Money in the pure consumption loan model

The purpose of this paper is to show how modern techniques of Temporary competitive equilibrium analysis can be applied to models of the “pure consumption loan model” type. One considers Samuelson's simplest model where traders live two periods and where money is the only store of value. It is proved that a temporary equilibrium exists if price expectations are sufficiently independent of current prices. A stationary market equilibrium is shown to exist if there is a set of traders (i) whose total resources are greater when they are young than when they are old, (ii) who are indifferent between present and future consumption. It is proved that this existence theorem still holds if the economy is sufficiently “close” to an economy which has this property. A stationary market equilibrium is shown to be Pareto optimal if all traders hold positive cash balances. It may be inefficient if this condition is not satisfied, for some traders may then be willing to borrow, which they cannot do in this model.     

Liquid markets and competition

A market is liquid if no individual's actions have a big effect on the prices of goods traded in that market. Perfectly competitive markets are therefore perfectly liquid. It is well known that market liquidity can be achieved by increasing the number of traders so that individual trades are small compared to total trades. We show that even when there are only few traders, market liquidity can be achieved through large short sales in which net trades are small relative to gross trades. In particular, for a natural variant of the market game which permits unlimited short sales, we show that there is always a Nash equilibrium allocation arbitrarily close to a competitive equilibrium allocation. Of course, not all NE are near competitive. Only the large-short-sales NE are nearly liquid and hence close to CE.     

Pollution Control in Open Economies: Implications of Within-period Interactions for Dynamic Game Equilibrium

This paper examines a two-country, dynamic game model of pollution control in the presence of economic interactions between countries within a period, as well as the environmental interaction between periods (i.e., a change in the stock of global pollution). These economic interactions emerge because of changes in the terms of trade of polluting goods or the market share of domestic polluting industries. It is shown that if within-period externalities exist, a noncooperative equilibrium may result in a smaller stock of global pollution in the steady state than does international cooperation. Moreover, the properties of equilibrium paths depend on the direction and size of such externalities. In addition, trigger strategy equilibria that achieve the outcome of the collusive solution are examined.     

Collusive behavior in noncooperative epsilon-equilibria of oligopolies with long but finite lives

In a game of a finite number of repetitions of a Cournot-type model of an industry, if firms are satisfied to get close to (but not necessarily achieve) their optimal responses to other firms' sequential strategies, then in the resulting noncooperative “equilibria” of the sequential market game, (1) if the lifetime of the industry is large compared to the number of firms, there are equilibria corresponding to any given duration of the cartel, whereas (2) if the number of firms is large compared to the industry's lifetime, all equilibria will be close (in some sense) to the competitive equilibrium.     

Globally evolutionarily stable portfolio rules

The paper examines a dynamic model of a financial market with endogenous asset prices determined by short-run equilibrium of supply and demand. Assets pay dividends that are partially consumed and partially reinvested. The traders use fixed-mix investment strategies (portfolio rules), distributing their wealth between assets in fixed proportions. Our main goal is to identify globally evolutionarily stable strategies, allowing an investor to “survive,” i.e., to accumulate in the long run a positive share of market wealth, regardless of the initial state of the market. It is shown that there is a unique portfolio rule with this property—an analogue of the famous Kelly rule of “betting your beliefs.” A game theoretic interpretation of this result is given.     

On the existence of a strictly strong Nash equilibrium under the student-optimal deferred acceptance algorithm

This study analyzes a preference revelation game in the student-optimal deferred acceptance algorithm in a college admission problem. We assume that each college's true preferences are known publicly, and analyze the strategic behavior of students. We demonstrate the existence of a strictly strong Nash equilibrium in the preference revelation game through a simple algorithm that finds it. Specifically, (i) the equilibrium outcome from our algorithm is the same matching as in the efficiency-adjusted deferred acceptance algorithm and (ii) in a one-to-one matching market, it coincides with the student-optimal von Neumann–Morgenstern (vNM) stable matching. We also show that (i) when a strict core allocation in a housing market derived from a college admission market exists, it can be supported by a strictly strong Nash equilibrium, and (ii) there exists a strictly strong Nash equilibrium under the college-optimal deferred acceptance algorithm if and only if the student-optimal stable matching is Pareto-efficient for students.     

Voluntary Contributions to Multiple Public Projects

The problem of financing a set of discrete public goods (facilities, projects) by private contributions is studied. The corresponding cooperative game, the realization game , is shown to be convex. For the noncooperative setting we study a realization scheme that induces a strategic game. This contribution game is shown to be a generalized ordinal potential game ; a best–response in the contribution game implies a best response in a coordination game in which the payoff to all players is the utilitarian collective welfare function, i.e., the sum of the utility functions of the players. Strategy profiles maximizing utilitarian welfare are strong Nash equilibria of the contribution game. Each strong Nash equilibrium corresponds in a natural way with a core element of the realization game, and vice versa. Moreover, each strong Nash equilibrium is coalitional proof.     

