Nash equilibrium without mutual knowledge of rationality

Summary. In a Nash equilibrium, players' rationality is mutual knowledge. However, both intuition and experimental evidence suggest that players do not know for sure the rationality of opponents. This paper proposes a new equilibrium concept, cautious equilibrium, that generalizes Nash equilibrium in terms of preferences in two person strategic games. In a cautious equilibrium, players do not necessarily know the rationality of opponents, but they view rationality as infinitely more likely than irrationality. For suitable models of preference, cautious equilibrium predicts that a player might take a “cautious” strategy that is not a best response in any Nash equilibrium. Received: January 28, 1998; revised version October 2, 1998     

Nash implementation with a private good

Summary. I construct a general model of social planning problems, including mixed production economies and regulatory problems with negative externalities as special cases, and I give simple mechanisms for Nash implementation under three increasingly general sets of assumptions. I first construct a continuous mechanism to implement the (constrained) Lindahl allocations of an economy, and I then extend this to arbitrary social choice rules based on prices. I end with a mechani sm to implement any monotonic social choice rule, assuming only the existence of a private (not necessarily transferable) good. In that general case, each agent simply reports an upper contour set, an outcome, and I need two agents to make binary numerical announcements. I do not require the usual no-veto-power condition. Received: February 19, 1998; revised version: January 30, 2002     

Economic theory and econometric dynamics in modelling wages and prices in the United Kingdom

We show that a “competing claims” model of imperfect competition can explain the movements of wages and prices in the United Kingdom, using quarterly data covering 1976–93. We argue that careful attention both to economic theory and to the interaction between dynamics and identification is crucial in the building of the model and to dynamic econometric models in general. We use a small numerical example with simulated cointegrated data to illustrate the potential pitfalls. First version received: January 1998/final version received: November 1998     

General equilibrium and resource economics

Summary. For a number of reasons a large class of general equilibrium models from the field of resource economics does not allow for an equilibrium analysis along the lines of the theory of infinite dimensional commodity spaces. The reasons concern the choice of the commodity space and the applicability of properness assumptions with respect to preferences and the technology. This paper illustrates the difficulties and shows for a prototype model how the problems can successfully be tackled by the use of a limit argument on equilibria in the truncated economies. Received: May 2, 1996; revised version: May 13, 1998     

Non-existence of Duopoly Equilibria: A Simple Numerical Example

We give a simple example to the non-existence of duopoly equilibrium in pure strategies in an economy with two goods and two types of consumers. This extends also the discussion on the incentive for trade in an oligopolistic framework initiated in Cordella and Gabszewicz (1998).     

Existence and local indeterminacy of periodic equilibrium paths in infinite horizon models with external effects

Summary. It is expected that every periodic equilibrium path may exist even under standard assumptions such as low discounting and the concavity of utility functions in infinite horizon models with external effects. Nevertheless, until now no such example has been presented. In this note we will first construct a bounded growth model that has an external effect and every periodic equilibrium path under any discount factor. Next we will study the conditions under which periodic equilibrium paths have a local indeterminacy. Received: December 23, 1998; revised version: April 19, 1999     

A note on asymmetric and mixed strategy equilibria in the search-theoretic model of fiat money

Summary. The simple search-theoretic model of fiat money has three symmetric Nash equilibria: all agents accept money with probability 1; all agents accept money with probability 0; and all agents accept money with probability y in (0,1). Here I construct an asymmetric pure strategy equilibrium, payoff-equivalent to the symmetric mixed strategy equilibrium, where a fraction N in (0,1) of agents always accept money and 1-N never accept money. Counter to what has been conjectured previously, I find N > y. I also introduce evolutionary dynamics, and show that the economy converges to monetary exchange iff the initial proportion of agents accepting money exceeds N. Received: September 10, 1997; revised version: April 24, 1998     

Saving behavior in stationary equilibrium with random discounting

Summary. We study the implications of random discount rates of future generations for saving behavior and capital holdings in a steady state competitive equilibrium with heterogeneous population. A well-known difficulty in deterministic economies with heterogeneous households is that in steady state only the most patient households hold capital. In this paper we state conditions under which this random discounting is sufficient for households other than the most patient ones to save. We thus provide a simple and natural way of overcoming the aforementioned difficulty. Received: December 28, 1998; revised version: May 19, 1999     

An experimental study of information and mixed-strategy play in the three-person matching-pennies game

