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).     

THE HIDDEN COST OF BARGAINING: EVIDENCE FROM A CHEATING-PRONE MARKETPLACE

It is widely believed that successful bargaining helps consumers increase their surplus. We present evidence from a field experiment showing that bargaining over price reduces buyer surplus in a marketplace where sellers cheat on the weight whose value may more than offset the price discount. Our results show that bargaining entails hidden costs since sellers cheat significantly more when buyers bargain than not and they cheat significantly more when bargaining succeeds than fails. Overall bargaining reduces buyer surplus than not bargaining. Our result is relevant for credence goods markets where bargaining over prices may induce sellers to “undertreat” more.     

Respecting entitlements in legislative bargaining: A matter of preference or necessity?

We investigate whether fairness concerns overrule strategic behaviour in legislative bargaining with entitlements. In a lab experiment, we vary bargaining power by using either majority rule or dictator rule to implement a division. We apply coarse measures in order to assess whether entitlements are respected. Our results show that with experience over one third of proposers make “extreme” offers, assigning at most 10% of the surplus to partners whose consent is not needed under the respective rule. Having observed extreme outcomes in the past increases the likelihood of own extreme proposals. Overall, we find significant limitations in the acknowledgment for others' entitlements, in particular for groups in which individual contributions differ.     

BARGAINING AMONG FARMERS,GOODWILL, AND THE SUCCESS OF COOPERATIVES

A model of concessional bargaining among farmers explains the success (or lack thereof) of cooperative institutions in rural farm settings in the developing regions. Concessional bargaining in day‐to‐day interactions generates goodwill, which helps smoothen future dealings amongst farmers as well as with outside agents. In particular, we model the existence of goodwill amongst farmers as enhancing their ability to collectively bargain with an outside dealer that buys their farm produce. Results suggest that when dealing with each other, farmers offer higher concessions when the risk of loss or reversal in bargaining power is high; however, the level of concession is also influenced by the degree of reciprocity and parameters that affect bargaining surplus. Findings provide further insights over the success of cooperative institutions in rural farm settings where inter‐farmer goodwill dynamics determines the cooperative's bargaining outcomes. Specifically, when farmers generously reciprocate each other's goodwill gestures, it leads to better outcomes through increasing their cooperative reservation price. In contrast, when the degree of reciprocity is lower, or when the risk of bargaining power switching is higher, farmers extract more surplus from other farmers, and this also lowers the cooperative's bargaining outcomes and makes the cooperative arrangement unviable in the long term.     

Communication in bargaining over decision rights

This paper develops a model of bargaining over decision rights between an uninformed principal and an informed but self-interested agent. We introduce two different bargaining mechanisms: tacit and explicit bargaining. In tacit bargaining, an uninformed principal makes a take-it-or-leave-it price offer to the agent, who then decides whether to accept or reject the offer. In the equilibrium of the game, the principal inefficiently screens out some agent types so that the agent's private information cannot be fully utilized when the decision is made. In explicit bargaining in which parties can communicate explicitly via cheap talk before tacit bargaining, however, an equilibrium with no such inefficient screening exists even when the conflict of interest is arbitrarily large. We also follow a mechanism design approach, showing that under certain conditions, explicit bargaining is an optimal bargaining mechanism that maximizes the joint surplus of the parties.     

Union–Firm Interaction and the Right to Manage

In the context of price-setting oligopoly, this paper shows that there may be consensus in union–employer bargaining for limiting the scope of bargaining to determining wage levels and allowing the employer to act unilaterally when competing in the product market. A strategic commitment by each union–firm pair to a right-to-manage framework, rather than a participatory approach, may benefit the bargaining parties since this entails higher negotiated wage rates which, by dampening competition in the product market, may allow for an increase in the amount of surplus generated by the parties.     

