It is argued that the Nash bargaining solution cannot serve as a principle of distributive justice because (i) it cannot secure stable cooperation in repeated interactions and (ii) it cannot capture our moral intuitions concerning distributive questions. In this article, I propose a solution to the first problem by amending the Nash bargaining solution so that it can maintain stable cooperation among rational bargainers. I call the resulting principle the stabilized Nash (...) class='Hi'>bargaining solution. The principle defends justice in the form 'each according to her basic needs and above this level according to her relative bargaining power'. In response to the second problem, I argue that the stabilized Nash bargaining solution can serve as a principle of distributive justice in certain situations where moral reasoning is reduced to instrumental reasoning. In particular, I argue that rational individuals would choose the stabilized Nash bargaining solution in Rawls' original position. (shrink)

The first-order condition of the Nash bargaining solution equates the ratio of utilities to the ratio of marginal utilities. It turns out that this common ratio plays a role in determining whether the Nash solution, roughly speaking, is “more utilitarian” or “more egalitarian.” More specifically, I propose a sense of proximity to utilitarianism and/or egalitarianism according to which, in bargaining problems with distinct utilitarian and egalitarian points, the Nash solution is closer to (...) utilitarianism if the aforementioned ratio is smaller than one, and closer to egalitarianism if that ratio is greater than one. (shrink)

In a recent article, McClennen (2012) defends an alternative bargaining theory in response to his criticisms of the standard Nash bargaining solution as a principle of distributive justice in the context of the social contract. McClennen rejects the orthodox concept of expected individual utility maximizing behavior that underlies the Nash bargaining model in favor of what he calls full rationality, and McClennen’s full cooperation bargaining theory demands that agents select the most egalitarian strictly (...) Pareto-optimal distributional outcome that is strictly Pareto-superior to the state of nature. I argue that McClennen’s full cooperators are best described as reasonable agents whose rationality is constrained by moral considerations and that McClennen’s bargaining theory is moralized in this regard. If, by contrast, the orthodox concept of rationality is assumed and plausible assumptions are made about human nature and social cooperation, then a modified version of the standard Nash bargaining solution, which I call the stabilized Nash bargaining solution (Moehler 2010), is justified. From the perspective of rational agents, the stabilized Nash bargaining solution can accommodate McClennen’s criticisms of the standard Nash bargaining solution in the context of the social contract and, for such agents, it can serve as a principle of distributive justice in deeply morally pluralistic societies. (shrink)

Skyrms has pointed out differences between the results of rational choice theory and evolutionary game theory. This commentary argues that there is a great deal of agreement on the Nash Bargaining Solution, which maximizes the product of player payoffs, in both rational-choice-based and evolution-based theories of equilibrium selection. While evolutionary game theory has the potential to explain how we arrive at the behavioural rules that govern what we do, realistic models will require calibration through laboratory experiments. Indeed, (...) experimental evidence strongly supports the Nash Bargaining Solution. (shrink)

We call a decision maker risk averse for losses if that decision maker is risk averse with respect to lotteries having alternatives below a given reference alternative in their support. A two-person bargaining solution is called invariant under risk aversion for losses if the assigned outcome does not change after correcting for risk aversion for losses with this outcome as pair of reference levels, provided that the disagreement point only changes proportionally. We present an axiomatic characterization of the (...) Nash bargaining solution based on this condition, and we also provide a decision-theoretic characterization of the concept of risk aversion for losses. (shrink)

We provide two alternative characterizations of the Nash bargaining solution. We introduce new simple axioms, strong undominatedness by the disagreement point, and egalitarian Pareto optimality. First, we prove that the Nash solution is characterized by symmetry, scale invariance, independence of irrelevant alternatives, and strong undominatedness by the disagreement point. Second, we replace the independence of irrelevant alternatives axiom with the sandwich axiom and egalitarian Pareto optimality. We then demonstrate that the Nash solution is (...) characterized by symmetry, scale invariance, strong undominatedness by the disagreement point, the sandwich axiom, and egalitarian Pareto optimality. (shrink)

In this paper we deal with the extension of Nash bargaining theory to nonconvex problems. By focussing on the Social Welfare Ordering associated with a bargaining solution, we characterize the symmetric Nash Bargaining Solution (NBS). Moreover, we obtain a unified method of proof of recent characterization results for the asymmetric single-valued NBS and the symmetric multivalued NBS, as well as their extensions to different domains.