Summary. Recent experiments on mixed-strategy play in experimental games reject the hypothesis that subjects play a mixed strategy even when that strategy is the unique Nash equilibrium prediction. However, in a three-person matching-pennies game played with perfect monitoring and complete payoff information, we cannot reject the hypothesis that subjects play the mixed-strategy Nash equilibrium. Given this support for mixed-strategy play, we then consider two qualitatively different learning theories (sophisticated Bayesian and naive Bayesian) which predict that the amount of information given to subjects will determine whether they can learn to play the predicted mixed strategies. We reject the hypothesis that subjects play the symmetric mixed-strategy Nash equilibrium when they do not have complete payoff information. This finding suggests that players did not use sophisticated Bayesian learning to reach the mixed-strategy Nash equilibrium. Received: August 9, 1996; revised version: October 21, 1998     

Externalities, expectations, and growth

Summary. The paper studies a model of accumulation and growth where a continuum of heterogeneous firms play dynamically optimal strategies along a (rational expectations) equilibrium. The key feature of the model is that firms' technological decisions are assumed subject to both friction and external effects. This gives rise to a wide multiplicity of equilibrium behavior, any path of sustained growth requiring that the economy tackle a never-ending chain of fresh coordination problems. This setup is modelled as a (non-atomic) dynamic game, suitable conditions being provided that partially characterize when sustained growth is a possible (never the unique) equilibrium outcome. Received: May 25, 1995; revised version: March 25, 1998     

Manipulation-proof equilibrium in atomless economies with commodity differentiation

Summary. In this paper, we introduce a perfect competition test which checks the incentives of arbitrarily small coalitions to behave strategically in endowments and preferences. We apply this coalitional incentive compatibility test to atomless economies with a continuum of differentiated commodities. We show that, under thickness conditions, economies with a finite number of types and economies whose set of agents' preferences is compact, pass this perfect competition test. Limiting results for replica economies are also presented. Received: July 25, 1997; revised version: December 5, 1998     

Quantal-response equilibrium models of the ultimatum bargaining game

This paper investigates the implications of quantal response equilibrium (QRE) models [McKelvey and Palfrey, 1995, Games Econ. Behav. 10, 6–38; 1998, Exper. Econ. 1, 9–41] in the ultimatum bargaining game. It is shown that, in a normal-form QRE (NQRE), each bargainer's decision depends critically on the anticipated behavior of the other, and there is a NQRE in which the proposer makes any offer between zero and equal split as a strict best response. The application of NQRE to the experimental data [Slonim and Roth, 1998, Econometrica 66, 569–596] suggests that the history dependence observed in the experiment is a result of the strategic interactions between bargainers.     

A model of intergenerational transfers

Summary. Extending some existing literature, this paper formalizes the idea that intergenerational transfers occur because people care about the “characteristics” (i.e quantity and quality) of their offspring, rather than their children's welfare per se or consumption. The model analyzes this transfer motive in an infinite Markovian game framework, and it proves the existence of a stationary Markov Perfect equilibrium. Further, the analysis shows that under certain conditions, the proposed transfer motive will diminish, as the average income of an economy is sufficiently high. Thus, it suggests that as incomes continue to rise beyond a certain level, the (extended) life-cycle hypothesis will likely be a better and better approximation for explaining most people's saving behavior. This result also provides an explanation for the decline of the saving rates in the U.S. and other developed countries. Received: December 28, 1998; revised version: February 17, 2000     

The Real Equilibrium South African Rand/US Dollar Exchange Rate: A Comparison of Alternative Measures

This article indicates how different measures of the real exchange rate, i.e., the exchange rate adapted for cost inflation, price inflation and labour costs, influence the equilibrium view and misalignment of the South African rand/US dollar exchange rate. The approach followed is based on the behavioural equilibrium exchange rate approach by Clark and MacDonald (1998), where the exchange rate is influenced by a number of fundamental and transitory factors. The real equilibrium exchange is estimated by using a single equation regression and a number of key explanatory variables. To determine the long-run relationship a Vector Error Correction Mechanism is used.     

Long run equilibria in an asymmetric oligopoly

Summary. Consider an oligopolistic industry composed of two groups (or populations) of firms, the low cost firms and the high cost firms. The firms produce a homogeneous good. I study the finite population evolutionarily stable strategy defined by Schaffer (1988), and the long run equilibrium in the stochastic evolutionary dynamics based on imitation and experimentation of strategies by firms in each group. I will show the following results. 1) The finite population evolutionarily stable strategy (ESS) output is equal to the competitive (or Walrasian) output in each group of the firms. 2) Under the assumption that the marginal cost is increasing, the ESS state is the long run equilibrium in the stochastic evolutionary dynamics in the limit as the output grid step, which will be defined in the paper, approaches to zero. Received: September 19, 1997; revised: June 18, 1998     

