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A new mechanism for resolving bargaining impasses between risk averse parties
Abstract
In a sequential bargaining game framework with complete information and no discounting, this paper proposes a mechanism in the spirit of a final offers arbitration (FOA). At each step, two parties may stop negotiating in order to implement a lottery between the two cur-rent proposals or go on making new proposals. A crucial difference with the FOA is that the list of past proposals is recorded and used by the mechanism. Once a lottery has been implemented, the parties can reject the offer which has been drawn and go back to a lottery between pro-posals made in the past. At the dominant subgame perfect equilibrium the two parties make gradual concessions leading to a final agreement which coincides with the Raiffa solution. The main incentive to reach an agreement comes from risk-aversion. The necessity to make step by step concessions generates evolving disagreement points and gradualism.
... This result has been confirmed recently in the framework of bargaining theory by Manzini and Mariotti (2001). In the opposite case in which a judge or an arbitrator does not have a preferred outcome to impose on the parties, we show in a companion paper (Tanimura and Thoron (2008)) that the chilling effect is maximized under COA and FOA. Then, the role of the arbitrator is reduced to splitting the pie into two equal halves in the case of the COA or to flipping a coin in the case of the FOA. ...
... Indeed, it is precisely in such situations that negotiation is useful. In Tanimura and Thoron (2008) we propose a new mechanism, ROC (Recursive Offer Conciliation). In a game theoretical framework, we show that ROC gives the parties to a negotiation the incentive to make concessions until they reach an agreement. ...
... When the players want to avoid the arbitration, for example because there is a small cost of arbitration or a small discounting, they reach the agreement at the last step. Otherwise, they call for an arbitration with non compatible but close proposals (Tanimura and Thoron 2008). Result 10 and 11 show that in the asymmetric treatment, the ROC procedure does better than the Free procedure in helping the subjects to reach the agreements which are closest to the ESS. ...
We run a series of experiments to compare the well known arbitration scheme FOA (Final Offer Arbitration) with a new arbitration scheme, non compulsory, we proposed in a companion paper (Tanimura and Thoron (2008)): ROC (Recursive Offer Conciliation). The two mechanisms are also compared with a negotiation without arbitration. We observe that the ROC mechanism seems to cumulate the advantages of the two other procedures, it avoids the high frequency of impasses observed under the FOA procedure and it is as efficient as the Free procedure in this respect. Furthermore, in an asymmetric treatment, it helps the subjects to find an agreement around the equal split of the surplus, like the arbitrator of the FOA procedure does, but without imposing anything on them.
This paper provides a non-cooperative foundation for (asymmetric generalizations of) the continuous Raiffa solution. Specifically, we consider a continuous-time variation of the classic Ståhl–Rubinstein bargaining model, in which there is a finite deadline that ends the negotiations, and in which each player’s opportunity to make proposals is governed by a player-specific Poisson process, in that the rejecter of a proposal becomes proposer at the first next arrival of her process. Under the assumption that future payoffs are not discounted, it is shown that the expected payoffs players realize in subgame perfect equilibrium converge to the continuous Raiffa solution outcome as the deadline tends to infinity. The weights reflecting the asymmetries among the players correspond to the Poisson arrival rates of their respective proposal processes.
We provide a new characterization of the n-person Nash bargaining solutions which does not involve Nash’s independence of irrelavant alternatives axiom, but mainly uses axioms which concern changes in the disagreement point and leave the feasible set fixed. The main axiom requires a convex combination of a disagreement point and the corresponding solution point to give rise to that same solution point. Further, we describe how the disagreement point approach can be applied to other bargaining solutions. The main result of the latter part is a first characterization of the so-called continuous Raiffa solution.
Final-offer arbitration is a procedure for settling disputes between two parties in which an arbitrator chooses the final offer of the party closest to what he considers a fair settlement. This procedure is modeled as a two-person, zero-sum game of imperfect information, in which the parties are assumed to know the probability distribution of the arbitrator's fair settlements and to make bids in an infinite strategy space that maximize their expected payoffs. Necessary and sufficient conditions for there to be local and global equilibria in pure strategies are derived, and necessary conditions for mixed strategies in a particular case are found. Such equilibria, when they exist in pure strategies, represent bids which are symmetric about the median and, for most common distributions, are separated from one another by two or more standard deviations. This finding suggests that final-offer arbitration may not accomplish its avowed purpose of inducing the two parties to converge on what they perceive to be the arbitrator's median fair settlement.
