Bargaining in committees as an extension of Nash's bargaining theory

This paper addresses the following issue: if a set of agents bargain on a set of feasible alternatives ‘in the shadow’ of a voting rule, that is, any agreement can be enforced if a ‘winning coalition’ supports it, what general agreements are likely to arise? In other words: what influence can the voting rule used to settle (possibly nonunanimous) agreements have on the outcome of consensus? We model the situation as an extension of the Nash bargaining problem in which an arbitrary voting rule replaces unanimity. In this setting a natural extension of Nash's solution is characterized.     

Bargaining with asymmetric information in non-stationary markets

Summary. The Rubinstein and Wolinsky bargaining-in-markets framework is modified by the introduction of asymmetric information and non-stationarity. Non-stationarity is introduced in the form of an arbitrary stochastic Markov process which captures the dynamics of market entry and pairwise matching. A new technique is used for establishing existence and characterizing the unique outcome of a non-stationary market equilibrium. The impact of market supply and demand on bilateral bargaining outcomes and matching probabilities is explored. The results are useful for examining such questions as why coordination failures and macroeconomic output fluctuations are correlated with real and monetary shocks. Received: July 22, 1994; revised version: January 21, 1998     

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).     

Bargaining one-dimensional social choices

We analyze bargaining over the one-dimension characteristic of a public good among n impatient players when decisions require q favorable votes, q?2. Stationary subgame perfect equilibrium strategies are characterized for all games with deterministic protocol. We provide a monotonicity condition (satisfied by all single-peak, strictly quasi-concave and concave utilities) that assures uniqueness for every q whenever player's utilities are symmetric around the peak. Without symmetry, the monotonicity condition assures uniqueness for qualified majorities, q>n/2, provided that agents are sufficiently patient and utilities satisfy an additional regularity condition. Asymptotic uniqueness is assured for qualified majorities by imposing only the monotonicity condition.     

A Bargaining Experiment to Motivate Discussion on Fairness

The author presents a classroom version of the popular research game called the Ultimatum Game. Researchers are placing growing importance on how fairness affects behavior, and this experiment provides a useful, fun, and engaging way in which a day or two of class time can be spent on the topic. The appendix contains all of the materials necessary to conduct this experiment, and the experiment can highlight several items of interest for the instructor. First, different individuals place different subjective weights on concerns for fairness versus money. Second, theories that incorporate concerns for fairness into agents' preferences can often explain behavior better than those that do not. Finally, when it is relatively cheap to purchase fairness (or equality) individuals purchase more of it. The classroom results can motivate discussion of a downward sloping demand curve for fairness.     

ECONOMIC NETWORKING AND STABILITY

Abstract. In this paper we discuss finite economies with the presence of transaction costs and with decreasing, constant or increasing returns. In general such an economy may have no general equilibrium existence and may even have an empty core. We analyse the trading networks of such an economy, introducing the concepts of locally stable network structure, un‐dominated locally stable network structures and most stable network structures. We point out that the set of most stable network structures could be treated as a solution concept for the empty core economies both in theoretical analysis and in application.     

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.     

Unique equilibrium in rent-seeking contests with a continuum of types

It is shown that rent-seeking contests with continuous and independent type distributions possess a unique pure-strategy Nash equilibrium.     

Large market games with demand uncertainty

We consider a market game with a continuum of consumers, where the measure of each type is stochastic. Nature selects the set of active consumers, who make bids and offers on ?−1 spot market trading posts. Existence of type-symmetric Nash equilibrium is proven. When facing price uncertainty, best responses are unique, and a Nash equilibrium to the sell-all game is typically not a Nash equilibrium to the original game. Under plausible circumstances, consumers strictly prefer to be on one side of the market.     

Balanced Bayesian mechanisms

In the transferable utility case, a number of authors have identified conditions on beliefs that guarantee the existence of Bayesian incentive compatible mechanisms with balanced transfers. We present a new, easy to interpret, condition and we show that it is (strictly) more general than all the other conditions found in the literature. We also study conditions guaranteeing the Bayesian implementability of all social decision rules with balanced budget mechanisms.     

Transfer Pricing and Hold-Ups in Supply Chains

Abstract. We reconsider the hold‐up problem under symmetric information when more than two parties form a ‘supply chain’. The parties are assumed to renegotiate bilaterally and sequentially. Potential trade distortions then arise in addition to the usual investment problem. Following Edlin and Reichelstein (1995, 1996), we consider fixed‐quantity contracts. First‐best allocations are shown to be attainable if the parties are able to commit to a ‘forced‐compliance’ regime where a central office monitors the consistency of the bilateral renegotiations.     