Bargaining and Sharing Innovative Knowledge

We consider the problem of bargaining over the disclosure of interimresearch knowledge between two participants in an R&D race for an ultimate,patentable invention. Licence fee schedules that are functions of the'amount of knowledge disclosed', by the leading to the laggingagent, are examined for their abilities to attain efficient outcomes andvarying shares of the surplus arising from disclosure. In hersequential-offers bargaining games, the uninformed buyer is able to elicitfull disclosures without sharing the incremental surplus with any type ofthe licensor, and thus do as well as a perfectly informed and discriminatingknowledge licensee.     

Nash bargaining model of HMO premiums

This paper estimates a model of commercial HMO premiums based on Nash's axiomatic approach to bargaining between HMOs and employers. The bargaining models incorporate variables that measure the?‘power’?of the parties to affect the division of potential gains from a contract. It is found that an increase in the number of competing HMOs increases the employer's bargaining power and leads to lower premiums, especially for for-profit HMOs. It is also found that employers’?bargaining power over non-profit HMOs is positively related to the ratio of the HMO's administrative expenses/total expenses.     

The Biodiversity Bargaining Problem

We employ cooperative bargaining theory and Nash’s ‘rational threats’ idea to cast light on the biodiversity bargaining problem. The problem of global environmental negotiations is argued to be of the nature of a bargaining problem, in which bargainers must agree on the distribution of cooperative surplus in order to move to the bargaining frontier. We discuss the importance of both efficiency (bargaining frontier) and fairness (recognition of characteristics of bargainers) in the choice of the appropriate contract. We show that the incremental cost contract, used to resolve the biodiversity bargaining problem, is of the form of an extreme point contract that fails to recognise the contributions of the South to the production of cooperative surplus. A rational response to such a contract is the use of threats of biodiversity destruction. Contracts must evince both efficiency and fairness in order to represent lasting solutions.     

Modelling and predicting the competitive effects of vertical mergers: The bargaining leverage over rivals effect

A new competitive effect of vertical mergers, based on the Nash bargaining model, has begun to play an important role in antitrust authorities’ evaluations of vertical mergers in the United States, Canada and abroad. The key idea is that a vertical merger will increase the bargaining leverage of the merged firm over its downstream rivals. Its bargaining leverage increases because it now takes into account the additional profit that its own downstream division will earn if it withholds inputs from downstream rivals, which changes its threat point in the bargaining game with downstream rivals. Consequently, the merged firm can increase the price that it charges rival downstream firms for inputs. One strong appeal of this theory is that it provides a simple and very intuitive formula to measure the upward pricing pressure caused by a vertical merger due to changes in bargaining leverage, based on variables whose values can generally be estimated using available data. This article describes this new competitive effect, which will be called the bargaining leverage over rivals (BLR) effect, and derives the upward pricing pressure formula. It also explains why this new competitive effect is distinct from the older raising rivals’ costs (RRC) effect that has been widely discussed in the economics literature, and discusses the relationship between the two different effects.     

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.     

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.     

A BARGAINING THEORY OF INEFFICIENT REDISTRIBUTION POLICIES*

When two policies are available to achieve the same goal why is the relatively inefficient one often observed? We address this question in the context of policies used to redistribute income towards special interest groups (SIGs) where in the first stage the constraints on policy instruments are chosen and in the second the government bargains with SIGs over the level of the available policies. Restrictions on the use of efficient policies and the use of inefficient ones reduce the surplus over which SIGs and governments can bargain but it also improves the government's bargaining position thus increasing its share of the surplus. The positive effect for the government dominates under plausible conditions. Inefficient policies are the equilibrium outcome under alternative policy selection mechanisms, e.g., election of policymakers and bargaining between SIGs and the government. The model also explains the coexistence of transfer policies. Moreover, we show why a weak government is more likely to choose the inefficient transfer and discuss how this result may be tested.     