This paper studies the settlements generated by several variants of a compulsory-arbitration scheme called ``final-offer arbitration'' (FOA). Some of these are now in use in several states, and one has been recommended by Clifford Donn as an improvement on existing schemes. Under reasonable economic assumptions, two versions of FOA now being used are equivalent to imposing z̄, the settlement the arbitrator would impose in conventional compulsory arbitration would impose in conventional compulsory arbitration, a result contrary to the intent of the FOA statues. However, a simple modification of Donn's proposal leads to a scheme that generates Pareto-efficient settlements that are at least as good for each agent as z̄. This suggests that substantial gains in welfare could be realized by a simple change in existing FOA statues and possibly also by using the new procedure in situations where compulsory arbitration is not now prescribed by law.
Corruption in the public sector erodes tax compliance and leads to higher tax evasion. Moreover, corrupt public officials abuse their public power to extort bribes from the private agents. In both types of interaction with the public sector, the private agents are bound to face uncertainty with respect to their disposable incomes. To analyse effects of this uncertainty, a stochastic dynamic growth model with the public sector is examined. It is shown that deterministic excessive red tape and corruption deteriorate the growth potential through income redistribution and public sector inefficiencies. Most importantly, it is demonstrated that the increase in corruption via higher uncertainty exerts adverse effects on capital accumulation, thus leading to lower growth rates.
Two players have to reach an agreement on the partition of a pie of size 1. Each has to make in turn, a proposal as to how it should be divided. After one player has made an offer, the other must decide either to accept it, or to reject it and continue the bargaining. Several properties which the players' preferences possess are assumed. The Perfect Equilibrium Partitions (P.E.P.) are characterized in all the models satisfying these assumptions. Specially, it is proved that when every player bears a fixed bargaining cost for each period (c1 and c2), then: (i) if c_{1}>c_{2}(1-\delta _{2})/(1-\delta _{1}\delta _{2})$.
A model of the final-offer arbitration (FOA) process is developed, and the Nash equilibrium pair of final offers is derived. It is shown that the more risk-averse party submits a more reasonable offer so that it has a higher probability of being chosen by the arbitrator. The contract zone of potential negotiated settlements is derived, and its size is shown to be directly related to the uncertainty of the parties concerning the arbitrators' preferences. However, the final offers of the parties diverge where there is increased uncertainty, so that there is a trade-off between the size of the contract zone and the extremity of arbitrated awards when negotiations do fail. Finally, it is shown that negotiated settlements under FOA are skewed against the more risk-averse party.
The Raiffa Solution to the Bargaining Problem, proposed in 1951, has several appealing properties, especially when viewed as a model of the negotiation process in an integrative bargaining situation. Unlike the well known solutions of Nash and Kalai-Smorodinsky, the Raiffa Solution has not been characterized by a set of axioms. We present two axiomatic characterizations of the Raiffa Solution. In addition, we present a new axiomatic characterization of the Kalai-Smorodinsky Solution.
In this concise book based on his Arne Ryde Lectures in 2002, Young suggests a conceptual framework for studying strategic learning and highlights theoretical developments in the area. He discusses the interactive learning problem; reinforcement and regret; equilibrium; conditional no-regret learning; prediction, postdiction, and calibration; fictitious play and its variants; Bayesian learning; and hypothesis testing. Young's framework emphasizes the amount of information required to implement different types of learning rules, criteria for evaluating their performance, and alternative notions of equilibrium to which they converge. He also stresses the limits of what can be achieved: for a given type of game and a given amount of information, there may exist no learning procedure that satisfies certain reasonable criteria of performance and convergence. In short, Young has provided a valuable primer that delineates what we know, what we would like to know, and the limits of what we can know, when we try to learn about a system that is composed of other learners. Available in OSO:
This paper reports the results of a systematic experimental comparison of the effect of alternative arbitration systems on dispute rates. The key to our experimental design is the use of a common underlying distribution of arbitrator "fair" awards in the different arbitration systems. This allows us to compare dispute rates across different arbitration procedures where we hold fixed the amount of objective underlying uncertainty about the arbitration awards. There are three main findings. First, dispute rates are inversely related to the monetary costs of disputes. Dispute rates were much lower in cases where arbitration was not available so that the entire pie was lost in the event of dispute. Second, contrary to conventional wisdom, the dispute rate in a final-offer arbitration system is at least as high as the dispute rate in comparable conventional arbitration system. Third, dispute rates are inversely related to the uncertainty costs of disputes. Dispute rates were lower in conventional arbitration treatments where the variance of the arbitration award was higher and imposed greater costs on risk-averse negotiators. Our results can also be interpreted as providing tentative evidence that the negotiators were risk-averse on average.