Local coordination and market equilibria

We reformulate the local stability analysis of market equilibria in a competitive market as a local coordination problem in a market game, where the map associating market prices to best-responses of all traders is common knowledge and well-defined both in and out of equilibrium. Initial expectations over market variables differ from their equilibrium values and are not common knowledge. This results in a coordination problem as traders use the structure of the market game to converge back to equilibrium. We analyse a simultaneous move and a sequential move version of the market game and explore the link with local rationalizability.     

Catalog competition and Nash equilibrium in nonlinear pricing games

We model strategic competition in a market with asymmetric information as a noncooperative game in which each seller competes for a buyer of unknown type by offering the buyer a catalog of products and prices. We call this game a catalog game. Our main objective is to show that catalog games have Nash equilibria. The Nash existence problem for catalog games is particularly contentious due to payoff discontinuities caused by tie-breaking. We make three contributions. First, we establish under very mild conditions on primitives that no matter what the tie-breaking rule, catalog games are uniformly payoff secure, and therefore have mixed extensions which are payoff secure. Second, we show that if the tie-breaking rule awards the sale to firms which value it most (i.e., breaks ties in favor of firms which stand to make the highest profit), then firm profits are reciprocally upper semicontinuous (i.e., the mixed catalog game is reciprocally upper semincontinuous). This in turn implies that the mixed catalog game satisfies Reny’s condition of better-reply security—a condition sufficient for existence (Reny in Econometrica 67:1029–1056, 1999). Third, we show by example that if the tie-breaking rule does not award the sale to firms which value it most (for example, if ties are broken randomly with equal probability), then the catalog game has no Nash equilibrium. This paper was written while the second author was Visiting Professor, Centre d’Economie de la Sorbonne, Universite Paris 1, Pantheon-Sorbonne. The second author thanks CES and Paris 1, and in particular, Bernard Cornet and Cuong Le Van for their support and hospitality. The second author also thanks the C&BA and EFLS at the University of Alabama for financial support. Both authors are grateful to Monique Florenzano and to participants in the April 2006 Paris 1 NSF/NBER Decentralization Conference for many helpful comments on an earlier version of the paper. Finally, both authors are especially grateful to an anonymous referee whose thoughtful comments led to substantial improvements in the paper. Monteiro acknowleges the financial support of Capes-Cofecub 468/04.     

Information aggregation in financial markets with career concerns

What are the equilibrium features of a dynamic financial market in which traders care about their reputation for ability? We modify a standard sequential trading model to include traders with career concerns. We show that this market cannot be informationally efficient: there is no equilibrium in which prices converge to the true value, even after an infinite sequence of trades. We characterize the most revealing equilibrium of this game and show that an increase in the strength of the traders' reputational concerns has a negative effect on the extent of information that can be revealed in equilibrium but a positive effect on market liquidity.     

The Effects of Subject Pool and Design Experience on Rationality in Experimental Asset Markets

Empirical evidence suggests that prices do not always reflect fundamental values and individual behavior is often inconsistent with rational expectations theory. We report the results of fourteen experimental asset markets designed to examine whether the interactive effect of subject pool and design experience (i.e., previous experience in a market under identical conditions) tempers price bubbles and improves forecasting ability. Our main findings are: 1) price run-ups are modest and dissipate quickly when traders are knowledgeable about financial markets and have participated in a previous market under identical conditions; 2) price bubbles moderate quickly when only a subset of traders are knowledgeable and experienced; 3) the heterogeneity of expectations about price changes is smaller in markets with knowledgeable and experienced traders, even if such traders only represent a subset of the market; and 4) individual forecasts of prices are not consistent with the predictions of the rational expectations model in any market, although absolute forecast errors are smaller for subjects who are knowledgeable of financial markets and for those subjects who have participated in a previous market. In sum, our findings suggest that markets populated by at least a subset of knowledgeable and experienced traders behave rationally, even though average individual behavior can be characterized as irrational.     

N-PERSON NASH BNARGAINING WITH VARIABEL THREATS*

We consider two models of n-person bargaining problems with the endogenous determination of disagreement points. In the first model, which is a direct extension of Nash's variable threat bargaining model, the disagreement point is determined as an equilibrium threat point. In the second model, the disagreement point is given as a Nash equilibrium of the underlying noncooperative game. These models are formulated as extensive games, and axiomatizations of solutions are given for both models. It is argued that for games with more than two players, the first bargaining model does not preserve some important properties valid for two-person games, e.g., the uniqueness of equilibrium payoff vector. We also show that when the number of players is large, any equilibrium threat point becomes approximately a Nash equilibrium in the underlying noncooperative game, and vice versa. This result suggests that the difference between the two models becomes less significant when the number of players is large.     

