Independence of irrelevant expansions

Nash characterized the only bargaining solution to satisfy a well-known list of axioms. Independence of Irrelevant Alternatives states invariance of the solution outcome under certain contractions of the bargaining problem. A dual of this axiom is proposed here, stating invariance under certainexpansions of the bargaining problem andNash's solution is characerized by substituting this axiom for IIA in Nash's original list. After a transposition from the domain of bargaining solutions to the domain of choice rules, and a weakening of Invariance with respect to Positive Affine Transformations toTranslation Invariance, this new list of axioms is shown to characterizeUtilitarian rules.     

Multi-attribute decision-making in individual and social choice

This paper provides an analysis of individual and social decision criteria for alternatives that are composed of several attributes. We derive additive and multiplicative criteria for individual decision-making with new axioms and apply these criteria to obtain new justifications of known social choice rules with a bargaining interpretation, namely the generalized utilitarian and Nash social choice functions. Unlike most axiomatizations of bargaining solutions, our approach is, to a large extent, based on the multi-attribute structure of the underlying alternatives and the resulting individual decision criteria instead of axioms that impose restrictions on the choice function directly.     

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.     

Labor unions and Nash bargaining using coalition formation games

In this paper we examine the properties of stable coalitions under sequential and simultaneous bargaining by competing labor unions. We do this using the Nash bargaining solution and various notions of stability, namely, Nash, coalitional, contractual and core stability.     

Bargaining with nonanonymous disagreement: Decomposable rules

We analyze bargaining situations where the agents’ payoffs from disagreement depend on who among them breaks down the negotiations. We model such problems as a superset of the standard domain of Nash (1950). We first show that this domain extension creates a very large number of new rules. In particular, decomposable rules (which are extensions of rules from the Nash domain) constitute a nowhere dense subset of all possible rules. For them, we analyze the process through which “good” properties of rules on the Nash domain extend to ours. We then enquire whether the counterparts of some well-known results on the Nash (1950) domain continue to hold for decomposable rules on our extended domain. We first show that an extension of the Kalai-Smorodinsky bargaining rule uniquely satisfies the Kalai and Smorodinsky (1975) properties. This uniqueness result, however, turns out to be an exception. We characterize the uncountably large classes of decomposable rules that survive the Nash (1950), Kalai (1977), and Thomson (1981) properties.     

Bargaining with nonanonymous disagreement: Decomposable rules

We analyze bargaining situations where the agents’ payoffs from disagreement depend on who among them breaks down the negotiations. We model such problems as a superset of the standard domain of Nash (1950). We first show that this domain extension creates a very large number of new rules. In particular, decomposable rules (which are extensions of rules from the Nash domain) constitute a nowhere dense subset of all possible rules. For them, we analyze the process through which “good” properties of rules on the Nash domain extend to ours. We then enquire whether the counterparts of some well-known results on the Nash (1950) domain continue to hold for decomposable rules on our extended domain. We first show that an extension of the Kalai–Smorodinsky bargaining rule uniquely satisfies the Kalai and Smorodinsky (1975) properties. This uniqueness result, however, turns out to be an exception. We characterize the uncountably large classes of decomposable rules that survive the Nash (1950), Kalai (1977), and Thomson (1981) properties.     

Relative impatience determines preference between contract bargaining and repeated bargaining

In this paper we consider the effect of the `impatience ratio' I (of the worker discount factor to the firm discount factor) on the preferences of the players between two bargaining schemes in an asymmetric information wage bargaining context. The firm has private information about the worker's value and the worker makes wage demands. In the contact bargaining scheme, a wage demand which is accepted in one period is binding for all future periods (and hence the bargaining ends after acceptance of a wage demand). In the repeated bargaining scheme, the parties continue to bargain irrespective of whether the worker has been hired or not, and any accepted wage demand is only valid for the period in which it was accepted. We establish the following results under the assumption that the worker's value is uniformly distributed on an interval: When the firm is more patient than the worker (I<1) both parties prefer contract bargaining, and when the worker is more patient than the firm (I >1) both prefer repeated bargaining. For any value of I, the preferred type of bargaining gives the lower unemployment.  The work of Bae has already shown that when players are equally patient (I=1) the players are indifferent between the two schemes, regardless of the distribution of the worker's value. This paper shows that Bae's indifference result (Bae, 1991) cannot be extended to unequally patient players. Received: December 1996/Final version: October 1998     

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.     

Scale changes and shared information in bargaining: An experimental study

This paper reports one of a series of experiments designed to test aspects of various game-theoretic models of bargaining. The results of this experiment consolidate those of previous experiments, which are first reviewed. The principal new result of this experiment is the observation, under conditions of partial information, of systematic violations of the axiom of independence of equivalent utility representations. The adequacy of various theories of bargaining to describe the observed data is also tested and discussed.     

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.     

