This is a paperback edition of a major contribution to the field, first published in hard covers in 1977. The book outlines a general theory of rational behaviour consisting of individual decision theory, ethics, and game theory as its main branches. Decision theory deals with a rational pursuit of individual utility; ethics with a rational pursuit of the common interests of society; and game theory with an interaction of two or more rational individuals, each pursuing his own interests in a (...) rational manner. (shrink)

When von Neumann's and Morgenstern's Theory of Games and Economic Behavior appeared in 1944, one thought that a complete theory of strategic social behavior had appeared out of nowhere. However, game theory has, to this very day, remained a fast-growing assemblage of models which have gradually been united in a new social theory - a theory that is far from being completed even after recent advances in game theory, as evidenced by the work of the three Nobel Prize winners, John (...) F. Nash, John C. Harsanyi, and Reinhard Selten. Two of them, Harsanyi and Selten, have contributed important articles to the present volume. This book leaves no doubt that the game-theoretical models are on the right track to becoming a respectable new theory, just like the great theories of the twentieth century originated from formerly separate models which merged in the course of decades. For social scientists, the age of great discover ies is not over. The recent advances of today's game theory surpass by far the results of traditional game theory. For example, modem game theory has a new empirical and social foundation, namely, societal experiences; this has changed its methods, its "rationality. " Morgenstern (I worked together with him for four years) dreamed of an encompassing theory of social behavior. With the inclusion of the concept of evolution in mathematical form, this dream will become true. Perhaps the new foundation will even lead to a new name, "conflict theory" instead of "game theory. (shrink)

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)

The Nash-Harsanyi theory of bargaining is usually taken as the correct theory of rational bargaining, and, as such, as the correct theory for the basic political contract for a society. It grafts a theory of cooperation to a base that essentially articulates the perspective of non-cooperative interaction. The resultant theory is supposed make clear how rational bargaining can fully realize the mutual gains that cooperation can make possible. However, its underlying commitment to the concepts of (...) non-cooperative interaction renders this doubtful. I argue for an alternative theory—the theory of Full Cooperation—that avoids this difficulty. As applied to bargaining over the basic political contract, it calls for the selection of the most egalitarian of the Strictly Pareto-Optimal outcomes. This is essentially a version of Rawls’ principle of Justice as Fairness, but it is derived, unlike Rawls’ theory, without appeal to a problematic theory of individual decision-making behind the veil of ignorance. It also provides an alternative basis for what Hart calls the Principle of Mutual Restrictions, and what Rawls’ calls the Duty of Fair Play. (shrink)

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)

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.

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 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)

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)

Contemporary discussions of the positive relation between rational choice and moral theory are a special case of a much older tradition that seeks to show that mutual agreement upon certain moral rules works to the mutual advantage, or in the interests, of those who so agree. I make a few remarks about the history of discussions of the connection between morality and self-interest, after which I argue that the modern theory of rational choice can be naturally understood as a continuation (...) of this older tradition. I then go on to argue for a controversial three-fold thesis: (1) that grounding a theory of morality in terms of rational self-interest is the only epistemologically respectable way to proceed with the justification of moral principles; (2) that despite this, most of the contemporary explorations of rational choice foundations for moral principles do not work—that the models of rational choice to which they appeal yield less than the substantial results that they are intended to yield; but (3) that if one rethinks just what it means to be rational, one can find in fact a promising way to connect the two—specifically through the development of a theory of genuinely cooperative activity. (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)

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 (...) class='Hi'>Nash bargaining solution based on this condition, and we also provide a decision-theoretic characterization of the concept of risk aversion for losses. (shrink)

In his recent book,Rational Behaviour and Bargaining Equilibrium In Games and Social Situations, John C. Harsanyi devotes a chapter to his new theory of morality, which he calls ‘Critical Rule Utilitarianism’, and which contains his solution to the problem of the interpersonal comparison of utility. After a detailed exposition of his theory, arguments will be presented to show that:there are certain formal difficulties in the solution that he offers which leads to a rejection of the axiom that there (...) is to be agreement between an individualj’s personal preferences and individuali’s (i ≠j) extended utility function out of which the social welfare function is to be constructed; andHarsanyi’s theory of critical rule utilitarianism cannot be accepted as a theory of morality because it presupposes a more fundamental theory in its actual construction. (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)

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)

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.

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)

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.

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)

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)

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)

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)

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.

