Bargaining Solutions as Social Compromises

A bargaining solution is a social compromise if it is metrically rationalizable, i.e., if it has an optimum (depending on the situation, smallest or largest) distance from some reference point. We explore the workability and the limits of metric rationalization in bargaining theory where compromising is a core issue. We demonstrate that many well-known bargaining solutions are social compromises with respect to reasonable metrics. In the metric approach, bargaining solutions can be grounded in axioms on how society measures differences between utility allocations. Using this approach, we provide an axiomatic characterization for the class of social compromises that are based on p-norms and for the attending bargaining solutions. We further show that bargaining solutions which satisfy Pareto Optimality and Individual Rationality can always be metrically rationalized.     

Loss Aversion and Bargaining

We consider bargaining situations where two players evaluate outcomes with reference-dependent utility functions, analyzing the effect of differing levels of loss aversion on bargaining outcomes. We find that as with risk aversion, increasing loss aversion for a player leads to worse outcomes for that player in bargaining situations. An extension of Nash's axioms is used to define a solution for bargaining problems with exogenous reference points. Using this solution concept we endogenize the reference points into the model and find a unique solution giving reference points and outcomes that satisfy two reasonable properties, which we predict would be observed in a steady state. The resulting solution also emerges in two other approaches, a strategic (non-cooperative) approach using Rubinstein's (1982) alternating offers model and a dynamic approach in which we find that even under weak assumptions, outcomes and reference points converge to the steady state solution from any non-equilibrium state.     

Bargaining with reasonable aspirations

Consider bargaining situations with two persons, where both have a specific idea of what would be an equitable outcome. In case these ideas differ, a procedure is needed which leads to a compromise between the different views. In the present paper the axioms of restricted homogeneity and of relative monotonicity are introduced, each of which, together with other standard conditions, allows one to determine a solution for this class of bargaining problems. An extension of this solution to bargaining problems with more than two persons is formulated.     

The role of risk preferences in bargaining when acceptance of a proposal requires less than unanimous approval

The role of risk preferences in determining the outcome to bargaining is examined for the case in which acceptance of a proposal requires less than unanimous approval. Using an n-agent extension of the Ståhl-Rubinstein alternating offer model, we find that risk preferences play a fundamentally different role when bargaining is settled using a nonunanimity voting rule. Risk preferences determine not only an agent's reservation price but also the likelihood that he is made part of the winning coalition. An implication of this analysis is that when the preferences of the agents are not too diverse, it is advantageous for an agent to be relatively risk-averse.The helpful comments and suggestions of Rich McLean and an anonymous referee are gratefully acknowledged. This article was presented as a paper at the 1988 Winter Econometric Society Meetings.     

The Effects of Beliefs Versus Risk Attitude on Bargaining Outcomes

In bargaining environments with uncertain disagreement or “impasse” outcomes (e.g., litigation or labor strike outcomes), there is an identification problem that confounds data interpretation. Specifically, the minimally acceptable settlement value from a risk-averse (risk-loving) but unbiased-belief bargainer is empirically indistinguishable from what one could get with risk-neutrality and pessimistically (optimistically) biased beliefs. This article reports results from a controlled bargaining experiment where data on both risk attitude and beliefs under uncertainty are generated in order to assess their relative importance in bargaining experiment outcomes. The average lab subject is risk-averse, yet optimistic with respect to uncertainty, which is consistent with existing studies that examine each in isolation. I also find that the effects of optimism dominate those of risk-aversion. Optimistic bargainers are significantly more likely to dispute and have aggressive final bargaining positions. Dispute rates are not statistically affected by risk attitude, but there is some evidence that risk aversion leads to a weakened bargaining position. Though additional research is needed to understand the limits of extending these results, a key implication follows. In uncertainty environments where optimism dominates, increased settlement rates are more likely achieved by minimizing impasse uncertainty (to limit the potential for optimism) rather than maximizing uncertainty (to weaken the reservation point of risk-averse bargainers), as has been argued in the dispute resolution literature.      

Now or Later?--Endogenous Timing of Threats

Whereas early threats are chosen before bargaining, late threats are determined after bargaining ended in conflict. Instead of exogenously imposing the timing of threats, these are derived endogenously as in indirect evolution or endogenous timing. Based on a duopoly market, we first derive the equilibrium for all possible constellations regarding the timing of threats. Our analysis surprisingly justifies the early timing of threats as suggested by Nash (1953).     