Evolutionary accounts of morality consider behavior in rather simple scenarios. Evolutionary work on fairness focuses on the division of a windfall and, importantly, assumes that the positions of those involved are entirely symmetric. I consider more complicated strategic settings and find that there is a strong tendency for evolution to produce divisions consistent with the so-called Nash bargaining solution. I also uncover the evolutionary importance of comprehensiveness, an often-overlooked feature of division problems.

“Randomized dictatorship,” one of the simplest ways to solve bargaining situations, works as follows: a fair coin toss determines the “dictator”—the player to be given his first-best payoff. The two major bargaining solutions, that of Nash and that of Kalai and Smorodinsky, Pareto-dominate this process. However, whereas the existing literature offers axiomatizations of the Nash solution in which this ex ante domination plays a central role, it does not provide an analogous result for Kalai–Smorodinsky. This (...) paper fills in this gap: a characterization of the latter is obtained by combining the aforementioned domination with three additional axioms: Pareto optimality, individual monotonicity, and a weakened version of the Perles–Maschler super additivity axiom. (shrink)

Miyagawa (Games and Economics Behavior 41(2), 292–308 [2002]) provides a simple extensive game form that implements a large class of two-agent bargaining solutions in subgame-perfect equilibrium. This class includes all of the Nash, Kalai–Smorodinsky, and relative utilitarian solutions. This note extends Miyagawa’s result to multi-agent bargaining problems.

I state and prove formal versions of the claim that the Nash bargaining solution creates a compromise between egalitarianism and utilitarianism, but that this compromise is “biased”: the Nash solution puts more emphasis on utilitarianism than it puts on egalitarianism. I also extend the bargaining model by assuming that utility can be transferred between the players at some cost ; I use the extended model to better understand the connections between egalitarianism and utilitarianism.

For every 2-person bargaining problem, the Nash bargaining solution selects a point that is “between” the relative utilitarian point and the relative egalitarian point. Also, it is “between” the utilitarian and egalitarian points. I improve these bounds. I also derive a new characterization of the Nash solution which combines a bounds property together with strong individual rationality and an axiom which is new to Nash’s bargaining model, the sandwich axiom. The sandwich axiom (...) is a weakening of Nash’s IIA. (shrink)

I argue in this paper that there are two considerations which govern the dynamics of a two-person bargaining game, viz. relative proportionate utility loss from conceding to one's opponent's proposal and relative non-proportionate utility loss from not conceding to one's opponent's proposal, if she were not to concede as well. The first consideration can adequately be captured by the information contained in vNM utilities. The second requires measures of utility which allow for an interpersonal comparison of utility differences. These (...) considerations respectively provide for a justification of the Nash solution and the Kalai egalitarian solution. However, none of these solutions taken by themselves can provide for a full story of bargaining, since, if within a context of bargaining one such consideration is overriding, the solution which does not match this consideration will yield unreasonable results. I systematically present arguments to the effect that each justification from self-interest for respectively the Nash and the Kalai egalitarian solution is vulnerable to this kind of objection. I suggest that the search for an integrative model may be a promising line of research. (shrink)

In this note, I provide an axiomatic characterization of the relative utilitarian bargaining solution to Nash bargaining problems. The solution is obtained when Nash’s independence of irrelevant alternatives axiom is replaced by the weak linearity axiom, while retaining the other three axioms. RU maximizes the sum of proportional gains, or, equivalently, minimizes the sum of proportional losses. RU is scale invariant and compared to the Nash and Kalai and Smorodinsky solutions, it is ex (...) ante efficient when the bargaining problem is considered as a lottery of future bargaining problems. (shrink)

In this paper, we study the role of fairness motivation in bargaining. We show that bargaining between two strongly fairness motivated individuals who have different views about what represents a fair division may end in disagreement. Further, by applying the Nash bargaining solution, we study the influence of fairness motivation on the bargaining outcome when an agreement is reached. In particular, we show that the bargaining outcome is sensitive to the fairness motivation of (...) the two individuals, unless they both consider an equal division fair. We argue that our results accommodate existing experimental and field data on bargaining. (shrink)

