993) one-period approach to the same problem and show that their approach does not lose much of the dynamic nature of the problem. In any equilibrium of the game, each bank waits in every period with high probability. I discuss the implications of these results for the long-run behaviour of banks on the secondary market and the resolution of debt overhang
JEL Classification Number: F34     

Rationalizable expectations and sunspot equilibria in an overlapping-generations economy

There are two theories for the treatment of market uncertainty: rationalizable expectations and sunspot equilibria. This paper shows how the game-theoretic solution concept of rationalizable expectations can be applied to an overlapping-generations exchange economy. Some general properties of these equilibria are discussed. It is shown that rationalizable-expectations equilibria are the predictions yielded by considering sunspot equilibria in which probability beliefs may differ across individuals. This result allows for a new interpretation of sunspot equilibria and helps to understand their relevance.     

The dynamics of capital accumulation in an overlapping generations model

This paper studies capital accumulation in a slightly altered, explicit OLG model. The fundamental difference with the standard model lies in the initial conditions. If a portion of the initial allocation of the capital stock is not assigned to retirees, the framework allowing for a genuine accumulation of capital is provided. Dynamic aspects of the resulting model are analyzed, including dynamics of the quotas of capital stock, shares of total output, partial influences of parameters, the connection between the depreciation rate and capital's contribution to production, and the relation of the latter to saddle-node bifurcations and the existence of real-valued equilibria. It is demonstrated that the model is able to describe the initial phase of accumulation.     

Quasi-fundamental exchange rate variation

Summary. This paper uses a general equilibrium model to study the determination of the exchange rate in an economy with fundamental uncertainty. The model has steady state equilibria in which the exchange rate is constant. These equilibria may coexist with “quasi-fundamental” equilibria – nonstationary equilibria in which the exchange rate displays stochastic fluctuations that are correlated with the fluctuations in fundamental random variables. The quasi-fundamental equilibria are Pareto dominated by the corresponding constant-exchange-rate steady states. They also converge to these steady states, inevitably or with positive probability. Received: October 2, 1999; revised version: March 26, 2002 RID="*" ID="*" This paper began as a joint project with Alex Mourmouras, who has made many helpful comments and suggestions but is not responsible for any errors or deficiencies. In addition, I thank an anonymous referee for helpful comments.     

Walrasian equilibria as limits of noncooperative equilibria. Part II: Pure strategies

We examine the connection between Walrasian equilibria of a limit economy (with infinitesimal firms) and noncooperative (Cournot) equilibria of approximating finite economies (with significant firms). Nonconvex production sets, decreasing returns in the aggregate, and endogenous determination of the number of active firms are allowed. A Walrasian equilibrium is a limit of pure strategy noncooperative equilibria only if a condition (loosely analogous to downward sloping demand in the partial equilibrium constant returns to scale case) holds. The condition is also sufficient to guarantee the existence of a robust sequence of pure strategy noncooperative equilibria which converges to the Walrasian equilibrium.     

Search, Money, and Prices

It is well known that models in which money is used as a medium of exchange to lubricate trading, frictions display multiplicity of equilibria. I show that the amount of activity varies as the value of money differs across these equilibria when production opportunities involve random fixed costs. When money has high value, trade is more profitable; therefore, there will be more agents engaged in trade relative to equilibria in which money has lower value. The higher-activity equilibria display higher production not only because more is produced and exchanged per transaction but also because more transactions occur per period. This Diamond-style result is obtained without increasing returns in the matching technology.