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.     

Walrasian bargaining

Given any two-person economy, consider an alternating-offer bargaining game with complete information where the proposers offer prices, and the responders either choose the amount of trade at the offered prices or reject the offer. We provide conditions under which the outcomes of all subgame-perfect equilibria converge to the Walrasian equilibrium (the price and the allocation) as the discount rates approach 1. Therefore, price-taking behavior can be achieved with only two agents.     

Competitive bargaining equilibrium

In a simple exchange economy we propose a bargaining procedure that leads to a Walrasian outcome as the agents become increasingly patient. The competitive outcome therefore obtains even if agents have market power and are not price-takers. Moreover, where in other bargaining protocols the final outcome depends on bargaining power or relative impatience, the outcome here is determinate and depends only on preferences and endowments. Our bargaining procedure involves bargaining over prices and maximum quantity constraints, and it guarantees convergence to a Walrasian outcome for any standard exchange economy. In contrast, without quantity constraints we show that equilibrium is generically inefficient.     

Nominal bargaining power, selection protocol, and discounting in legislative bargaining

The comparative static predictions of the Baron and Ferejohn [Baron, D.P., and Ferejohn, J.A., (1989). Bargaining in legislatures, American Political Science Review 83 (4), 1181-1206] model better organize behavior in legislative bargaining experiments than Gamson's Law. Regressions similar to those employed in field data produce results seemingly in support of Gamson's Law (even when using data generated by simulating agents who behave according to the Baron-Ferejohn model), but this is determined by the selection protocol which recognizes voting blocks in proportion to the number of votes controlled. Proposer power is not nearly as strong as predicted in the closed rule Baron and Ferejohn model, as coalition partners refuse to take the small shares given by the continuation value of the game. Discounting pushes behavior in the direction predicted by Baron and Ferejohn but has a much smaller effect than predicted.     

Demand bargaining in legislatures

We analyze a pure bargaining problem when decisions require simple majority and self interested players make unilateral demands. In contrast to the case where proposals consist of complete sharing profiles, this content of proposals prevents implicit side-payments inside the committee, and so non-discriminatory outcomes might be expected. We show that in some settings this is the case and the surplus is universally shared.     

On the convergence to the Nash bargaining solution for action-dependent bargaining protocols

We consider a non-cooperative multilateral bargaining game and study an action-dependent bargaining protocol, that is, the probability with which a player becomes the proposer in a round of bargaining depends on the identity of the player who previously rejected. An important example is the frequently studied rejector-becomes-proposer protocol. We focus on subgame perfect equilibria in stationary strategies which are shown to exist and to be efficient. Equilibrium proposals do not depend on the probability to propose conditional on the rejection by another player. We consider the limit, as the bargaining friction vanishes. In case no player has a positive probability to propose conditional on his rejection, each player receives his utopia payoff conditional on being recognized. Otherwise, equilibrium proposals of all players converge to a weighted Nash bargaining solution, where the weights are determined by the probability to propose conditional on one's own rejection.     

The bargaining family revisited

We suggest a family bargaining model where human capital investment decisions are made non-cooperatively in a first stage, while day-to-day allocation of time is determined later through Nash bargaining, but with non-cooperative behaviour as the fall-back. One finding is that overinvestment in education may be even more of a problem in such a semi-cooperative model than in a fully non-cooperative one. Even though both the semi-cooperative model and the fully non-cooperative model predict overinvestment in education, policy conclusions that follow from the two models are distinctly different. JEL Classification: D13, J24
Les auteurs suggèrent un modèle de famille qui marchande où les décisions d'investissement en capital humain sont prises de manière non-coopérative dans un premier temps, alors que l'allocation du temps au jour le jour est déterminée plus tard par un marchandage à la Nash, mais avec un comportement noncoopératif comme choix de second ordre. On découvre que le surinvestissement dans l'éducation peut être encore plus problématique dans un tel modèle de semi-coopération que dans un modèle de non coopération. Même si les deux modèles prévoient un surinves;chtissement dans l'éducation, les conclusions au plan de la politique publique qui découlent de ces deux modèles sont fort différentes.     

Wage bargaining and inflation

This paper investigates the issue of time inconsistency of monetary policy in a game with perfect information and infinite repetitions. The private sector is described by a wage negotiation process between a labour union and a firm. Unlike in the standard literature, the model has the feature that as the distortion of the economy gets larger, namely as the bargaining power of the union increases, the reputational equilibrium with low inflation becomes more likely to occur. This finding is consistent with the observation that higher levels of the labour cost are not typically associated with higher levels of inflation.     

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.     

Bilateral bargaining in networks

Each connected pair of nodes in a network can jointly produce one unit of surplus. A maximum number of linked nodes is selected in every period to bargain bilaterally over the division of the surplus, according to the protocol proposed by Rubinstein and Wollinsky [Equilibrium in a market with sequential bargaining, Econometrica 53 (1985) 1133-1150]. All pairs, which reach an agreement, obtain the (discounted) payoffs and are removed from the network. This bargaining game has a unique subgame perfect equilibrium that induces the Dulmage-Mendelsohn decomposition (partition) of the bipartite network (of the set of nodes in this network).     

