Coordination and bargaining power in contracting with externalities

Building on Genicot and Ray [G. Genicot, D. Ray, Contracts and externalities: How things fall apart, J. Econ. Theory 131 (2006) 71-100] we develop a model of non-cooperative bargaining that combines the two main approaches in the literature of contracting with externalities: the offer game (in which the principal makes simultaneous offers to the agents) and the bidding game (in which the agents make simultaneous offers to the principal). Allowing for agent coordination, we show that the outcome of our bargaining procedure may differ remarkably from those of the offer and the bidding games. In particular, we find that bargaining can break agents' coordination and that the principal's payoff can be decreasing in his own bargaining power.     

Imitation and the evolution of Walrasian behavior: Theoretically fragile but behaviorally robust

A well-known result by Vega-Redondo (1997) [18] implies that in symmetric Cournot oligopolies, imitation leads to the Walrasian outcome. We show that this result is not robust to the slightest asymmetry in costs, since every outcome where agents choose identical actions will be played some fraction of the time in the long run. We then conduct experiments to check this fragility. We obtain that, contrary to the theoretical prediction, the Walrasian outcome is a good predictor of market outcomes. Finally, we suggest a new theory based on a mix of imitation and other learning processes that explains subjects' behavior fairly well.     

The equilibrium of the bargaining game and core convergence theorem on an exchange economy with limited traders

Debreu and Scarf (1963), Hildenbrand (1974), Aumann (1964), Dierker (1975), Bewley (1973), and others have shown that the core of an exchange economy with infinitely many or finitely many traders converges. However, an exchange economy does not always consist of infinitely many or finitely many traders. This note provides proof of the core convergence theorem on an exchange economy with limited traders by a bargaining game methodology. The main contribution of this note is to innovate the equilibrium solution to the bargaining game in the exchange economy. In this note, the concept of common payoff is introduced; in the bargaining game of a coalition on its common payoff, all coalition members will get the same distribution, thus the distribution scheme of the cooperation surplus of the exchange economy is determined. This note shows that the bargaining game among the traders on the distribution of the cooperation surplus will make the pure exchange economy with limited traders converge to the Walrasian equilibrium, all the allocations other than the Walrasian equilibrium will be eliminated from the core of this economy.     

Non-marketed options, non-existence of equilibria, and non-linear prices

This paper presents a surprising example that shows that the lattice theoretic properties in Mas-Colell's (1986) seminal work are relevant to the existence of equilibrium even when the commodity space is finite dimensional.The example is a two-period securities model with a three-dimensional portfolio space and two traders. The paper identifies a non-marketed call option that fails to have a minimum cost super-replicating portfolio. Using this option, we construct an economy that satisfies all of Mas-Colell's assumptions, except that the three-dimensional commodity space is not a vector lattice. In this economy, there is no Walrasian equilibrium and the second theorem of welfare economics fails.Our example has important finite- as well as infinite-dimensional implications. It is also an example of a “well behaved” economy in which optimal allocations that are not supported by linear Walrasian prices are decentralized by the non-linear prices studied in Aliprantis-Tourky-Yannelis (2001).     

Bargaining in a network of buyers and sellers

We analyze bargaining between buyers and sellers who are connected by an exogenously given network. Players can make repeated alternating public offers that may be accepted by any of the responders linked to each specific proposer. Our purpose is to find the conditions of the network which drive the price distribution in equilibrium. This paper uses graph theory tools to provide necessary and sufficient conditions regarding the architecture of networks for the subgame perfect equilibrium of the bargaining game to coincide with the Walrasian outcome.     

Bargaining and competition revisited

We show the robustness of the Walrasian result obtained in models of bargaining in pairwise meetings. Restricting trade to take place only in pairs, most of the assumptions made in the literature are dispensed with. These include assumptions on preferences (differentiability, monotonicity, strict concavity, bounded curvature), on the set of agents (dispersed characteristics) or on the consumption set (allowing only divisible goods).     

