Sequential Bargaining Research Articles

Sequential bargaining with common values

We study the alternating-offers bargaining problem of assigning an indivisible and commonly valued object to one of two players who jointly own this object. The players are asymmetrically informed about the object’s value and have veto power over any settlement. There is no depreciation during the bargaining process which involves signalling of private information. We characterise the perfect Bayesian equilibrium outcome of this game which is unique if offers are required to be strictly increasing. Equilibrium agreement is reached gradually and non-deterministically. The better informed player obtains a rent.

Channel Negotiations with Information Asymmetries: Contingent Influences of Communication and Trustworthiness Reputations

This article reports three experiments that examine how communication types (informational, relational, and coercive messages) and mutual trustworthiness reputations influence sequential bargaining between an uncertain manufacturer and an informed distributor in a marketing channel. In Experiment 1, bargainers use informational and relational messages to establish a positive social tenor in the interaction. Compared with when bargainers communicate only through offers and counteroffers, explicit communication produces quicker and more efficient agreements. The effects are stronger when manufacturer uncertainty is relatively high. In Experiment 2, mutual reputations of high (versus low) trustworthiness also produce quicker and more efficient agreements. In both studies, the larger extracted surplus increases manufacturer profits without affecting distributor profits. However, contrary to economic intuition, the gains from communication accrue asymmetrically to the uninformed manufacturer. Experiment 3 shows the effects of communication type are contingent on the prevailing level (high or low) of trustworthiness reputations in the dyad. Compared with no communication, relational messages elicit the most positive (negative) outcomes when trustworthiness reputations are high (low). Informational messages have a smaller but positive impact on bargaining outcomes in both trustworthiness conditions and appear to build trust.

Distribution of surplus in sequential bargaining with endogenous recognition

I examine a sequential bargaining situation in which agents contest the right to propose an allocation. The contest can either take place at a pre-bargaining stage, yielding “persistent recognition” to propose, or recur throughout the bargaining, yielding “transitory recognition”. Equilibrium analysis reveals that surplus is distributed more unequally under persistent recognition; social cost is higher under persistent recognition if and only if it attracts a sufficient number of “active” bargainers; and individual’s incentive to propose under transitory recognition may actually increase in the number of agents, while this incentive always diminishes under persistent recognition.

Sequential Bargaining in a New Keynesian Model with Frictional Unemployment and Staggered Wage Negotiation

We consider a model with frictional unemployment and staggered wage bargaining where hours worked are negotiated every period. The workers' bargaining power in the hours negotiation affects both unemployment volatility and inflation persistence. The closer to zero this parameter, (i) the more firms adjust on the intensive margin, reducing employment volatility, (ii) the lower the effective workers' bargaining power for wages and (iii) the more important the hourly wage in the marginal cost determination. This set-up produces realistic labor market statistics together with inflation persistence. Distinguishing the probability to bargain the wage of the existing and the new jobs, we show that the intensive margin helps reduce the new entrants wage rigidity required to match observed unemployment volatility.

Sequential Bargaining in a New-Keynesian Model with Frictional Unemployment and Wage Negotiation

Sequential Bargaining in a New-Keynesian Model with Frictional Unemployment and Wage Negotiation

Sequential Bargaining in a New-Keynesian Model with Frictional Unemployment and Staggered Wage Negotiation

We consider a model with frictional unemployment and staggered wage bargaining where hours worked are negotiated every period. The workers' bargaining power in the hours negotiation affects both unemployment volatility and inflation persistence. The closer to zero this parameter, (i) the more firms adjust on the intensive margin, reducing employment volatility, (ii) the lower the effective workers' bargaining power for wages and (iii) the more important the hourly wage in the marginal cost determination. This set-up produces realistic labor market statistics together with inflation persistence. Distinguishing the probability to bargain the wage of the existing and the new jobs, we show that the intensive margin helps reduce the new entrants wage rigidity required to match observed unemployment volatility.