Sequential bargaining and competition

Summary This paper studies a sequential bargaining model of a decentralised market. A main objective is to explore the conditions under which the unique subgame perfect equilibrium outcome of the market game approximates the Walrasian outcome of the market. The three main messages that emerge from our results are as follows. First, contrary to conventional wisdom, frictionless markets need not be Walrasian. Second, the relative magnitudes of frictions can have a profound impact on the market outcome even in the limit as the absolute magnitudes of the frictions become negligible. And third, the relative magnitudes of certain types of frictions may have to be significantly large in order for markets to be Walrasian, reflecting that certain types of frictions are needed in the market in order to induce the Walrasian outcome.This paper is based on a chapter of my Ph.D. thesis. I would like to thank Ken Binmore, David Canning, Partha Dasgupta and Frank Hahn for their helpful comments. I owe special thanks to Ariel Rubinstein for his comments, remarks and encouragement. The comments and suggestions of an anonymous referee have significantly improved the exposition at several places.     

Wage bargaining and employment revisited: separability and efficiency in collective bargaining*

We analyse the two-dimensional Nash bargaining solution (NBS) by deploying the standard labour market negotiations model of McDonald and Solow. We show that the two-dimensional bargaining problem can be decomposed into two one-dimensional problems, such that the two solutions together replicate the solution of the two-dimensional problem if the NBS is applied. The axiom of “independence of irrelevant alternatives” is shown to be crucial for this type of decomposability. This result has significant implications for actual negotiations because it allows for the decomposition of a multi-dimensional bargaining problem into one-dimensional problems – and thus helps to facilitate real-world negotiations.     

Collective bargaining and school district test scores: evidence from Ohio bargaining agreements

We revisit the relationship between collective bargaining by teachers unions and school performance. The empirical literature in this area has found mixed results at both the state and district levels. We contribute to this literature in two ways. First, rather than simply dummy union status, we proxy for the restrictiveness of collective bargaining agreements with the number of pages per agreement. Second, we employ Bayesian spatial methods to deal with spatial dependence in school district activities. Our reduced-form results indicate that collective bargaining directly lowers scores on high school math scores, but that the total effect is zero.     

Subbalanced games and bargaining sets

Summary. In defining a bargaining set, it is desirable to require that a counterobjecting coalition has a non-empty intersection with the objecting coalition. We refer to this as the intersection property and define a bargaining set, MB ₁, that imposes this property on a variant of the bargaining set defined by Vohra (1991). To study the existence of MB ₁, a new version of the KKM theorem is proposed and the concept of a subbalanced game is introduced. We also provide conditions for the non-emptiness of MB ₂, a bargaining set introduced by Zhou (1994) which imposes the additional restriction that the objecting coalition not be a subset of the counterobjecting coalition.Received: 9 December 2002, Revised: 6 December 2004, JEL Classification Numbers: C71. Correspondence to: Chih ChangThe authors are very grateful to a referee who proposes many helpful comments on both substantive matters and exposition which much improve the paper.     

Matching markets with price bargaining

The extant microeconomic literature on matching markets assumes ordinal preferences for matches, while bargaining within matches is mostly excluded. Central for this paper, however, is bargaining over joint profits from potential matches. We investigate, both theoretically and experimentally, a seemingly simple allocation task in a 2×2 market with repeated negotiations. When inefficiency is possible, about 1/3 of the complete matches are inefficient and, overall, more than 3/4 of the experimental allocations are unstable. These results strongly contradict existing bargaining theories requiring efficient matches. Even with regard to efficient matches, the tested theories perform poorly. Standard bargaining and behavioral concepts, such as Selten’s (1972) Equal Division Core, are outperformed by the simplistic ε-Equal Split, i.e., an equal split of the joint profit plus/minus ε.     

Equilibrium selection in bargaining models

This paper examines evolutionary equilibrium selection in bargaining models. We show that random best-response and continuous best-response learning dynamics give rise to (different) simple sufficient conditions for identifying outcomes as stochastically stable. This allows us to characterize the implications of these dynamics in simple bargaining games.     

Subgame-perfect implementation of bargaining solutions

We study house allocation problems introduced by L. Shapley and H. Scarf (1974, J. Math. Econ.1, 23–28). We prove that a mechanism (a social choice function) is individually rational, anonymous, strategy-proof, and nonbossy (but not necessarily Pareto efficient) if and only if it is either the core mechanism or the no-trade mechanism, where the no-trade mechanism is the one that selects the initial allocation for each profile of preferences. This result confirms the intuition that even if we are willing to accept inefficiency, there exists no interesting strategy-proof mechanism other than the core mechanism. Journal of Economic Literature Classification Numbers: C71, C78, D71, D78, D89.     

Implementing the Kalai-Smorodinsky bargaining solution

The bargaining game is proposed where the agents bid fractions of dictatorship that are used by all non-winners of the auction to threaten acceptance of the winner's proposal. That procedure non-cooperatively implements the Kalai-Smorodinsky bargaining solution.     

Proto-coalition bargaining and the core

In the proto-coalition model of government formation, formateur F appoints a proto-coalition and asks its members whether to start negotiating a coalition contract. If all accept, then the proto-coalition forms and starts negotiating; otherwise, a caretaker government assumes office. I extend this model by allowing F to revise the chosen proto-coalition after rejections, that he states pre-conditions for the subsequent negotiations, and that F??s opponents may publicly pre-commit to accept/reject certain proposals. The set of equilibrium outcomes is identified as the core if F??s opponents can pre-commit and as the convex hull of the core if they cannot pre-commit credibly. This extended model eliminates two flaws of the standard model: it explains why F cannot always install his favored coalition (whatever the status quo) and why ??important?? coalition members may have more bargaining power in the subsequent negotiations than others.