The most important analytical tool in non-cooperative game theory is the concept of a Nash equilibrium, which is a collection of possibly mixed strategies, one for each player, with the property that each player's strategy is a best reply to the strategies of the other players. If we do not go into normative game theory, which concerns itself with the recommendation of strategies, and focus instead entirely on the positive theory of prediction, two alternative interpretations of the Nash (...) equilibrium concept are predominantly available.In the more traditional one, a Nash equilibrium is a prediction of actual play. A game may not have a Nash equilibrium in pure strategies, and a mixed strategy equilibrium may be difficult to incorporate into this interpretation if it involves the idea of actual randomization over equally good pure strategies. In another interpretation originating from Harsanyi, see also Rubinstein, and Aumann and Brandenburger, a Nash equilibrium is a ‘consistent’ collection of probabilistic expectations, conjectures, on the players. It is consistent in the sense that for each player each pure strategy, which has positive probability according to the conjecture about that player, is indeed a best reply to the conjectures about others. (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.

“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)

We add a stage to Nash’s demand game by allowing the greedier player to revise his demand if the demands are not jointly feasible. If he decides to stick to his initial demand, then the game ends and no one receives anything. If he decides to revise it down to 1-x\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1-x$$\end{document}, where x is his initial demand, the revised demand is implemented with certainty. The implementation probability changes linearly between these (...) two extreme cases. We derive a condition on the feasible set under which the two-stage game has a unique subgame perfect equilibrium. In this equilibrium, there is first-stage agreement on the egalitarian demands. We also study two n-player versions of the game. In either version, if the underlying bargaining problem is “divide-the-dollar,” then equal division is sustainable in a subgame perfect equilibrium if and only if the number of players is at most four. (shrink)

The publication in English of Karl R. Popper's The Logic of Scientific Discovery twenty-five years after the appearance of the German original, is an important event. At the time when many philosophers questioned the cognitive value of scientific hypotheses , Popper has shown how to reconcile the free use of bold explanatory hypotheses with an insistence on empirical testing. Many of Popper's views have now been accepted even by most of his earlier opponents, which is no small tribute to a (...) philosopher who had challenged an important current of opinion. But, though the basic aspects of Popper's theory have attracted considerable attention in recent years, some of his finer points have received insufficient discussion. It is hoped that the publication of this important book in English translation will now help to remedy this situation. (shrink)

"Teaching College Students How to Solve Real-Life Moral Dilemmas" will speak to the sometimes confounding, real-life, moral challenges that quarterlife students actually face each and every day of their lives. It will spell out an original, all-inclusive approach to thinking about, and applying, ethical problem-solving that takes into consideration people's acts, intentions, circumstances, principles, background beliefs, religio-spiritualities, consequences, virtues and vices, narratives, communities, and the relevant institutional and political structures. This approach doesn't tell students exactly what to do as much (...) as it evokes important information in order to help them think more deeply and expansively about ethical issues in order to resolve actual ethical dilemmas. There is no text like it on the market today. "Teaching College Students How to Solve Real-Life Moral Dilemmas" can be used in a variety of ethics courses. (shrink)

With a focus on the areas of theory, literature, culture, society and film, this collection of essays examines, questions and broadens the applicability of Postcolonialism and Islam from a multifaceted and cross-disciplinary perspective.Topics covered include the relationship between Postcolonialism and Orientalism, theoretical perspectives on Postcolonialism and Islam, the position of Islam within postcolonial literature, Muslim identity in British and European contexts, and the role of Islam in colonial and postcolonial cinema in Egypt and India. At a time at which Islam (...) continues to be at the centre of increasingly heated and frenzied political and academic deliberations, Postcolonialism and Islam offers a framework around which the debate on Muslims in the modern world can be centred.Transgressing geographical, disciplinary and theoretical boundaries, this book is an invaluable resource for students of Islamic Studies, Cultural Studies, Sociolgy and Literature. (shrink)

The purpose of this paper is to show how some of the controversial questions concerning utilitarianism can be clarified by the modelling techniques and the other analytical tools of decision theory (and, sometimes, of game theory). It is suggested that the moral rules of utilitarian ethics have a logical status similar to that of the normative rules (theorems) of such formal normative disciplines as decision theory and game theory.The paper argues that social utility should be defined, not in hedonistic or (...) in ideal-utilitarian terms, but rather in terms of individual preferences, in accordance with the author's equiprobability model of moral value judgments. (shrink)