Bargaining and markets: complexity and the competitive outcome

Rubinstein and Wolinsky (Rev. Econ. Stud. 57 (1990) 63-78) consider a simple decentralised market game in which agents meet randomly or voluntarily and bargain over the terms of trade. They show that any individually rational price can be sustained as a sequential equilibrium even though the model has a unique competitive outcome. Here, I consider Rubinstein and Wolinsky's model and show that if complexity costs of implementing strategies enter players’ preferences, together with the standard payoff in the game, then every equilibrium is stationary/Markov and induces the unique competitive price. Thus, I demonstrate that aversion to complexity may provide a justification for the competitive outcome.     

Bargaining under a deadline: evidence from the reverse ultimatum game

We study a “reverse” ultimatum game, in which proposers have multiple chances to offer responders a division of some fixed pie. The game ends if the responder accepts an offer, or if, following a rejection, the proposer decides not to make a better offer. The unique subgame perfect equilibrium gives the proposer the minimum possible payoff. Nevertheless, the experimental results are not too different from those of the standard ultimatum game, although proposers generally receive slightly less than half of the surplus.We use the reverse ultimatum game to study deadlines experimentally. With a deadline, the subgame perfect equilibrium prediction is that the proposer gets the entire surplus.Deadlines are used strategically to influence the outcome, and agreements are reached near the deadline. Strategic considerations are evident in the differences in observed behavior between the deadline and no deadline conditions, even though agreements are substantially less extreme than predicted by perfect equilibrium.     

Bargaining and network structure: An experiment

We consider bargaining in a bipartite network of buyers and sellers, who can only trade with the limited number of people with whom they are connected. We perform an experimental test of a graph-theoretic model that yields unique predictions about equilibrium prices for the networks in our sessions. The results diverge sharply depending on how a connection is made between two separate simple networks, typically conforming to the theoretical directional predictions. Payoffs can be systematically affected even for agents who are not connected by the new link, and we find evidence of a form of social learning.     

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.     

A MARKET WITH A SOCIAL CONSUMPTION EXTERNALITY*

We model a spatial market in which the utility of each consumer is affected by the consumers who buy precisely the same product. The marginal contribution of consumers x's purchase on consumer y depends on |x–y|, which declines as |x–y| increases. Such modelling of preferences fits goods that signal a consumer's place in society—clothing styles, automobiles and jewellry are examples. For 2n + 1 firms we find the unique symmetric equilibrium and derive comparative statics on the optimal number of firms, the largest number of firms the market can support, and the behaviour of profits per firm as n increases.     

Bargaining power and enforcement in credit markets

In a credit market with enforcement constraints, we study the effects of a change in the outside options of a potential defaulter on the terms of the credit contract, as well as on borrower payoffs. The results crucially depend on the allocation of “bargaining power” between the borrower and the lender. We prove that there is a crucial threshold of relative weights such that if the borrower has power that exceeds this threshold, her expected utility must go up whenever her outside options come down. But if the borrower has less power than this threshold, her expected payoff must come down with her outside options. In the former case a deterioration in outside options brought about, say, by better enforcement, must create a Lorenz improvement in state-contingent consumption. In particular, borrower consumption rises in all “bad” states in which loans are taken. In the latter case, in contrast, the borrower's consumption must decline, at least for all the bad states. These disparate findings within a single model permit us to interpret existing literature on credit markets in a unified way.     

Bargaining and inequity aversion: On the efficiency of the double auction

In a bargaining setting with asymmetrically informed, inequity-averse parties, a fully efficient mechanism (i.e., the double auction) exists if and only if compassion is strong. Less compassionate parties do not trade in the double auction in the limit of strong envy.     

Optimal agenda-setter timing

Abstract .  We analyze the optimal timing problem of an agenda setter who can propose a project that is then voted on by a committee. The payoff consists of a common stochastic component and an idiosyncratic component that differs among committee members. The agenda setter may be biased for or against the project, relative to the median committee member, and chooses when to call the vote. We analyze how the timing decision depends on the political environment and the bias of the agenda setter. We show that both positively and negatively biased agenda setters can implement decisions that differ from those preferred by the median committee member.