A New Insight into Three Bargaining Solutions in Convex Problems

We reconsider the three well-known solutions: the Nash, the egalitarian and the Kalai-Smorodinsky solutions, to the classical domains of convex bargaining problems. A new proof for the Nash solution that highlights the crucial role the axiom Contraction Independence plays is provided. We also give new axiomatic characterizations for both the egalitarian and the Kalai-Smorodinsky solutions. Our results focus on both contraction and expansion independence properties of bargaining problems and, as a consequence, some new insights on the three solutions from the perspective of rational choice may be derived.

Proportional Nash solutions - A new and procedural analysis of nonconvex bargaining problems

This paper studies the Nash solution to nonconvex bargaining problems. The Nash solution in such a context is typically multi-valued. We introduce a procedure to exclude some options recommended by the Nash solution. The procedure is based on the idea of the Kalai-Smorodinsky solution which has the same informational requirement on individual utilities as the Nash solution does and has an equity consideration as well. We then use this procedure to introduce two new solutions to nonconvex bargaining problems and study them axiomatically.

Conceptions of Individual Rights and Freedom in Welfare Economics: A Re-examination

This paper examines the literature in welfare economics with a focus on individual rights and freedom, two important components in welfare economics. The paper discusses conceptions of rights and freedom intuitively and presents a critical examination of the existing literature. Working Paper 07-3

The Fundamental Theorems of Welfare Economics in a Non-Welfaristic Approach

This paper investigates extensions of the two fundamental theorems of welfare economics to the framework in which each agent is endowed with three types of preference relations: an allocation preference relation, an opportunity preference relation, and an overall preference relation. It is shown that, under certain conditions, the two theorems can be extended. It is also pointed out that the conditions underlying the positive results are restrictive.

Rationality and Solutions to Nonconvex Bargaining Problems: Rationalizable, Asymmetric and Nash Solutions

Conditions α and β are two well-known rationality conditions in the theory of rational choice. This paper examines the implications of weaker versions of these two rationality conditions in the context of solutions to nonconvex bargaining problems. It is shown that, together with the standard axioms of efficiency and strict individual rationality, they imply rationalizability of solutions to nonconvex bargaining problems. We then characterize asymmetric Nash solutions by imposing a continuity and the scale invariance requirements. We also give a characterization of the Nash solution by using the two rationality conditions. These results make a further connection between solutions to non-convex bargaining problems and rationalizability of choice function in the theory of rational choice.

The Walrasian Distribution of Opportunity Sets: An Axiomatic Characterization

Economic systems generate various distributions of opportunity sets for individuals to choose consumption bundles. This paper presents an axiomatic analysis on distributions of opportunity sets. We introduce several reasonable properties of distributions of opportunity sets, and characterize the distributions of opportunity sets in the market economy by these properties.distribution of opportunity sets, market economy, Walrasian distribution, axiomatic characterization

Nonconvex bargaining problems

This paper studies compact and comprehensive bargaining problems for n players and axiomatically characterize the extensions of the three classical bargaining solutions to nonconvex bargaining problems: the Nash solution, the egalitarian solution and the Kalai-Smorodinsky solution. Our characterizing axioms are various extensions of Nash's original axioms.

Bargaining Theory over Opportunity Assignments and the Egalitarian Solution

This paper discusses issues of axiomatic bargaining problems over opportunity assignments. The fair arbitrator uses the principle of "equal opportunity" for all players to make the recommendation on resource allocations. A framework in such a context is developed and the egalitarian solution to standard bargaining problems is reformulated and axiomatically characterized.Opportunity sets, bargaining over opportunity assignments, egalitarian solution

Rationality and the Nash Solution to Non-convex Bargaining Problems

Conditions α and β are two well-known rationality conditions in the theory of rational choice. This paper examines the implication of weaker versions of these two rationality conditions in the context of solutions to non-convex bargaining problems. It is shown that, together with the standard axioms of efficiency, anonymity and scale invariance, they characterize the Nash solution. This result makes a further connection between solutions to non-convex bargaining problems and rationalizability of choice functions in the theory of rational choice.