The Nash bargaining solution in general n-person cooperative games

We present a noncooperative foundation for the Nash bargaining solution for an n-person cooperative game in strategic form. The Nash bargaining solution should be immune to any coalitional deviations. Our noncooperative approach yields a new core concept, called the Nash core, for a cooperative game based on a consistency principle. We prove that the Nash bargaining solution can be supported (in every subgame) by a stationary subgame perfect equilibrium of the bargaining game if and only if the Nash bargaining solution belongs to the Nash core.     

Trading networks with price-setting agents

In a wide range of markets, individual buyers and sellers trade through intermediaries, who determine prices via strategic considerations. Typically, not all buyers and sellers have access to the same intermediaries, and they trade at correspondingly different prices that reflect their relative amounts of power in the market. We model this phenomenon using a game in which buyers, sellers, and traders engage in trade on a graph that represents the access each buyer and seller has to the traders. We show that the resulting game always has a subgame perfect Nash equilibrium, and that all equilibria lead to an efficient allocation of goods. Finally, we analyze trader profits in terms of the graph structure — roughly, a trader can command a positive profit if and only if it has an “essential” connection in the network, thus providing a graph-theoretic basis for quantifying the amount of competition among traders.     

The number of commodities required to represent a market game

An n-person game with side payments that can arise from an economic market is called a market game. It is proved here that any n-person market game can be obtained from a market with at most n ? 1 commodities. Moreover, no smaller number will suffice in some cases (e.g., the unanimity game). This result is then applied to settle a question regarding market games with a continuum of traders.     

Cooperative equilibria in finite horizon noncooperative supergames

It is well known that cooperative outcomes can be supported by noncooperative equilibrium strategy combinations in games that are infinitely repeated; however, the example of the repeated prisoner's dilemma has led people to conclude that such cooperative outcomes cannot be sustained if the game is repeated finitely often. In this paper it is proved that the belief about finitely repeated games is false. Conditions are given that allow the existence of cooperative outcomes in finitely repeated games that are supported by subgame perfect noncooperative equilibrium strategies.     

Informed trading and the ‘leakage’ of information

This paper examines the effect of ‘leakage’ of information, private information becoming available to uninformed traders at a later date, on information acquisition and revelation. Using a Shapley-Shubik market game framework it is shown that (a) if information acquisition by the informed traders is costless, this leads to faster revelation of information; (b) if information acquisition is costly, there may be no acquisition of information; (c) information leakage leads to a fall in value of information but does not affect the incentive for informed traders to sell the information.     

A DYNAMIC ENTRY AND PRICE GAME WITH CAPACITY INDIVISIBILITY

Strategic market interaction is here modelled as a two‐stage game in which potential entrants choose capacities and next active firms compete in prices. Due to capital indivisibility, the capacity choice is made from a finite grid and there are economies of scale. In the simplest version of the model with a single production technique, the equilibrium turns out to depend on the ratio between the level of total output at the long‐run competitive equilibrium and the firm's minimum efficient scale: if that ratio is sufficiently large (the market is sufficiently ‘large’), then the competitive price emerges at a subgame‐perfect equilibrium of the capacity and price game; if not, then the firms randomize in prices on the equilibrium path. The role of the market size for the competitive outcome is shown to be even more important if there are several available production techniques.     

Strategic market games quantal response equilibria

Summary. The paper explores a model of boundedly rational traders who act strategically. The general framework of analysis is the sell all model of Shapley and Shubik [6] whereas the behavioral rule of traders is related to the bounded rationality of McKelvey and Palfrey [5] and the subsequent of Chen Friedman and Thisse [1]. A new equilibrium concept is introduced appropriate to integrate in the basic model market participants that may choose an inferior action with positive probability. Further, assuming that these market participants are engaged in an infinite repeated game and making them able to learn playing rationally, we demonstrate that in the limit the original equilibrium of Shapley and Shubik is attained and basically emerges as a special case of our equilibrium concept.Received: 20 September 2003, Revised: 11 December 2004, I am indebted to Yanis Varoufakis and especially to Dimitrios P. Tsomocos for their helpful comments.     

Persuasion and learning by countersignaling

We model countersignaling (i.e., very high types refraining from signaling) arising from the tradeoff between persuasion and learning in a signaling game. We assume that the agent has imperfect private information regarding his/her productivity, which the signaling action provides additional verifiable information about. A higher-type agent benefits more from providing such objective, albeit imprecise, “proof” for the market, but may also gain less from learning about his/her productivity. When the latter effect dominates the former for the very high types, the equilibrium exhibits countersignaling: very high and low types pool on refraining from signaling, and only the medium types signal. Under certain conditions, the countersignaling equilibrium is the unique pure-strategy perfect sequential equilibrium.