Multiple-issue bargaining and axiomatic solutions

We study two-person, multiple-issue bargaining problems and identify four procedures by which the bargaining may take place. Drawing on some logic from non-cooperative game theory, we propose axioms which relate the outcomes of the procedures. We also promote a weak monotonicity axiom on solutions, called issue-by-issue monotonicity, which is geared toward multiple-issue bargaining. Our main result concerns the relationship between a sequential bargaining procedure — with the rule that agreements are implemented only after all issues are resolved — and global bargaining (in which all issues are negotiated simultaneously). If a bargaining solution predicts the same outcome with these two procedures, then we say that it satisfiesagenda independence. We prove that a solution satisfies axioms of efficiency, symmetry, scale invariance, issue-by-issue monotonicity, and agenda independence if and only if it is the Nash solution. This result provides new intuition for Nash's independence of irrelevant alternatives axiom. Among other results, we show that a solution is invariant to all four of the procedures and satisfies efficiency and symmetry if and only if it is the utilitarian solution with equal weights. We comment on the results of other authors who address multiple-issue bargaining.     

Stable bargaining outcomes in patent licensing: A cooperative game approach without side payments

By formulating negotiations about licensing payments as cooperative games without side payments, we investigate stable bargaining outcomes in licensing a cost-reducing technology of an external patent holder to oligopolistic firms producing a homogeneous product under two policies: fee and royalty. The final bargaining outcome in fee licensing is uniquely determined, because the bargaining set for a coalition structure in which the patent holder can gain the maximum profit is a singleton. Under the royalty policy, the non-empty core for a coalition structure suggests that the patent holder should license his patented technology to all firms. Moreover, royalty licensing may be superior to fee licensing for the patent holder, when licensing is carried out through bargaining.     

Bargaining solutions at work: Qualitative differences in policy implications

Traditional bargaining theory characterizes solutions to bargaining problems by their properties in the utility space. In applications, however, one is usually interested in the implications of the conflict resolution within the economic environment, where the properties of axiomatic bargaining solutions are less well understood. By means of a standard bargaining model for the labor market we demonstrate that economic policy implications may be very sensitive to the choice of the bargaining solution. More specifically, the induced employment effects of a change in the reservation wage under the Nash-solution may differ substantially from those under the Kalai–Smorodinsky, the egalitarian, or the equal-loss solution. Hence, the choice of the bargaining solution is not innocuous, even if one is only interested in qualitative policy conclusions.     

多目标协商模型的标量化方法

多目标协商问题是协商理论的一个新的研究领域.本文讨论了由Bronisz和Krus提出的多目标协商模型和Bronisz-Krus-协商解概念,构造了由Bronisz-Krus多目标协商模型诱导的单目标协商模型并对其提出了一套公理系统和引入了Raiffa-协商解概念,讨论了诱导结局空间的性质,给出了Bronisz-Krus多目标协商模型与其诱导的单目标协商模型在某种意义下的等价性,即Bronisz-Krus-协商解与Raiffa-协商解可以互相确定,并给出了这种相互确定的关系式.     

Share the gain,share the pain? Almost transferable utility,changes in production possibilities,and bargaining solutions

We consider an n-person economy in which efficiency is independent of distribution but the cardinal properties of the agents’ utility functions may preclude transferable utility (a property we call “Almost TU”). Holding the disagreement point fixed, we show that Almost TU is a necessary and sufficient condition for all agents to either benefit jointly or suffer jointly with any change in production possibilities under well-behaved generalized utilitarian bargaining solutions (of which the Nash bargaining and the utilitarian solutions are special cases). We apply the result to policy analysis and to incentive compatibility.     

Uncovered bargaining solutions

An uncovered bargaining solution is a bargaining solution for which there exists a complete and asymmetric relation (tournament) such that, for each feasible set, the bargaining solution set coincides with the uncovered set of the tournament. We provide a characterization of a class of uncovered bargaining solutions.     