A bargaining model in general equilibrium

The goal of the paper is to present a simple model of rational endogenous household formation in a general equilibrium framework in which Pareto optimality at the economy level is not necessarily obtained. The simplest example of household formation is the case in which pairs of individuals engage themselves in a bargaining process on the division of some wealth: if an agreement on the distribution is (not) reached, we can say that the household is (not) formed. The vast majority of existing bargaining models predicts agreements on an efficient outcome. A seminal paper by Crawford (Econometrica 50:607–637, 1982) describes a very simple game with incomplete information in which, even with rational agents, disagreement causes welfare losses. We embed that model in a general equilibrium framework and present some results on equilibria both in the bargaining game and the associated exchange economy. Crawford’s results support Schelling’s intuition on the reasons of disagreement: it may arise if players’ commitments are reversible. Crawford shows that high probabilities of reversibility tend to favor the bargaining impasse, in fact with low probability. We prove that even if those probabilities are arbitrarily close to zero, disagreement is an equilibrium outcome, with high probability. That conclusion seems to be an even stronger support to Schelling’s original viewpoint. In the exchange economy model with that noncooperative bargaining game as a first stage, we present significant examples of economies for which equilibria exist. Because of disagreement, Pareto suboptimal exchange economy equilibria exist for all elements in the utility function and endowment spaces and they may coexist with Pareto optimal equilibria even at the same competitive prices.     

Stores

Summary There is scope and incentive for stores to endogenously arise in an exchange economy when agents possess different levels of bargaining power and coalition formation is costly. In the absence of stores, agents face a trading lottery where the expected outcome for an individual agent depends upon his relative bargaining strength. By setting appropriate, preannounced prices, a store can profitably offer relatively weak bargainers trading opportunities which they prefer to the trading lottery. While relatively weak bargainers are attracted to the store, relatively strong bargainers prefer the trading lottery to the store. Thus, the simultaneous existence of barter and mediated trade is explained.The work reported here was conceived while both authors were visiting the University of Southern California. We thank Martine Quinzii and two anonymous referees for helpful comments.     

General equilibrium with nonconvexities and money

In a general-equilibrium economy with nonconvexities, there are sunspot equilibria with good welfare properties; sunspots can ameliorate the effects of the nonconvexities. For these economies, we show that agents act as if they have quasi-linear utility functions. We use this result to construct a new model of monetary exchange along the lines of Lagos and Wright, where trade occurs in both centralized and decentralized markets, but instead of quasi-linear preferences we assume general preferences but with indivisible labor. This suggests that modern monetary theory is more robust than one might have thought. It also constitutes progress on the classic problem of integrating monetary economics and general-equilibrium theory.     

Bargaining foundations of the median voter theorem

We give a game-theoretic foundation for the median voter theorem in a one-dimensional bargaining model based on Baron and Ferejohn's [D. Baron, J. Ferejohn, Bargaining in legislatures, Amer. Polit. Sci. Rev. 83 (1989) 1181-1206] model of distributive politics. We prove that as the agents become arbitrarily patient, the set of proposals that can be passed in any pure strategy, subgame perfect equilibrium collapses to the median voter's ideal point. While we leave the possibility of some delay, we prove that the agents' equilibrium continuation payoffs converge to the utility from the median, so that delay, if it occurs, is inconsequential. We do not impose stationarity or any other refinements. Our result counters intuition based on the folk theorem for repeated games, and it contrasts with the known result for the distributive bargaining model that as agents become patient, any division of the dollar can be supported as a subgame perfect equilibrium outcome.     

The rate of convergence to perfect competition of matching and bargaining mechanisms

We study the steady state of a market with incoming cohorts of buyers and sellers who are matched pairwise and bargain under private information. A friction parameter is τ, the length of the time period until the next meeting. We provide a necessary and sufficient condition for the convergence of mechanism outcomes to perfect competition at the linear rate in τ, which is shown to be the fastest possible among all bargaining mechanisms. The condition requires that buyers and sellers always retain some bargaining power. The bargaining mechanisms that satisfy this condition are called nonvanishing bargaining power (NBP) mechanisms. Simple random proposer take-it-or-leave-it protocols are NBP, while k-double auctions (k-DA) are not. We find that k-DAs have equilibria that converge to perfect competition at a linear rate, converge at a slower rate or even do not converge at all.     

On mixed markets with asymmetric information

In asymmetric information exchange economies involving both non-negligible and negligible agents, one should expect the failure of the private Core-Walras Equivalence Theorem. This paper shows that if “large” traders are similar to each other, then they lose their market power and hence the Equivalence Theorem can be restored. We also investigate on weaker equivalences among Walrasian expectations allocations, Aubin private core and private core allocations of the original mixed economy and the atomless one associated to it, without the assumption that all atoms are of the same type. Furthermore, extensions of Hervés-Moreno-Yannelis and Schmeidler Theorems (compare Hervés et al. in J Math Econ 41:844–856, 2005a; Schemidler in Econometrica 40:579–580, 1972) are given for differential information economies in which the feasibility constraints are imposed with an equality (exact feasibility).     