This paper analyzes and compares arbitrator behavior under conventional and final-offer arbitration. Simple models of arbitrator behavior are developed under each of these alternative mechanisms. These models are estimated and tested using data on the outcomes of both forms of arbitrationin New Jersey, a state in which arbitration is mandatory for unresolved pay disputes involving police officer unions and public employers. The major findings are (1) that the high proportion of union victories under final-offer arbitration were generated by a set of impartial arbitrators applying the same standards used in conventional arbitration, and (2) that union bargainers appear to be considerably more risk averse than employer bargainers, with the wage increases under final-offer arbitration having a lower mean and a lower variance than under conventional arbitration.
This study develops two models of the behavior of interest arbitrators in which the arbitrator has some exogenous notion of an equitable settlement and yet is also influenced to some extent by the positions of the parties. The author argues that it is the arbitrator's notion of an equitable outcome that determines the positions of the parties, and empirical evidence suggesting that the arbitrator merely splits the difference is misleading. In fact, the parties are likely to position themselves around the expected arbitration award, suggesting that the expected arbitration outcome shapes the parties' bargaining positions rather than the reverse. There is nevertheless some truth to the notion that an arbitrator who is sensitive to the demands of the parties can chill bargaining. The author therefore proposes that the arbitration award be made independent of actual negotiating positions through a closed-offer mechanism. (Abstract courtesy JSTOR.)
This paper identifies a source of gradualism in bargaining andcontribution games. In the bargaining games we examine, each partycan opt out at any time, and the outside option outcome is assumed todepend on the offers made in the negotiation phase. Specifically, we assumethat (1) making a concession in the negotiation phase increases the otherparty's outside option pay-off and (2) the outside option outcome inducesan efficiency loss as compared with a negotiated agreement. The mainfinding is that the mere presence of such history-dependent outside optionsforces equilibrium concessions in the negotiation phase to be gradual,and the degree of gradualism is characterized. The model also applies tocontribution games in which the outside option may be interpreted as theoption to implement a partial project using the total contributions made sofar. Copyright The Review of Economic Studies Limited, 2004.
We develop and implement a collocation method to solve for an equilibrium in the dynamic legislative bargaining game of Duggan and Kalandrakis (2008). We formulate the collocation equations in a quasi-discrete version of the model, and we show that the collocation equations are locally Lipchitz continuous and directionally differentiable. In numerical experiments, we successfully implement a globally convergent variant of Broyden's method on a preconditioned version of the collocation equations, and the method economizes on computation cost by more than 50% compared to the value iteration method. We rely on a continuity property of the equilibrium set to obtain increasingly precise approximations of solutions to the continuum model. We showcase these techniques with an illustration of the dynamic core convergence theorem of Duggan and Kalandrakis (2008) in a nine-player, two-dimensional model with negative quadratic preferences.
This article examines the incentive effects of final-offer arbitration (FOA) when disputants have optimistic (i.e., biased) beliefs about the arbitrator's settlement preferences. Optimism is shown to increase the divergence in Nash equilibrium final offers, and the divergence is largest under naïve, rather than sophisticated, optimism. Therefore, though FOA rules were instituted to lessen the “chilling” effect of arbitration, FOA interacts with optimism to worsen the chilling effect. Data from controlled laboratory experiments confirm that optimism leads to more divergent final bargaining positions and higher dispute rates. These results highlight the role that de-biasing expectations can play in improving bargaining outcomes.
A two-person bargaining problem is considered. It is shown that under four axioms that describe the behavior of players there is a unique solution to such a problem. The axioms and the solution presented are different from those suggested by Nash. Also, families of solutions which satisfy a more limited set of axioms and which are continuous are discussed.
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07 file: mechanism.tex date
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imsart ver. 2006/03/07 file: mechanism.tex date: November 13, 2008