Over-investment in marriage-specific capital

We consider the decisions of a married couple in a risky environment. The distribution of spouses’ bargaining power may change as a result of new outside opportunities that become available to them, so that individual consumption may fluctuate over time. This is what we call “bargaining risk”. To reduce this risk, spouses may decide to over-invest in marriage-specific capital (which, by definition, is completely lost in the case of divorce) and thereby limit the attractiveness of spouses’ outside opportunities. This strategy is shown to be optimal. More surprisingly, over-investment in marriage-specific capital remains an optimal strategy when spouses are confronted with a (small) risk of divorce. This is in contrast to the usual intuition.     

Share the gain, share the pain? Almost transferable utility, changes in production possibilities, and bargaining solutions

We consider an n-person economy in which efficiency is independent of distribution but the cardinal properties of the agents’ utility functions may preclude transferable utility (a property we call “Almost TU”). Holding the disagreement point fixed, we show that Almost TU is a necessary and sufficient condition for all agents to either benefit jointly or suffer jointly with any change in production possibilities under well-behaved generalized utilitarian bargaining solutions (of which the Nash bargaining and the utilitarian solutions are special cases). We apply the result to policy analysis and to incentive compatibility.     

Fuzzy extensions of bargaining sets and their existence in cooperative fuzzy games

Recently, the concept of classical bargaining set given by Aumann and Maschler in 1964 has been extended to fuzzy bargaining set. In this paper, we give a modification to correct some weakness of this extension. We also extend the concept of the Mas-Colell's bargaining set (the other major type of bargaining sets) to its corresponding fuzzy bargaining set. Our main effort is to prove existence theorems for these two types of fuzzy bargaining sets. We will also give necessary and sufficient conditions for these bargaining sets to coincide with the Aubin Core in a continuous superadditive cooperative fuzzy game which has a crisp maximal coalition of maximum excess at each payoff vector. We show that both Aumann-Maschler and Mas-Colell fuzzy bargaining sets of a continuous convex cooperative fuzzy game coincide with its Aubin core.     

Bargaining on whales: A differential game model with pareto optimal equilibria

A two-country differential game model of whaling is used for analysing a dynamic bargaining problem. At a given initial time, the two countries may either continue on a noncooperative mood of play characterized by an open-loop Nash-equilibrium, or negotiate a bargaining solution which we define as the Kalaï-Smorodinsky solution. The cooperative solution calls for a restraint in the whaling efforts which leaves a temptation to cheat for any player. The model shows how, by announcing a credible threat, namely to make whaling an ‘open-access’ fishery, a country can eliminate this temptation to cheat and transform the cooperative solution into an equilibrium.     

Bargaining order and delays in multilateral bargaining with heterogeneous sellers

We consider a complete-information multilateral bargaining game in which a single buyer negotiates with two heterogeneous sellers selling perfect complementary units. While bilateral negotiations take place through a sequence of offers and counteroffers, the bargaining order is exogenously given. We solve for the conditions under which (a) the buyer prefers to negotiate with the lower-valuation seller first and (b) efficient (inefficient) outcomes emerge for the two bargaining orders. We find that the buyer prefers to negotiate with the lower-valuation seller first whenever the players are relatively impatient or the sellers are sufficiently heterogeneous. We show that there exists a unique efficient outcome when the buyer negotiates first with the lower-valuation seller and the sellers are sufficiently heterogeneous; however, significant delay in reaching agreements may arise when they are not. In case the buyer bargains with the higher-valuation seller first, an inefficient outcome is shown to exist even when players are extremely impatient.     

Sequential share bargaining

This paper presents a new extension of the Rubinstein-St?hl bargaining model to the case with n players, called sequential share bargaining. The bargaining protocol is natural and has as its main feature that the players’ shares in the surplus are determined sequentially rather than simultaneously. The protocol also assumes orderly voting, a restriction on the order in which players respond to a proposal. The bargaining protocol requires unanimous agreement for proposals to be implemented. Unlike all existing bargaining protocols with unanimous agreement, the resulting game has unique subgame perfect equilibrium utilities for any value of the discount factor. The result builds on the analysis of so-called one-dimensional bargaining problems. We show that also one-dimensional bargaining problems have unique subgame perfect equilibrium utilities for any value of the discount factor.     