Moral hazard and general equilibrium in large economies

Summary. The paper analyzes a two period general equilibrium model with individual risk, aggregate uncertainty and moral hazard. There is a large number of households, each facing two individual states of nature in the second period. These states differ solely in the household's vector of initial endowments, which is strictly larger in the first state (good state) than in the second state (bad state). In the first period each household chooses a non-observable action. Higher levels of action give higher probability of the good state of nature to occur, but lower levels of utility. Households' utilities are assumed to be separable in action and the aggregate uncertainty is independent of the individual risk. Insurance is supplied by a collection of firms who behave strategically and maximize expected profits taking into account that each household's optimal choice of action is a function of the offered contract. The paper provides sufficient conditions for the existence of equilibrium and shows that the appropriate versions of both welfare theorems hold. Received: December 7, 1998; revised version: October 25, 1999     

Inequalities and fluctuations in a dynamic general equilibrium model

   Summary. In the present paper a tractable two-sector neo-classical growth model with heterogeneous agents is considered. The local dynamic properties of the equilibrium path are analyzed in relation with the underlying characteristics of the economy. In particular, the existence of fluctuations is related to the degree of heterogeneity in labor and in capital endowments. When applied to international trade theory, the analysis shows that free trade may distabilize a world economy that is originally stable under the regime of autarky. Received: December 28, 1998; revised version: October 29, 1999     

Equilibrium interest rate and liquidity premium with transaction costs

Summary. In this article we study the effects of transaction costs on asset prices. We assume an overlapping generations economy with two riskless assets. The first asset is liquid while the second asset carries proportional transaction costs. We show that agents buy the liquid asset for short-term investment and the illiquid asset for long-term investment. When transaction costs increase, the price of the liquid asset increases. The price of the illiquid asset decreases if the asset is in small supply, but may increase if the supply is large. These results have implications for the effects of transaction taxes and commission deregulation. Received: December 5, 1997; revised version: March 19, 1998     

Assessing policies to equalize opportunity using an equilibrium model of educational and occupational choices

The inter-generational correlation of education in the U.S. is tremendous. For instance, in PSID data from 1990, young males with college-educated parents had a 70% chance of attending college. But those with high school drop-out parents had only a 15% chance. In this paper, we analyze the impact of college attendance bonus schemes designed to increase college attendance rates (and PV of lifetime income) of youth from disadvantaged backgrounds. Of course, policies that increase the supply of skilled labor may reduce the college wage premium (see Heckman et al. [Heckman, James, Lochner, Lance and Taber, Christopher, Explaining rising wage inequality: explorations with a dynamic equilibrium model of labor earnings with heterogeneous agents, Review of Economic Dynamics, 1 (1998a), 1–58; Heckman, James, Lochner, Lance and Taber, Christopher, General-equilibrium treatment effects: a study of tuition policy, American Economic Review, 88:2 (1998b), 381–386]). This may have the unintended consequence of wiping out most of the gains to the targeted groups. The strength of such equilibrium effects on wages depends on the substitutability between different types of labor. Thus, it is important to evaluate education subsidies within an equilibrium framework that allows for flexible patterns of substitution across factor inputs. This is exactly what we do here, using an overlapping generations equilibrium model of the U.S. labor market fit to PSID data from 1968 to 1996. The model allows for imperfect substitution among types of labor differentiated by education, gender, age and ten (1-digit level) occupations — a much finer differentiation than has been considered in prior work.We find that very large college attendance bonuses are necessary to equate college attendance rates between youth whose parents had only high school degrees or were high school dropouts and youth whose parents attended at least some college. The size of these bonuses far exceeds any reasonable measure of college costs; suggesting the “costs” the bonuses overcome are primarily psychic or effort costs. For example, youth from disadvantaged backgrounds may be poorly prepared for college. This suggests that bonuses targeted at college age youth are probably a very inefficient way to reduce inequality. Earlier intervention is likely called for.     

Signaling bargaining power: Strategic delay versus restricted offers

Summary. I study the first-round separating equilibrium of a buyer-seller bargaining game, extended to allow for asymmetric information, strategically delayed offers and offers restricted to a portion of the good. When bargaining is over a consumption good, in equilibrium the “strong” buyer uses a restricted offer if his optimal consumption path is conservative relative to the “weak” buyer. A pure restricted offer may even be a costless, efficient signal. When the good is durable, a pure strategic delay is involved in signaling a strong bargaining position if the discount factor is high. Received: June 24, 1998; revised version: May 30, 1999