Axiomatic Bargaining Theory Research Articles

Bargaining and the dynamics of divisional norms

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.

On Non-Cooperative Foundation and Implementation of the Nash Solution in Subgame Perfect Equilibrium via Rubinstein's Game

The alternating offers game due to Rubinstein (1982) had been used by Binmore (1980) and by Binmore et.al. (1986) to provide via its unique subgame perfect equilibrium an approximate non-cooperative support for the Nash bargaining solution of associated cooperative two-person bargaining games. These results had strengthened the prominent role of the Nash bargaining solution in cooperative axiomatic bargaining theory and its application, for instance in labor markets, and have often even be interpreted as a mechanism theoretical implementation of the Nash solution. Our results in the present paper provide exact non-cooperative foundations first, in our Proposition, via weakly subgame perfect equilibria of a game that is a modification of Rubinstein´s game, then in our Theorem, via sub-game perfect equilibria of a game that is a further modification of our first game. Moreover, they provide a general rule how to transform approximate support results into exact ones. Finally, we discuss the relation of the above mentioned support results, including our present ones, with mechanism theoretic implementation in (weakly) subgame perfect equilibrium of the Nash solution. There we come to the conclusion that a sound interpretation as an implementation can hardly be found except in very rare cases of extremely restricted domains of players´ preferences.

Judicial precedent as a dynamic rationale for axiomatic bargaining theory

Axiomatic bargaining theory (e.g., Nash’s theorem) is static. We attempt to provide a dynamic justification for the theory. Suppose a judge or arbitrator must allocate utility in an (infinite) sequence of two-person problems; at each date, the judge is presented with a utility possibility set in R 2 . He/she must choose an allocation in the set, constrained only by Nash’s axioms, in the sense that a penalty is paid if and only if a utility allocation is chosen at date T that is inconsistent, according to one of the axioms, with a utility allocation chosen at some earlier date. Penalties are discounted with t and the judge chooses any allocation, at a given date, that minimizes the penalty he/she pays at that date. Under what conditions will the judge’s chosen allocations converge to the Nash allocation over time? We answer this question for three canonical axiomatic bargaining solutions—Nash, Kalai–Smorodinsky, and “egalitarian”—and generalize the analysis to a broad class

Fairness Strategies for Wireless Resource Allocation Among Autonomous Multimedia Users

Recent research in wireless multimedia streaming has focused on optimizing the multimedia quality in isolation, at each station. However, the cross-layer transmission strategy deployed at one station impacts and is impacted by the other stations, as the wireless network resource is shared among all competing users. Hence, efficient and fair resource management for autonomous wireless multimedia users becomes very important. We consider quality-based fairness schemes based on axiomatic bargaining theory, which can ensure that the autonomous multimedia stations incur the same drop in multimedia quality as compared to a maximum achievable quality for each wireless station. Implementing this quality-based fairness solution in the time-varying channel condition requires high-computational complexity and communication overheads. Hence, we develop solutions that significantly reduce the computational complexity and communication overheads. Our simulations show that the proposed game-theoretic resource management can indeed guarantee desired utility-fair allocations when wireless stations deploy different cross-layer strategies.

A Bargaining Theoretic Approach to Quality-Fair System Resource Allocation for Multiple Decoding Tasks

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> In this paper, we propose a new resource allocation framework for multimedia systems that perform multiple simultaneous video decoding tasks. We jointly consider the available system resources (e.g., processor cycles) and the video decoding task's characteristics such as the sequence's content, the bit-rate, and the group of pictures (GOP) structure, in order to determine a fair and optimal resource allocation. To this end, we derive a quality-complexity model that determines the quality [in terms of peak signal-to-noise ratio (PSNR)] that a task can achieve given a certain system resource allocation. We use these quality-complexity models to determine a quality-fair and Pareto-optimal resource allocation using the Kalai–Smorodinski Bargaining Solution (KSBS) from axiomatic bargaining theory. The KSBS explicitly considers the resulting multimedia quality when performing a resource allocation and distributes quality-domain penalties proportional to the difference between each video decoding task's maximum and minimum quality requirements. We compare the KSBS with other fairness policies in the literature and find that, because it explicitly considers multimedia quality, it provides significantly fairer resource allocations in terms of the resulting PSNR compared with policies that operate solely in the resource domain. To weight the quality impact of the resource allocations to the different decoding tasks depending on application-specific requirements or user preferences, we generalize the existing KSBS solution by introducing bargaining powers based on each video sequence's motion and texture characteristics. </para>

Dynamic approach to solving bargaining games

The article examines the solution of bargaining games on the basis of the previously proposed paradigm of stationary strategies in supergames. The value of axiomatic bargaining theory for choosing the unique solution in agreement games is considered. The “splitting the dollar” game for two and three players is discussed as an application.

Equity considerations in health care: the relevance of claims.

The general issues of equity and efficiency are central to the analysis of resource allocation problems in health care. We examine them using axiomatic bargaining theory. We study different solutions that have been proposed and relate them to previous literature on health care allocation. In particular, we focus on the solutions based on axiomatic bargaining with claims, and show that they are appealing as distributive criteria in health policy. Finally, we present the results of a survey that tries to elicit moral intuitions of people about resource allocation problems and their different solutions.