An acyclic relation for comparison of bargaining powers of coalitions and its interrelationship with bargaining set

This paper proposes a method to compare bargaining power of coalitions within the framework of games in coalition form with transferable utility. The method is expressed by a relation on the set of all coalitions in a game, the relation which is defined based on the players’ bargaining power. It is shown in this paper that the newly defined relation satisfies acyclicity. Also, it is verified in this paper that the set of all individually rational payoff configurations under which all coalitions have the equal bargaining power coincides with the bargaining set. Some examples demonstrate how the newly proposed method works.     

All in good time

Why is issue-by-issue bargaining a common phenomenon, even though it disallows the beneficial trade-offs across issues that are possible when negotiating a global solution? We show that under asymmetric information, issue-by-issue bargaining has two attractive features. First, it avoids bundling a good deal on one issue with a bad deal on another issue, when the lack of gains to agreement on the latter is not a priori common knowledge. Second, it avoids the imposition of the asymmetric information inefficiency of “harder” issues on issues which turn to be “easier” to solve. That’s why when the agenda is not imposed on the parties but is rather left for them to determine when negotiating, they may very well opt for issue-by-issue bargaining. We demonstrate this in a natural game where bargainers communicate, whenever they choose to do so, their willingness to discuss or make offers either on one of the issues or on a bundle of issues.     

The semireactive bargaining set of a cooperative game

The semireactive bargaining set, a solution for cooperative games, is introduced. This solution is in general a subsolution of the bargaining set and a supersolution of the reactive bargaining set. However, on various classes of transferable utility games the semireactive and the reactive bargaining set coincide. The semireactive prebargaining set on TU games can be axiomatized by one-person rationality, the reduced game property, a weak version of the converse reduced game property with respect to subgrand coalitions, and subgrand stability. Furthermore, it is shown that there is a suitable weakening of subgrand stability, which allows to characterize the prebargaining set. Replacing the reduced game by the imputation saving reduced game and employing individual rationality as an additional axiom yields characterizations of both, the bargaining set and the semireactive bargaining set. Received September 2000/Revised version June 2001     

Two-player bargaining problems with unilateral pre-donation

This paper characterizes conditions for two-player bargaining problems and bargaining rules under which unilateral pre-donation always yields Pareto utility gains. The paper also computes the optimal pre-donation of each player under the class of proportional bargaining rules.     

A Note on Multi-Issue Bargaining with a Finite Set of Alternatives

We extend the results of van Damme et al. (1990) and Muthoo (1991) to two bilateral multi-issue bargaining)procedures with complete information and endogenous agenda, where each issue is associated with a finite set of alternatives. We show that in the first procedure (issue-by-issue bargaining), the stationary subgame perfect equilibria alone may support a large multiplicity of inefficient agreements. Confronting a recent study, the results for the second procedure imply that it is not necessary to appeal to “strictly controversial” issues in a bargaining problem in order to find multiplicity and delay in agreements     

运输问题的合作对策求解方法

产地间或销地间往往存在竞争,在这种情况下,使用运输问题最优化方法是不合理的。因此,从个体理性的视角提出运输问题的合作对策求解方法,方法将运输问题看作是一个博弈问题,各个产地或销地是博弈的局中人,求解其纳什均衡与纳什讨价还价解。在此基础上,说明了运输问题的非合作形式是一个指派问题,并证明指派问题的最优解是一个纳什均衡点。接着,通过实验验证运输问题的最优解是一个纳什讨价还价解,满足产地或销地的自身利益。在此基础上,针对纳什讨价还价解不唯一的问题,从决策者的视角给出最大可能激励成本的计算方法。最后,为弥补纳什讨价还价解不唯一及纳什讨价还价解不允许出现子联盟的缺陷,给出运输收益分配或成本分摊的Shapely值计算方法。     

A bargaining set for monotonic simple games based on external and internal stability

A new bargaining set based on notions of both internal and external stability is developed in the context of endogenous coalition formation. It allows one to make an explicit distinction between within-group and outside-group deviation options. This type of distinction is not present in current bargaining sets. For the class of monotonic proper simple games, the outcomes in the bargaining set are characterized. Furthermore, it is shown that the bargaining set of any homogeneous weighted majority game contains an outcome for which the underlying coalition structure consists of a minimal winning coalition and its complement.