Perfect competition in asymmetric information economies: compatibility of efficiency and incentives

The idea of perfect competition for an economy with asymmetric information is formalized via an idiosyncratic signal process in which the private signals of almost every individual agent can influence only a negligible group of agents, and the individual agents’ relevant signals are essentially pairwise independent conditioned on the true states of nature. Thus, there is no incentive for an individual agent to manipulate her private information. The existence of incentive compatible, ex post Walrasian allocations is shown for such a perfectly competitive asymmetric information economy with or without “common values”. Consequently, the conflict between incentive compatibility and Pareto efficiency is resolved exactly, and its asymptotic version is derived for a sequence of large, but finite private information economies.     

Evolution of Walrasian equilibrium in an exchange economy

We study the stochastic stability of a dynamic trading process in an exchange economy. We use a simplified version of a trading model à la Shapley and Shubik (J Polit Econ 85:937–968, 1977). Two types of agents equipped with Leontief preferences trade goods in markets by offering endowments, and actual trades occur at market clearing prices. Better behavior tends to spread through the same type of agents by imitation, and agents also make mistakes occasionally. We provide a sufficient condition for the perturbed dynamic process to have a unique stochastically stable state that is a Walrasian equilibrium allocation. In this sense, we give a rationale for Walrasian behavior.     

Characterizations of bargaining solutions in production economies with unequal skills

In production economies with unequal skills, this paper characterizes bargaining solutions by using axioms on allocation rules rather than axioms on classical bargaining solutions. We introduce a new axiom, consistency w.r.t. technological innovations, so that the non-welfaristic characterizations of bargaining solutions in the production economies are provided. By the characterizations, we can classify the three bargaining solutions (the Nash, the Kalai-Smorodinsky, and the Egalitarian solutions) from the viewpoint of responsibility and compensation discussed by Dworkin.     

MONEY HOLDINGS,INFLATION, AND WELFARE IN A COMPETITIVE MARKET*

This article examines an environment where money is essential and agents exchange in perfectly competitive, Walrasian markets. Agents consume and produce a homogeneous good, but hold money to purchase consumption in the event of a relatively low productivity shock. A Walrasian market delivers a nondegenerate distribution of money holdings across agents and avoids some of the computational difficulties associated with the market assumption of bilateral bargaining common to search‐theoretic environments. The model is calibrated to long‐run U.S. velocity, and the welfare costs of inflation are assessed for variable buyer–seller ratios and persistent states of buying and selling.     

Bargaining, coalitions and competition

We study a Gale-like matching model in a large exchange economy, in which trade takes place through non-cooperative bargaining in coalitions of finite size. Under essentially the same conditions of core equivalence, we show that the strategic equilibrium outcomes of our model coincide with the Walrasian allocations of the economy. Our method of proof makes use of the theory of the core. With respect to previous work, our positive implementation result applies to a substantially larger class of economies: the model relaxes differentiability and convexity of preferences, and also admits an arbitrary number of divisible and indivisible goods.     

Bargaining with endogenous disagreement: The extended Kalai-Smorodinsky solution

Following Vartiainen (2007) we consider bargaining problems in which no exogenous disagreement outcome is given. A bargaining solution assigns a pair of outcomes to such a problem, namely a compromise outcome and a disagreement outcome: the disagreement outcome may serve as a reference point for the compromise outcome, but other interpretations are given as well. For this framework we propose and study an extension of the classical Kalai-Smorodinsky bargaining solution. We identify the (large) domain on which this solution is single-valued, and present two axiomatic characterizations on subsets of this domain.     

Macroeconomic fluctuations and bargaining

I study the limit rule for bilateral bargaining when agents recognize that the aggregate economy (and thus the match surplus) follows a finite-state Poisson process. The rule derived in this paper is of special importance for decentralized exchange economies with bargaining. Two simple applications are presented to illustrate this fact. The first example is a model of wage bargaining and trade externalities. I show that in such situations sophisticated bargaining tends to increase the volatility of the wage bill. The second example is based on the Kiyotaki-Wright model of money. I explain how equilibrium prices depend in a fundamental way on the dynamic bargaining solution.     

On the core and Walrasian expectations equilibrium in infinite dimensional commodity spaces

In this paper, we establish two different characterizations of Walrasian expectations allocations by the veto power of the grand coalition in an asymmetric information economy having finitely many agents and states of nature and whose commodity space is a Banach lattice. The first one deals with Aubin non-dominated allocations, and the other claims that an allocation is a Walrasian expectations allocation if and only if it is not privately dominated by the grand coalition, by considering perturbations of the original initial endowments in precise directions.