Bargaining and efficiency in networks

We study an infinite horizon game in which pairs of players connected in a network are randomly matched to bargain over a unit surplus. Players who reach agreement are removed from the network without replacement. The global logic of efficient matchings and the local nature of bargaining, in combination with the irreversible exit of player pairs following agreements, create severe hurdles to the attainment of efficiency in equilibrium. For many networks all Markov perfect equilibria of the bargaining game are inefficient, even as players become patient. We investigate how incentives need to be structured in order to achieve efficiency via subgame perfect, but non-Markovian, equilibria. The analysis extends to an alternative model in which individual players are selected according to some probability distribution, and a chosen player can select a neighbor with whom to bargain.     

NASH BARGAINING AND CO-OPERATIVES

This paper develops the generalised Nash bargaining solution for a bargaining co-operative selling its output to a single buyer. Three assumptions for co-operative members' behaviour are examined: profit maximisation, co-operative surplus maximisation and maximising members' price. Solutions are compared and comparative statics presented for these alternative assumptions and the bargaining over price and quantity transacted. The most striking feature of the results is that pursuing the objective of maximising members' price does not necessarily lead to the highest members' price     

Self-interest and fairness: self-serving choices of justice principles

We introduce non-enforceable property rights over a bargaining surplus in a dictator game with production, where the agent’s effort is differentially rewarded and subsequently determines the size of the surplus. Using experimental data, we elicit individual preferences over the egalitarian, accountability and libertarian principles and provide evidence to support the inability of these justice principles to individually account for the observed behavior. We show that the justice principle that can be used to explain dictators’ choices depends on whether dictators are paid more or less than recipients for their effort. Our findings suggest that dictators do employ justice principles in self-serving ways and choose in each context the justice principle that maximizes their financial payoffs.     

The impact of bargaining on markets with price takers: Too many bargainers spoil the broth

In this paper we study how bargainers impact on markets in which firms set a list price to sell to those consumers who take prices as given. The list price acts as an outside option for the bargainers, so the higher the list price, the more the firms can extract from bargainers. We find that an increase in the proportion of consumers seeking to bargain can lower consumer surplus overall, even though new bargainers receive a lower price. The reason is that the list price for those who do not bargain and the bargained prices for those who were already bargaining rise: sellers have a greater incentive to make the bargainers’ outside option less attractive, reducing the incentive to compete for price takers. Competition Authority exhortations to bargain can therefore be misplaced. We also consider the implications for optimal seller bargaining.     

BARGAINING WITH OPTIMISM: IDENTIFICATION AND ESTIMATION OF A MODEL OF MEDICAL MALPRACTICE LITIGATION

We study a model of bargaining with optimism where players have heterogeneous beliefs about the final resolution. Beliefs and bargaining surplus are identified from the settlement probability and the distribution of accepted transfers. Using data from medical malpractice lawsuits in Florida, we estimate doctor and patient beliefs and the distribution of potential compensation. We find that patients are more optimistic and doctors more pessimistic when the severity of injury is higher, and the joint optimism diminishes as severity increases. We quantify the increase in settlement probability and the reduction in accepted settlement offers under counterfactual caps on the total compensation.     

Sorting by search intensity

In this paper, I characterize matching in an on-the-job search model with endogenous search intensity, heterogeneous workers and firms, and match surplus is shared between workers and firms through bargaining. I provide proof of existence and uniqueness of steady state equilibrium. Given equally efficient matched and unmatched search, the worker skill conditional distribution of firm productivity over matches is stochastically increasing (decreasing) in worker skill if the production function is supermodular (submodular). I also show that this strong notion of sorting does not obtain everywhere for the firm productivity conditional match distribution.     

On the cultural basis of gender differences in negotiation

We study how culture and social structure influence bargaining behavior across gender, by exploring the negotiation culture in matrilineal and patriarchal societies using data from a laboratory experiment and a natural field experiment. One interesting result is that in both the actual marketplace and in the laboratory bargaining game, women in the matrilineal society earn more than men, at odds with years of evidence observed in the western world. We find that this result is critically driven by which side of the market the person is occupying: female (male) sellers in the matrilineal (patriarchal) society extract more of the bargaining surplus than male (female) sellers. In the buyer role, however, we observe no significant differences across societies.