Nick Bostrom and others have suggested treating decision-making under moral uncertainty as analogous to parliamentary decision-making. The core suggestion of this “parliamentary approach” is that the competing moral theories function like delegates to the parliament, and that these delegates then make decisions by some combination of bargaining and voting. There seems some reason to hope that such an approach might avoid standard objections to existing approaches (for example, the “maximise expected choiceworthiness” (MEC) and “my favourite theory” approaches). However, the (...) parliamentary approach is so far extremely underspecified, making it largely indeterminate how such a model will in fact behave in the respects that those concerned with moral uncertainty care about. This paper explores one way of making it precise. We treat predicaments of moral uncertainty as analogous to bargaining situations alone (setting aside voting), and apply a version of the Nash solution that is standard in bargaining theory. The resulting model does indeed perform in many of the hoped-for ways. However, so also does a version of MEC that employs a structural approach to intertheoretic comparisons. It seems to us an open question which, regarding this version of MEC and the bargaining-theoretic approach, is superior to the other. We identify the key points on which the two differ. (shrink)

Within this paper we consider a model of Nash bargaining with incomplete information. In particular, we focus on fee games, which are a natural generalization of side payment games in the context of incomplete information. For a specific class of fee games we provide two axiomatic approaches in order to establish the Expected Contract Value, which is a version of the Nash bargaining solution.

For contractarians, justice is the result of a rational bargain. The goal is to show that the rules of justice are consistent with rationality. The two most important bargaining theories of justice are David Gauthier’s and those that use the Nash’s bargaining solution. I argue that both of these approaches are fatally undermined by their reliance on a symmetry condition. Symmetry is a substantive constraint, not an implication of rationality. I argue that using symmetry to generate (...) uniqueness undermines the goal of bargaining theories of justice. (shrink)

We characterize equilibrium behavior in a finite horizon multiple-pie alternating offer bargaining game in which both agents have outside options and threat points. In contrast to the infinite horizon case the strength of the threat to delay agreement is non-stationary and decreases over time. Typically the delay threat determines equilibrium proposals in early periods, while the threat to opt out characterizes those in later ones. Owing to this non-stationarity both threats may appear in the equilibrium shares immediately agreed upon (...) in the first period. When the threat to opt out is empty for both agents, the outcome corresponds exactly with the (generalized) Nash bargaining solution. The latter observation may prove useful for designing experiments that are meant to test economic models that include a bargaining stage. (shrink)

This paper reconsiders Rubinstein's alternating-offer bargaining game with complete information. We define rationalizability and trembling- hand rationalizability (THR) for multi-stage games with observed actions. We show that rationalizability does not exclude perpetual disagreement or delay, but that THR implies a unique solution. Moreover, this unique solution is the unique subgame perfect equilibrium (SPE). Also, we reconsider an extension of Rubinstein's game where a smallest money unit is introduced: THR rules out the non-uniqueness of SPE in some particular (...) case. Finally, we investigate the assumption of boundedly rational players. Perpetual disagreement is excluded, but not delay. Furthermore, we cannot use the asymmetric Nash bargaining solution as an approximation of the alternating-offer bargaining model once the players are boundedly rational ones. (shrink)

Virtual bargaining theory suggests that social agents aim to resolve non-cooperative games by identifying the strategy profile which they would agree to play if they could openly bargain. The theory thus offers an explanation of how social agents resolve games with multiple Nash equilibria. One of the main questions pertaining to this theory is how the principles of the bargaining theory could be applied in the analysis of hypothetical bargaining in non-cooperative games. I propose a (...) class='Hi'>bargaining model based on the benefit-equilibrating bargaining solution concept for non-cooperative games, broadly in line with the principles underlying Conley and Wilkie's ordinal egalitarian solution for Pareto optimal point selection problems with finite choice sets. I provide formal characterizations of the ordinal and the cardinal versions of BES, discuss their application to n-player games, and compare model's theoretical predictions with the data available from several experiments involving `pie games'. (shrink)

My concern in this paper is with the illumination that the theory of rational bargaining sheds on the formulation of principles of justice. I shall first set out the bargaining problem, as treated in the theory of games, and the Nash solution, or solution F. I shall then argue against the axiom, labeled “independence of irrelevant alternatives,” which distinguished solution F, and also against the Zeuthen model of the bargaining process which F formalizes.