The price of fairness with the extended Perles–Maschler solution

In Nash bargaining problem, due to fairness concerns of players, instead of maximizing the sum of utilities of all players, an implementable solution should satisfy some axioms or characterizations. Such a solution can result in the so-called price of fairness, because of the reduction in the sum of utilities of all players. An important issue is to quantify the system efficiency loss under axiomatic solutions through the price of fairness. Based on Perles–Maschler solution of two-player Nash bargaining problem, this paper deals with the extended Perles–Maschler solution of multi-player Nash bargaining problem. We give lower bounds of three measures of the system efficiency for this solution, and show that the lower bounds are asymptotically tight.     

The Kalai-Smorodinsky bargaining solution with loss aversion

We consider bargaining problems under the assumption that players are loss averse, i.e., experience disutility from obtaining an outcome lower than some reference point. We follow the approach of Shalev (2002) by imposing the self-supporting condition on an outcome: an outcome z in a bargaining problem is self-supporting under a given bargaining solution, whenever transforming the problem using outcome z as a reference point, yields a transformed problem in which the solution is z.We show that n-player bargaining problems have a unique self-supporting outcome under the Kalai-Smorodinsky solution. For all possible loss aversion coefficients we determine the bargaining solutions that give exactly these outcomes, and characterize them by the standard axioms of Scale Invariance, Individual Monotonicity, and Strong Individual Rationality, and a new axiom called Proportional Concession Invariance (PCI). A bargaining solution satisfies PCI if moving the utopia point in the direction of the solution outcome does not change this outcome.     

二人谈判问题

本文避开了Nash谈判公理,根据实际情况建立了支付可转让和支付不可转让两类谈判问题模型,并通过引入谈判因子,给出了类似的谈判解.     

Bargaining and negative externalities

Two important issues in distributive bargaining theory are, first, the conditions under which a negotiation breakdown occurs, and second, what and how source of parties’ bargaining powers influences the properties of a possible agreement. Research based on classic Nash’s demand game has explored both questions by sophisticating the original game a lot. As an attempt to deal with both issues under a simpler framework, we propose a modification of the Nash demand game in which bargainers suffer negative externalities proportional to the share of the surplus captured by their rival. It is shown that the negotiator experiencing a relatively high externality level has greater bargaining power and thus, appropriates a larger proportion of the surplus at stake. However, if externality levels are sufficiently high, bargaining powers become incompatible and a negotiation breakdown emerges from the bargaining process. We compare our results with the previous literature, and argue that they can be especially relevant in negotiations held under highly polarized environments.     

Collective bargaining: A differential game

Earlier differential game models of collective bargaining deal only with the strike phase. The model proposed here allows for negotiations without and with a strike.This paper is based on research supported by NSF under Grant No. GP-24205.     

Delay in the alternating-offers model of bargaining

Alternating offers bargaining has been extensively used to model two-sided negotiations. The celebrated model of Rubinstein [Econometrica 50(1):97–109, 1982] has provided a formal justification for equitable payoff division. A typical assumption of these models under risk is that the termination event means a complete and irrevocable breakdown in negotiations. In this paper, the meaning of termination is reinterpreted as the imposition to finish negotiations immediately. Specifically, bargaining terminates when the last offer becomes definitive. While Rubinstein’s model predicts an immediate agreement with stationary strategies, we show that the same payoff allocation is attainable under non-stationary strategies. Moreover, the payoffs in delayed equilibria are potentially better for the proposer than those in which agreement is immediately reached.     

A characterization of a limit solution for finite horizon bargaining problems

We investigate a two-person random proposer bargaining game with a deadline. A bounded time interval is divided into bargaining periods of equal length and we study the limit of the subgame perfect equilibrium outcomes as the number of bargaining periods goes to infinity while the deadline is kept fixed. This limit is close to the discrete Raiffa solution when the time horizon is very short. If the deadline goes to infinity the limit outcome converges to the time preference Nash solution. Regarding this limit as a bargaining solution under deadline, we provide an axiomatic characterization.     

Delay of Payments for Extraordinary Purchases

This paper considers the problem of a vendor attempting to dispose of unanticipated inventory levels through an offer to a prospective buyer of a credit-period within which no payment is required. For each party, a decision rule is developed in the form of a feasibility range beyond which the offer is not acceptable. Then, the interaction between the decision rules associated with each party is analysed. This includes a bargaining range of the different combinations of credit-period and extra-stock acceptable to both parties. In addition, a profit-sharing ratio is computed as a measure of the competitive advantage or disadvantage that the respective cost-profit structures provide to each side.     

非对称心理压力下的低碳环境友好技术国际转移博弈研究

在全球积极应对和适应气候变化的背景下,研究了心理压力和信息条件因素对低碳环境友好技术(LCEFT)转让企业与受让企业决策行为的影响。通过引入对谈判区间、还价策略和不同心理压力的假设,构造了非对称信息下的LEFCT转移讨价还价博弈模型,深入分析了收益贴现参数、心理压力参数和谈判区间等因素对博弈双方报价策略、还价策略以及成交价格所产生的影响。研究表明,心理压力和信息条件都会直接影响博弈双方的报价策略、还价策略和最终的成交价格,并得出了不同信息条件下受让企业“见好就收”和“对半侃价”的还价策略。本文为受让企业在应对全球气候变化中面对不同的心理压力和信息条件所应采取何种还价策略提供了一定的决策支持。     

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.