Sequential Bargaining in a Neo-Keynesian Model with Frictional Unemployment and Staggered Wage Negotiations

We consider a model with frictional unemployment and staggered wage bargaining where hours worked are negotiated every period. The workers’ bargaining power in the hours negotiation affects both unemployment volatility and inflation persistence. The closer to zero this parameter, (i) the more firms adjust on the intensive margin, reducing employment volatility, (ii) the lower the effective workers’ bargaining power for wages and (iii) the more important the hourly wage in the marginal cost determination. This set-up produces realistic labor market statistics together with inflation persistence. Distinguishing the probability to bargain the wage of the existing and the new jobs, we show that the intensive margin helps reduce the new entrants wage rigidity required to match observed unemployment volatility.

Sequential entry in many-to-one matching markets

We study sequential bargaining in many-to-one matching markets. We show that there is an advantage to entering late in the market, and that the last agent to enter the market will receive his or her best partner in a stable matching, extending the results of Blum and Rothblum (J Econ Theory 103(2):429–443, 2002) and Cechlarova (Randomized matching mechanism revisited. Mimeo, Safarik University, 2002) for the marriage model. We also discuss the relation between sequential bargaining and a possible alternative formulation based on the NTU Shapley value.

Sequential Bargaining with Common Values

We study the alternating-offers bargaining problem of assigning an indivisible and commonly valued object to one of two players who jointly own the object. The players are asymmetrically informed about the object's value and have veto power over any settlement. There is no depreciation during the bargaining process which involves signaling of private information. We characterize the perfect Bayesian equilibrium outcome of this game which is unique for strictly increasing offers. Equilibrium agreement is reached gradually and non-deterministically. The better informed player obtains a rent.

The influence of seller learning and time constraints on sequential bargaining in an artificial perishable goods market

In this paper we test some hypotheses about the formation of prices through sequential bilateral bargaining on a perishable goods market under the assumption of behavioural learning by buyers and sellers. We constructed a multi-agent simulation model based on a survey concerning the fruit and vegetables market in Marseille, France. In our model, the agents bargain the price of a perishable good. The representation of agents' rationality is inspired by a literature relative to markets of perishable goods (Kirman [6] [7] and Rouchier [18] [19] [20]) as well as on artificial bargaining (Brenner[2], Weisbuch[22]). We study the influence of three parameters (the sellers' initial beliefs concerning the buyers' willingness to pay, the time spent by buyers on the market, and the heterogeneity in the sellers' limit value) on the evolution of prices and of agents' representations of others agents. We compare our results with empirical observations and some existing literature on bargaining. We find that our assumptions concerning the learning process give consistent results and lead the transactions prices to converge toward the sellers' limit value.

Bargaining with endogenous information

This paper analyses information acquisition in ultimatum bargaining with common values. Because of an endogenous lemons problem the equilibrium payoffs of the agents are non-monotonic in the information cost. The mere possibility of information acquisition can cause no trade although the agents maintain symmetric information in equilibrium and the gain from trade is common knowledge. The agent responding to a take-it-or-leave-it offer may capture some or even the full trading surplus in a perfect Bayesian equilibrium. The implications for sequential bargaining are discussed.

Basel II: A Contracting Perspective

Financial safety nets are incomplete social contracts that assign responsibility to various economic sectors for preventing, detecting, and paying for potentially crippling losses at financial institutions. Basel II forces signatory countries to reopen safety-net bargaining across affected sectors. This paper uses the theories of incomplete contracts and sequential bargaining to interpret the Basel Accords as a framework for endlessly renegotiating minimal duties and standards of safety-net management across the community of nations. Modelling the stakes and stakeholders represented by different regulators helps us to understand that inconsistencies were bound to exist in prior understandings about the range of sectoral effects that the 2004 Basel II agreement might produce. The analysis seeks to explain why, in the U.S., attempting to resolve what turned out to be intolerable inconsistencies spawned an embarrassingly fractious debate and repeatedly pushed back Basel II’s scheduled implementation.

Real Options, Sequential Bargaining Game and Network Effects in Natural Gas Production

This paper addresses a common problem in the petroleum industry, using techniques of real options in a cooperative game setting. It has the added twist of a network effect that encourages early development. In the model, two natural gas producers have adjacent undeveloped land with uncertain reserves. They must decide when to develop (drill and connect) their fields. In addition, one or both of them must build a gas processing plant to remove corrosive and toxic impurities, to make the gas suitable for entering a pipeline. Then, they must induce a pipeline company to build a gathering system to take their gas to market. There is a real option for both producers to delay until they have suitable price and reserves conditions. But, there are incentives to be the first mover who can also build a gas plant to its own specifications and locational preference. This gives a first mover advantage that encourages early development. Also, there is a beneficial network effect from encouraging the follower to enter immediately and reduce the unit toll cost needed to induce the pipeline builder to enter. Thus, the first mover has to decide when to build, what capacity to build and what processing lease rate to offer the second mover. We believe that the problem is more general than the specific petroleum industry problem we model, insofar as it reflects a combination of real option theory to develop, coupled with competitive game theory between a leader and a follower in the development of a common-use asset and cooperative game theory between the leader and the follower to capture a network effect.