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. (shrink)

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. (shrink)

In 1986 David Gauthier proposed an arbitration scheme for two player cardinal bargaining games based on interpersonal comparisons of players’ relative concessions. In Gauthier’s original arbitration scheme, players’ relative concessions are defined in terms of Raiffa-normalized cardinal utility gains, and so it cannot be directly applied to ordinal bargaining problems. In this paper I propose a relative benefit equilibrating bargaining solution for two and n-player ordinal and quasiconvex ordinal bargaining problems with finite sets of feasible (...) basic agreements based on the measure of players’ ordinal relative individual advantage gains. I provide an axiomatic characterization of this bargaining solution and discuss the conceptual relationship between RBEBS and ordinal egalitarian bargaining solution proposed by Conley and Wilkie. I show the relationship between the measurement procedure for ordinal relative individual advantage gains and the measurement procedure for players’ ordinal relative concessions, and argue that the proposed arbitration scheme for ordinal games can be interpreted as an ordinal version of Gauthier’s arbitration scheme. (shrink)

Peter Vanderschraaf’s Strategic Justice provides a defense of the egalitarian bargaining solution. Vanderschraaf’s discussion of the egalitarian solution invokes three arguments typically given to support the Nash bargaining solution. Overall, we reinforce Vanderschraaf’s criticism of arguments in favor of the Nash solution and point to potential weaknesses in Vanderschraaf’s positive case for the egalitarian solution.

I raise a few questions about key points in the argument of Natural Justice. 1. The pivotal role assigned to the theory of indefinitely repeated games appears to be both implausible and unnecessary. 2. The evolutionary foundations of the Nash bargaining solution are not completely secure, and its role in the account of interpersonal comparisons of utility is questionable. 3. Free renegotiation behind the veil of ignorance appears neither to have an evolutionary rationale nor to be a (...) brute fact about the way men are. (shrink)

Courts frequently engage in the weighing of competing values; perhaps most obviously, such balancing constitutes an integral aspect of proportionality analysis in many states’ constitutional law. However, such balancing raises a difficult theoretical question: What does it mean that one value “outweighs” another in any particular case? If the values at issue are incommensurable — as they often will be — such balancing may appear to break down. As Justice Scalia has stated, balancing in the presence of incommensurable values “is (...) more like judging whether a particular line is longer than a particular rock is heavy.” It may appear that if a judge is asked in a particular case to decide, for example, whether a state interest is sufficiently strong to justify the limitation of a constitutional right, he will be forced to a) either abandon the notion of a genuine plurality of values, or b) make an arbitrary decision. This article argues that neither of these options need be accepted and that rational choice is indeed possible in the presence of incommensurable values. Specifically, it contends that the Nash bargaining solution provides a means, at least in certain circumstances, of rationally understanding and undertaking the weighing of distinct and mutually irreducible values which adjudication frequently requires. The Nash framework can both elucidate proportionality analysis by providing a social choice-based framework for understanding the structure of proportionality analysis and also justify proportionality analysis by demonstrating that the weighing of competing values is not necessarily mere judicial hand-waving. (shrink)

During the past two decades non-cooperative game theory has become a central topic in economic theory. Many scholars have contributed to this revolution, none more than John Nash. Following the publication of von Neumann and Morgenstern's book, it was Nash's papers in the early fifties which pointed the way for future research in game theory. The notion of Nash equilibrium is indispensable. Nash's formulation of the bargaining problem and the Nash bargaining solution (...) constitute the cornerstone of modern bargaining theory. His insights into the non-cooperative foundations of cooperative game theory initiated an area of research known as the Nash program. Nash's analysis of the demand game in which he uses a perturbation of a game to select an equilibrium inspired the construction of several refinements of the notion of Nash equilibrium. A scholar's influence does not necessarily qualify him for a Nobel prize. One may argue that such awards are a social institution established to serve social goals. It is legitimate to ask what message the Swedish Academy sends to the scientific community and the rest of the world. (shrink)

A generalization of the standard n-person game is presented, with flexible information requirements suitable for players constrained by bounded rationality. Strategies (complete contingency plans) are replaced by "policies," i. e., end-mean pairs of candidate goals and "controls" (partial contingency plans). The existence of individual objective functions over the joint policy choice set is axiomatized in terms of primitive preference and probability orders. Conditions are given for the existence of pure policy Nash equilibrium points in n-person games, and pure policy (...) Nash bargaining and equilibrium threat solutions in 2-person policy games. Connectedness of the policy and payoff sets is not required. (shrink)

offers an evolutionary approach to morality, in which moral rules form a cultural system that is robust and evolutionarily stable. The folk theorem is the analytical basis for his theory of justice. I argue that this is a mistake, as the equilibria described by the folk theorem lack dynamic stability in games with several players. While the dependence of Binmore's argument on the folk theorem is more tactical than strategic, this choice does have policy implications. I do not believe that (...) moral rules are solutions to the Nash bargaining problem. Rather, I believe that human beings are emotionally constituted, by virtue of their evolutionary history, to embrace prosocial and altruistic notions of in-group–out-group identification and reciprocity. These aspects of human nature are incompatible with Binmore's notion that humans are self-regarding creatures. I present empirical evidence supporting a specific form of human, other-regarding preferences known as strong reciprocity. Key Words: justice • ethics • folk theorem • evolutionary game theory. (shrink)