Equity Considerations in Health Care: An Axiomatic Bargaining Approach

The general issues of equity and efficiency are placed at the center of the analysis of resource allocation problems in health care. We examine them using axiomatic bargaining theory. We study different solutions that have been proposed and relate them to previous literature on health care allocation. In particular, we focus on the solutions based on axiomatic bargaining with claims and suggest that they may be particularly appealing as distributive criteria in health policy. Finally, we present the results of a survey that tries to elicit moral intuitions of people about resource allocation problems and their different solutions.

Collective choice functions on non-convex problems

Collective choice problems on sets in \({\frak R}_+^n\) arise naturally in economics. Such problems have been extensively studied both in the theory of revealed preferences (Peters and Wakker, 1991) and in axiomatic bargaining theory under the assumption of convexity. However, our knowledge of collective choice functions on non-convex problems is still patchy. In this paper I study the existence and characterisation of continuous choice functions on the domain \(\Gamma\) of comprehensive problems. The main result completely characterises rational choice functions that are continuous and satisfy Weak Pareto Optimality: they form the class of Monotone Path Choice Functions on \(\Gamma\). I also show that any discontinuous rational and weakly Pareto optimal choice function must be non- anonymous.

Revealed group preferences on non-convex choice problems

This paper studies the conditions under which the basic results of the revealed preference theory can be established on the domain of choice problems which include non-convex feasible sets; the exercise is closely related to the works of Peters and Wakker (1991) and Bossert (1994). We show that while no continuous choice function can satisfy strong Pareto optimality over the class of all compact and comprehensive choice problems, strong Pareto optimality, Arrow's choice axiom, upper hemicontinuity and a weak compromisation postulate turn out to be necessary and sufficient to represent choice correspondences by continuous, strictly increasing and quasiconcave real-valued functions. Some applications of our main findings to axiomatic bargaining theory are also studied.

An Inquiry into Well-Being and Destitution

Part 1 Well-being - theory and realization: the commodity basis of well-being political morality and the state the object of social contracts well-being - from theory to measurement appendix - political and civil rights indices. Part 2 Allocation of resources among households - the standard theory: resource allocation mechanisms public goods and common property resources decentralization and central guidance real national income as a measure of general well-being uncertainty, insurance and social norms. Part 3 The household and its setting - extensions of the standard theory: land, labour, savings and credit households and credit constraints poverty and the environmental resource base net national product in a dynamic economy food, care and work - the household as an allocation mechanism axiomatic bargaining theory fertility and resources - the household as a reproductive unit strategic complementarities in fertility decisions population and savings - normative considerations classical utilitarianism in a limited world food needs and work capacity adaptation to nourishment inequality, malnutrition and the disenfranchised analysis of allocation mechanisms when nutrition affects productivity incentives and development policies. Subject index: agrarian reform food subsidies employment guarantee schemes and rural infrastructure community participation and credit facilities health and education envoi.

On the Interpretation of Nonsymmetric Bargaining Solutions and Their Extension to Nonexpected Utility Preferences

In a recent paper, Rubinstein, Safra, and Thomson reexamine the foundations of the axiomatic bargaining theory as formulated by Nash. In it they reinterpret the Nash bargaining solution and extend it to a family of nonexpected utility preferences, providing an interpretation of this solution concept and an axiomatization by means of a suitable translation of Nash axioms. This paper extends the work of these authors to the family, characterized by Kalai, of nonsymmetric solutions that appear from the Nash bargaining solution when the symmetry axiom is dropped. This extension requires an axiom relating the solution outcomes of isomorphic games. Journal of Economic Literature Classification Number: C78.

The bargaining problem without convexity: Extending the egalitarian and Kalai-Smorodinsky solutions

We relax the assumption used in axiomatic bargaining theory that the feasible set be convex. Instead we require only that it be 7 comprehensive. We show that on this domain, Kalai's (1977) characterization of the egalitarian solution remains true, as does Kalai and Smorodinsky's (1975) theorem if we use weak Pareto optimality.

Axiomatic bargaining theory on economic environments

Axiomatic bargaining theory is reexamined by focusing upon the economic exhange environment instead of the traditional utility possibility set. It is argued that the axioms of the traditional theory impose stronger restrictions than can be supported by their motivating economic intuitions. Weaker alternative axioms, making explicit use of economic information, are used to characterize the standard bargaining solutions. A key idea is to impose consistency of the solution with respect to changes in the dimension of the commodity space. Even these weaker economic axioms, however, may be unrealistic restrictions to impose on the bargaining solution in the context of many economic bargaining problems.

A note on additive utility and bargaining

Necessary and sufficient conditions are given under which a decision maker's von Neumann-Morgenstern utility function on the Cartesian product of two prospect spaces can be expressed as a sum of coordinate utility functions, assuming that all preferences are given. A main motivation for this result is an application in axiomatic bargaining theory.