Guaranteed Renewability with Group Insurance

This paper investigates a multiple-period level premium insurance policy equilibrium in a model in which loss probabilities increase for a fixed time period for a set of persons buying insurance in a group. We show that a level-premium sequence which induces risk averse persons to become and remain members of the group exists. We also show that the availability of the Medicare program can prevent the emergence of optimal level-premium private group insurance, but that a system of bonuses for remaining in the group can permit optimality to be retained.     

The effect of computer intervention and task structure on bargaining outcome

This paper reports on a study that examined the impact of computer presentation of suggested solutions during negotiation, in bargaining situations that can be characterized as integrative or distributive. It was found that in the integrative task, the bargainers achieved higher joint outcomes when presented with suggestions. They had a more negative perception of the negotiation atmosphere, however. In the distributive task, the suggestions did not help achieve joint gains, but it lessened negative attitudes of the bargainers. Bargainers who received suggestions felt both they and their partner had been somewhat more flexible, cooperative, considerate, and less suspicious. Thus, regardless of negotiation situation, the suggestions resulted in some benefit to the negotiators.     

Regular updating

This article presents a new model aimed at predicting behavior in games involving a randomized allocation procedure. It is designed to capture the relative importance and interaction between procedural justice (defined crudely in terms of the difference between one’s expected payoff and average expected payoff in the group) and distributive justice (difference between own and average actual payoffs). The model is applied to experimental games, including “randomized” variations of simple sequential bargaining games, and delivers qualitatively correct predictions. In view of the model redistribution of income can be seen as a substitute for vertical social mobility. This contributes to the explanation of greater demand for redistribution in European countries vis-a-vis the United States. I conclude with suggestions for further verification of the model and possible extensions.     

Competing allocation principles: time for compromise?

A small set of allocation principles is said to be behind several theories of distributive justice. However, disagreement about the appropriate relationship between these notions remains, so that compromises between principles may generate more agreement. Truncated utilitarianism is a prominent candidate. It demands maximising total wealth subject to a floor level of individual wealth for all people. Based on some well-known distributive notions, we developed a questionnaire setting and confronted student respondents with corresponding allocation problems, where an exogenously given poverty line served as a floor. However, support for allocations resulting from this specific interpretation of truncated utilitarianism remained rather low. This is surprising because the respective solution was close to an equal split of resources, and aspects of efficiency and responsibility were explicitly introduced to promote more general acceptance. We argue that people may either wish to see higher floor levels or are more inequality averse than probably expected. Moreover, high support for an unconditional consideration of the poverty line can be witnessed, even though aspects of responsibility, but not efficiency arguments, display an influence. In general, attitudes with respect to the equality?Cefficiency trade-off are found to remain heterogeneous, although different equality concerns are prominent. Furthermore, trade-offs are moderated by the responsibility principle.     

Two-person sequential bargaining behavior with exogenous breakdown

We examine bargaining behavior in a noncooperative game in which players alternate in making and responding to proposals over the division of a given surplus. Although the number of bargaining periods is unlimited and time is not discounted, the bargaining is subject to exogenous breakdown at each period with a fixed probability which is common knowledge. We manipulate three probabilities of break-down in a between-subjects design that allows comparison with previous studies of two-person bargaining with time discounting. Assuming that subjects maximize expected utility, and this utility is measured by monetary payoffs, our results reject both the subgame perfect equilibrium and equal split solutions. Data analyses reveal that a substantial percentage of subjects behave adaptively in that they systematically search for the highest acceptable demands.     

教育程度与分配公平感:结构地位与相对剥夺视角下的双重考察

基于结构决定与相对剥夺的两种视角,本文研究发现了教育程度对收入分配公平感的复杂影响路径。教育程度作为优势性地位获得,对分配公平感存在正向影响。教育程度越高,收入分配公平感越强。但这种正向影响也存在条件性：教育作为个人地位投资,激发相应的回报期待,随着基于教育投入的期待收入与实际收入差距的扩大,这种正向影响会降低,且教育程度越高,降低的幅度越大。这一条件性的发现有利于解释既有研究的矛盾结论,具有重要的社会意涵：当教育投资作为“制度化手段”无法实现地位获得这一“文化目标”时,这种“断裂”可能会引发“分配不公”的心理失范。     

Moral structures and axiomatic theory

Axiomatic decision theory has proven to be a valuable analytical tool in many disciplines, and in this paper I discuss its application to moral theory. The first part of the paper discusses the general structure of moral theory, and it argues that morality need not be identified with a particular moral principle. The concept of a moral framework is introduced, and a framework for use in analyzing issues of distributive justice is presented in the second section. The application of this framework is discussed in the paper's final section, and two different moral situations are analyzed. The utilitarian principle is argued to be appropriate for the first situation in which a scarce good is to be efficiently distributed, while Rawls' difference principle is claimed to be the correct one for the more abstract issue of basic institutional justice.     