This paper critically reviews Ken Binmore’s non- utilitarian and game theoretic solution to the Arrow problem. Binmore’s solution belongs to the same family as Rawls’ maximin criterion and requires the use of Nash bargaining theory, empathetic preferences, and results in evolutionary game theory. Harsanyi has earlier presented a solution that relies on utilitarianism, which requires some exogenous valuation criterion and is therefore incompatible with liberalism. Binmore’s rigorous demonstration of the maximin principle for the first time (...) presents a real alternative to a utilitarian solution. (shrink)

In this study we introduce two new properties, the Midpoint Outcome on a Linear Frontier (MOLF) and Balanced Focal Point (BFP) properties, to replace the Weak Pareto Optimality (WPO), Symmetry (SYM) and Independence of Equivalent Utility Representations (IEUR) properties in the axiomatic characterizations of the two most prominent solution concepts, namely the Nash and Kalai/Smorodinsky solutions, respectively.

The question of what a group of rational agents would agree on were they to deliberate on how to organise society is central to all hypothetical social contract theories. If morality is to be based on a social contract, we need to know the terms of this contract. One type of social contract theory, contractarianism, aims to derive morality from rationality alone. Contractarians need to show, amongst other things, that rational and self-interested individuals would agree on an impartial division of (...) a cooperative surplus. But it is often claimed that contractarians cannot show this without introducing moral assumptions. This paper argues that on the right understanding of the question contractarians are asking, these worries can be answered. Without relying on moral assumptions, the paper offers a novel derivation of symmetry, which is the axiom responsible for the impartiality of the most famous economic bargaining solutions appealed to by contractarians. (shrink)

Collaboration is increasingly popular across academia. Collaborative work raises certain ethical questions, however. How will the fruits of collaboration be divided? How will the work for the collaborative project be split? In this paper, we consider the following question in particular. Are there ways in which these divisions systematically disadvantage certain groups? -/- We use evolutionary game theoretic models to address this question. First, we discuss results from O'Connor and Bruner (unpublished). In this paper, we show that underrepresented groups in (...) academia can be disadvantaged in such situations by dint of their small numbers. Second, we present novel results exploring how the hierarchical structure of academia can lead to bargaining disadvantage. We investigate models where one actor has a higher baseline of academic success, less to lose if collaboration goes south, or greater rewards for non-collaborative work. We show that in these situations, the less powerful partner is disadvantaged in bargaining over collaboration. (shrink)

Recently, philosophers have investigated the emergence and evolution of the social contract. Yet extant work is limited as it focuses on the use of simple behavioral norms in rather rigid strategic settings. Drawing on axiomatic bargaining theory, we explore the dynamics of more sophisticated norms capable of guiding behavior in a wide range of scenarios. Overall, our investigation suggests the utilitarian bargaining solution has a privileged status as it has certain stability properties other social arrangements lack.

Applying the solutions defined in the axiomatic bargaining theory to actual bargaining problems is a challenge when the problem is not described by its Utility Possibility Set (UPS) but as a social choice environment specifying the set of alternatives and utility profile underlying the UPS. It requires computing the UPS, which is an operational challenge, and then identifying at least one alternative that actually achieves the bargained solution’s outcome. We introduce the axioms of Independence of Non-Strongly-Efficient Alternatives (...) (resp. Weakly) and Independence of Redundant Alternatives. A solution satisfying these axioms can be applied to a simplified problem based on any reduced set of alternatives generating the strong (resp. weak) Pareto frontier of the initial problem, without changing the outcome, making the application of bargaining solutions to actual problems easier. We compare our axioms to usual independence axioms, and discuss their consistency with usual bargaining solutions. Then, we introduce monotonicity conditions corresponding to the existence of an interest group, i.e., agents ranking the alternatives in the same order. For such monotonic social choice environments, we provide a parameterized family of alternatives that generates the Pareto frontier of the bargaining problem, in line with our previous results. Our analysis illustrates that an axiomatic approach can be useful to foster the application of bargaining solutions, in complement to usual computational methods. (shrink)