Regularity of pure strategy equilibrium points in a class of bargaining games

We develop an index theory for the Stationary Subgame Perfect (SSP) equilibrium set in a class of n-player $(n\ge 2)$ sequential bargaining games with probabilistic recognition rules. For games with oligarchic voting rules (a class that includes unanimity rule), we establish conditions on individual utilities that ensure that for almost all discount factors, the number of SSP equilibria is odd and the equilibrium correspondence lower-hemicontinuous. For games with general, monotonic voting rules, we show generic (in discount factors) determinacy of SSP equilibria under the restriction that the agreement space is of dimension one. For non-oligarchic voting rules and agreement spaces of higher finite dimension, we establish generic determinacy for the subset of SSP equilibria in pure strategies. The analysis also extends to the case of fixed delay costs. Lastly, we provide a sufficient condition for uniqueness of SSP equilibrium in oligarchic games.

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).

Analysis on the Parameters of the Evolving Artificial Agents in Sequential Bargaining Game

Over the past few years, a considerable number of studies have been conducted on modeling the bargaining game using artificial agents on within-model interaction. However, very few attempts have been made at study on the interaction and co-evolutionary process among heterogeneous artificial agents. Therefore, we present two kinds of artificial agents, based on genetic algorithm (GA) and reinforcement learning (RL), which play a game on between-model interaction. We investigate their co-evolutionary processes and analyze their parameters using the analysis of variance.

Collective bargaining under perfect information. The negotiation of national agreements

We structurally estimate a perfect information bargaining model of collective negotiations using data on national agreements for Spain. The model is a stochastic model of sequential bargaining in which we allow for the possibility of negotiations ending without agreement, a common feature in the data. Delays in equilibrium are the result of uncertainty about the surplus to be divided among the players and not of information asymmetries. The model fits the data well regardless of the limitations imposed by the parametric specification adopted. Our results show that agents are patient and that the advantage from proposing is large.

Bounded rationality in laboratory bargaining with asymmetric information

Summary. This paper reports an experiment on two-player sequential bargaining with asymmetric information that features some forces present in multi-round monopoly pricing environments. Buyer-seller pairs play a series of bargaining games that last for either one or two rounds of offers. The treatment variable is the probability of continuing into a second round. Equilibrium predictions do a poor job of explaining levels of prices and treatment effects. As an alternative to the conventional equilibrium model, we consider models that allow for bounded rationality of subjects. The quantal response equilibrium model captures some of the important features of the results.

Communication, Reputation, and Punishment in Sequential Bargaining Experiments

Experiments on sequential bargaining have shown that subjects' behavior is far from the equilibrium prediction. Whereas previous models explain these deviations by some kind of social preferences, we investigate an alternative interpretation of behavior based on the assumption of bounded rational self-interest. Our analyses reveal that, in line with this interpretation, bargaining outcomes depend on subjects' payoff consequences from punishment. However, after preplay communication, we find a much weaker effect of these payoff consequences and a tremendous increase in the number of equal splits. This communication effect can be attributed to reputation effects only to a minor degree, if at all.

Bargaining Outcomes as the Result of Coordinated Expectations

Experimental studies of two-person sequential bargaining demonstrate that the concept of subgame perfection is not a reliable predictor of actual behavior. Alternative explanations argue that fairness influences outcomes and that bargainer expectations matter and are likely not to be coordinated at the outset. This study examines the process by which bargainers in dyads coordinate their expectations on a bargaining convention and how this convention is supported by the seemingly empty threat of rejecting positive but small subgame perfect offers. To organize the data from this experiment, a Markov model of adaptive expectations and bounded rationality is developed. The model predicts actual behavior quite closely.