Risk Aversion in the Nash Bargaining Problem with ISHARA Utility Functions

Abstract:I examine from a conventionalist perspective the Nash bargaining problem that philosophers use as a tool for analyzing fair division. From this perspective, the solutions to bargaining problems are conventions that can emerge from inductive learning and focal point effects. I contrast the conventionalist approach to analyzing the bargaining problem with the better-known rational choice approach, which I criticize for having overly demanding epistemic presuppositions and for producing disappointing results. I apply a simple model of inductive learning to specific bargaining problems to show that agents can learn from repeated experience to follow a variety of bargaining conventions in a given problem. I conclude that such agents can come to regard two such conventions as focal for the bargaining problem, one that assigns claimants equal shares of a good and another egalitarian solution of equal payoff gains, and that the egalitarian solution tends to prevail when these two solutions differ. I conclude further that the above analysis lends support for admitting interpersonal utility comparisons into the analysis of fair division problems, and also suggests a focal point explanation of the wide acceptance of the Aristotelian proportionality principle of distributive justice.

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An extension of the Nash bargaining problem and the Nash social welfare function

Theory and Decision ◽

10.1007/bf00154358 ◽

1980 ◽

Vol 12 (2) ◽

pp. 135-148 ◽

Cited By ~ 58

Author(s):

Mamoru Kaneko

Keyword(s):

Social Welfare ◽

Social Welfare Function ◽

Bargaining Problem ◽

Nash Bargaining ◽

Nash Bargaining Problem

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Power Law with Exponential Cut‐off Utility

Metamorphosis ◽

10.1177/0972622520140105 ◽

2014 ◽

Vol 13 (1) ◽

pp. 26-32

Author(s):

Afreen Arif H. ◽

T.P.M. Pakkala

Keyword(s):

Risk Aversion ◽

Utility Function ◽

Power Law ◽

Risk Preferences ◽

Portfolio Allocation ◽

Utility Functions ◽

Relative Risk Aversion ◽

Optimal Solutions ◽

New Class ◽

Exponential Power

Most of the utility functions studied earlier concentrated on properties of risk aversion. In this article, the authors have introduced a new class of utility function called the Power Law with Exponential Cut-off (PLEC) utility function, which exhibits all the absolute and relative risk aversion and risk loving preferences of individuals, under various conditions. It generalises and encompasses other systems of utility functions like that of exponential power. Certain properties of this utility function are discussed. Sensitivity analysis exhibits different portfolio allocations for various risk preferences. The analysis also shows that arbitrary risk preferences may lead to biased risk response estimates. Performance of PLEC utility function in portfolio allocation problem is demonstrated through numerical examples. This is evaluated through optimal solutions.

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