Threshold Value: how binding thresholds affect the outcome of a negotiation

The objective of this paper is to give the prospective outcome or "prospect" of a negotiation when the players' value can only be realized if a certain threshold is reached. Thresholds can be of different forms such as a certain number of players, a certain coalition of players or a certain total level of contribution. A value is proposed, which is defined for a given game and a given threshold. It is derived from a decomposition of the Shapley value.threshold, commitment, Shapley value, coalition structures, weights

Which Acceptable Agreements are Equilibria?

I propose a normal form game of agreement formation in which each player's strategy is to say for each size of agreement whether it is acceptable or not. I propose a refinement, which guarantees that each one of these choices is self-enforcing. For general payoff functions, which exhibit positive externalities, I analyse situations in which symmetric players have the possibility to reach a unique agreement. I prove the uniqueness of this equilibrium. I give two specific examples: a cartel and an agreement to contribute to a public good.coalition formation, normal form games, agreement, cartel, environmental agreement, public good

Experimental comparison of compulsory and non compulsory arbitration mechanisms

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.negotiation; bargaining; arbitration; Raiffa solution; chilling effect; dispute resolution; experiments

A mechanism for solving bargaining problems between risk averse players

We propose a mechanism for resolving bargaining problems.The mechanism allows two players to make a sequence of simultaneous propositions. At any step, as long as the players have not reached an agreement, they can choose to implement a lottery between the different propositions. In this aspect, the mechanism is similar to the so called final others arbitration. However, contrary to the existing scheme, our mechanism is not compulsory. The history of the negotiation process is recorded and players can refuse an offer and go back in the process to a previous step. This generates an evolving sequence of status-quo points and results in a sequence of equilibrium others of the two play-ers that gradually converge towards each other. Our model assumes nodiscounting and complete information. Rather than time preferences, the main incentive to reach an agreement under our mechanism comes from risk aversion. Players have an incentive to avoid the uncertainty related to the lotteries that occur when offers do not result in an agreement. Rather than incomplete information, the process gradualism is driven by the necessity to make step by step concessions in order to generate evolving threat points. We show that under this mechanism, the unique subgame perfect equilibrium that does not use weakly dominated strategies coincides with a well-known static solution concept, the Raiffa solution.bargaining theory ; Raiffa bargaining solution ;risk aversion ; final offers arbitration ; chilling effect ; gradualism

Sign, then Ratify : Negotiating under Threshold Constraints

The procedure for implementing any international treaty necessarily involves two steps. The negotiation phase which culminates in the signature of the treaty is followed by a ratification phase. This last phase is governed by a rule which determines how far the ratification process has to advance before the treaty can come into effect. The purpose of this paper is to analyse, using a game theoretical approach, the possible consequences of this minimum participationrule for the ratification phase and for the negotiation phase. I consider the case of International Environmental Agreements in which, during the negotiation phase, the different parties have to decide on the level of a global target and on how to share the efforts necessary to reach it. I use a cooperative approach to define what is called the threshold value (T-value). For a given coalition of parties, the T-value gives the expected outcome of the negotiation oversharing a global target, when the parties take into account the minimum participation rule. Given this T-value, I use a non-cooperative approach to determine which coalition will sign the agreement and what will be its global target. The minimum participation constraint has in fact no impact on the ratification phase because it is always better to refuse to sign rather thanto sign and then refuse to ratify. However, I show that the minimum participation constraint can modify the outcome of the negotiation phase. Indeed, it plays a role in a mechanism which can be used by a coalition to signal its leadership commitment. I analyse the conditions under which, at the equilibrium, the leading coalition can provoke an expansion of the signingcoalition

Threshold Value: how binding thresholds affect the outcome of a negotiation

The objective of this paper is to give the prospective outcome or "prospect" of a negotiation when the players' value can only be realized if a certain threshold is reached. Thresholds can be of different forms such as a certain number of players, a certain coalition of players or a certain total level of contribution. A value is proposed, which is defined for a given game and a given threshold. It is derived from a decomposition of the Shapley value

Do binding agreements solve the social dilemma?

We investigate whether "binding agreements" can provide a solution to the social dilemma that arises in the presence of pure public goods. Signing a binding agreement can prevent players to free ride on the contributions to the public good. However, a well known theoretical result is that the outcome of the endogenous formation of agreements is not necessarily efficient. In our setting, the individual level of contribution to the public good increases with the size of the coalition reaching an agreement and the global agreement is always the socially optimal structure. Agreements form sequentially. The equilibrium outcome is an asymmetric structure, which consists of two coalitions of different sizes, the small one free riding on the contributions of the bigger one. In our experiment, we propose two treatments which differ in the degree of strategic uncertainty with which the subjects are faced. The results lend force to the theoretical conclusion that outcomes may be inefficient. The average gains achieved are sub-optimal. They are even lower than predicted by the equilibrium agreement structure in the treatment in which the strategic uncertainty is high. They are larger than predicted in the treatment in which the strategic uncertainty is limited. However, it seems that subjects "learn to cooperate" over time and reach the global agreement more often towards the end of sessions.

Experimental comparison of compulsory and non compulsory arbitration mechanisms

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

A mechanism for solving bargaining problems between risk averse players

We propose a mechanism for resolving bargaining problems.The mechanism allows two players to make a sequence of simultaneous propositions. At any step, as long as the players have not reached an agreement, they can choose to implement a lottery between the different propositions. In this aspect, the mechanism is similar to the so called final others arbitration. However, contrary to the existing scheme, our mechanism is not compulsory. The history of the negotiation process is recorded and players can refuse an offer and go back in the process to a previous step. This generates an evolving sequence of status-quo points and results in a sequence of equilibrium others of the two play-ers that gradually converge towards each other. Our model assumes nodiscounting and complete information. Rather than time preferences, the main incentive to reach an agreement under our mechanism comes from risk aversion. Players have an incentive to avoid the uncertainty related to the lotteries that occur when offers do not result in an agreement. Rather than incomplete information, the process gradualism is driven by the necessity to make step by step concessions in order to generate evolving threat points. We show that under this mechanism, the unique subgame perfect equilibrium that does not use weakly dominated strategies coincides with a well-known static solution concept, the Raiffa solution

Do binding agreements solve the social dilemma ?

We investigate whether "binding agreements" can provide a solution to the social dilemma that arises in the presence of pure public goods. By signing a binding agreement, players can prevent free riding by the contributors to a public good. However, a well known theoretical result is that the outcome of the endogenous formation of agreements is not necessarily efficient. In our setting, the individual level of contribution to the public good increases with the size of the coalition reaching an agreement and the global coalition is always the socially optimal structure. Agreements form sequentially and the equilibrium outcome is an asymmetric structure, which consists of two coalitions. Our experiment therefore lends force to the theoretical result that outcomes may be inefficient. In fact, we observe an outcome which is even less efficient than that predicted by the equilibrium agreement structure. However, it seems that when subjects reach agreements they do so with the intention of cooperating rather than free riding. Furthermore, it seems that they “learn to cooperate” over time and reach the global agreement more often towards the end of sessions.Keyword