Climate negotiations under the United Nations Framework Convention on Climate Change have so far failed to achieve a robust international agreement to reduce greenhouse gas emissions. Game theory has been used to investigate possible climate negotiation solutions and strategies for accomplishing them. Negotiations have been primarily modelled as public goods games such as the Prisoner’s Dilemma, though coordination games or games of conflict have also been used. Many of these models have solutions, in the form of equilibria, corresponding to possible (...) positive outcomes—that is, agreements with the requisite emissions reduction commitments. Other work on large-scale social dilemmas suggests that it should be possible to resolve the climate problem. It therefore seems that equilibrium selection may be a barrier to successful negotiations. Here we use an N-player bargaining game in an agent-based model with learning dynamics to examine the past failures of and future prospects for a robust international climate agreement. The model suggests reasons why the desirable solutions identified in previous game-theoretic models have not yet been accomplished in practice and what mechanisms might be used to achieve these solutions. (shrink)

Conventionalism as a distinct approach to the social contract received significant attention in the game-theoretic literature on social contract theory. Peter Vanderschraaf’s sophisticated and innovative theory of conventional justice represents the most recent contribution to this tradition and, in many ways, can be viewed as a culmination of this tradition. In this article, I focus primarily on Vanderschraaf’s defense of the egalitarian bargaining solution as a principle of justice. I argue that one particular formal feature of this (...) class='Hi'>bargaining solution, the baseline consistency requirement, may stand in tension with other features of conventionalism as an approach to the social contract and limit the scope of Vanderschraaf’s theory to societies in which de facto an egalitarian sense of justice evolves. It limits the scope of Vanderschraaf’s theory in the face of moral diversity. A similar limitation applies to Vanderschraaf’s theory of democratic political authority. Despite these minor limitations, Vanderschraaf’s theory can only be seen as a major success and significant contribution to social contract theory. (shrink)

Two agents endowed with different categorisations engage in bargaining to reach an understanding and agree on a common categorisation. We model the process as a simple non-cooperative game and demonstrate three results. When the initial disagreement is focused, the bargaining process has a zero-sum structure. When the disagreement is widespread, the zero-sum structure disappears and the unique equilibrium requires a retraction of consensus: two agents who individually associate a region with the same category end up rebranding it under (...) a different category. Finally, we show that this last equilibrium outcome is Pareto dominated by a cooperative solution that avoids retraction; that is, the unique equilibrium agreement may be inefficient. (shrink)

This paper provides an ethical intepretation of the Nash choice rule. In a setting in which (cardinal) utilities are interpersonally comparable, this procedure is characterised by an impartiality requirement and by the assumption that choices are not responsive to the agents' relative ability to convert resources into utility.

In Strategic Bargaining and Cooperation in Greenhouse Gas Mitigations, Zili Yang connects these two important approaches by incorporating various game theoretic solution concepts into a well-known integrated assessment model of climate ...

Men and women have always bargained for sex. In Hard Bargains, philosopher-lawyer Linda Hirshman and legal historian Jane Larson provide the first complete analysis of power in heterosexual relationships, combining an eye-opening legal history of sexual regulation with thought-provoking predictions of what the future might bring. Hirshman and Larson tell a riveting tale that spans the centuries--from early accounts of adulterers hanging from the gibbet, to the impact of the Kinsey Reports and Hugh Hefner's playboy philosophy, to the 1960s judge (...) who argued in favor of sex with eleven-year-olds. The book examines the factors that have shaped our notions of sex, from Catholic teaching to the theories of Sigmund Freud, and it explores the Supreme Court decisions of the last few decades that revolutionized the politics of sex. And Hard Bargains not only provides a deep understanding of historical and current disputes, it also offers striking predictions of what sexual bargaining will look like in the future--rape laws replaced by laws of sexual autonomy, adultery subjected to breach of contract action, fornicators responsible for each other's rent, prostitution considered an unfair labor practice. These are a few of the surprising--and surprisingly workable--solutions the authors foresee in the 21st century. Hard Bargains takes a forthright and level-headed look at all aspects of one of the biggest controversies in contemporary American society--heterosexual sex--and delivers a radically new perspective on the sexual lives of women and men. (shrink)