SPECIAL ISSUE： DISTRIBUTION OF NATIONAL INCOME IN A TRANSITIONAL ECONOMY Changes in the labor share of GDP： a U-shaped curve

本文的目的在于探讨经济发展过程中,劳动份额在初次分配中演变的一般规律,以及当前导致中国初次分配中劳动份额不断下降的结构性因素。我们的研究发现,在世界各国的经济发展过程中,在初次分配中劳动份额变化趋势呈现U型规律,即劳动份额先下降后上升,转折点约为人均GDP6000美元（2000年购买力平价）。我们提出了一个解释u型规律的理论模型。这一发现为库兹涅茨“倒U曲线假说”提供了更深层次的解释。我们还发现,中国初次分配中劳动份额的变动趋势是基本符合这一规律的。除此之外,影响我国劳动份额的因素还包括产业结构的以及劳动者相对谈判能力的变化。这些发现意味着,中国经济未来两年在初次分配中劳动份额可能会进入上升通道,中央政府为应对世界性金融危机而采取的一些政策性、结构性调整则有助于加快这一进程。     

A Non-cooperative Axiomatization of the Core

We treat a class of multi-person bargaining mechanisms based on games in coalitional form. For this class of games we identify properties of non-cooperative solution concepts, which are necessary and sufficient for the equilibrium outcomes to coincide with the core of the underlying coalitional form game. We view this result as a non-cooperative axiomatization of the core. In contrast to most of the literature on multi-person bargaining we avoid a precise specification of the rules of the game. Alternatively, we impose properties of such games, which give rise to a large class of mechanisms, all of which are relevant for our axiomatization.     

The Basic Principles and Value Dimensions of Achieving Distributive Justice through Social Institutions

人类社会需要借助社会制度的合理设计和安排实现分配正义的价值目标。以实现分配正义为价值目标的社会制度建设应该遵循机会平等原则、利益与责任同等分配原则、分配标准与程序合理原则、纠正不公原则等四个分配正义原则。在这些原则基础上建构的社会制度具有内在公正性，能够保证社会资源的分配达到公正。以社会制度建设保障分配正义具有重要的现实意义，有助于一个社会将个人追求分配正义的个体意向性整合为集体意向性，形成审视分配正义问题的社会视角，树立平等主义分配正义观，更有效地保护伸张分配正义的行为和惩罚破坏分配正义的行为，并维护和增进强势群体和弱势群体的分配利益。     

Effects of fixed costs in two-person sequential bargaining

Rubinstein (1982) considered the problem of dividing a given surplus between two players sequentially, and then proposed a model in which the two players alternately make and respond to each other's offers through time. He further characterized the perfect equilibrium outcomes, which depend on the players time preferences and order of moves. Using both equal and unequal bargaining cost conditions and an unlimited number of rounds, two experiments were designed to compare the perfect equilibrium model to alternative models based on norms of fairness. We report analyses of final agreements, first offers, and number of bargaining rounds, which provide limited support to the perfect equilibrium model, and then conclude by recommending a shift in focus from model testing to specification of the conditions favoring one model over another.     

Simultaneous moves multi-person continuous time concession game

The alternating offers strategic bargaining approach (Rubinstein, 1982) suggest a unique perfect equilibrium. In this equilibrium the bargaining ends immediately and the outcome is Pareto optimal. In this paper we consider a bargaining game in which players move simultaneously. Since we allow players only to lower their demands over time we denote this game as a concession game. We demonstrate that in this game there is a perfect equilibrium in which the bargaining lasts long enough so that the pie shrinks to zero. We show that we can generalize this game to a multi-player concession game in a straightforward manner and so avoiding the difficulties of generalizing the alternating offers game to the multi-player case.     

Normalized measures of concavity and Ross’s strongly more risk averse order

The Arrow-Pratt (A-P) definitions of absolute and relative risk aversion dominate the discussion of risk aversion and defining “more risk averse”. Ross (Econometrica 49:621–663, 1981) notes, however, that being A-P more risk averse is not sufficient for addressing many important comparative static questions. Consequently he introduces “a new and stronger measure for comparing two agents’ attitudes towards risk…”. Ross does not provide a corresponding measure of risk aversion. This paper uses a normalized measure of concavity to characterize the Ross definition of strongly more risk averse on bounded intervals. Other properties and uses of these normalized measures of concavity are also presented.