Fairness, Efficiency, and the Nash Bargaining Solution

A bargaining solution balances fairness and efficiency if each player's payoff lies between the minimum and maximum of the payoffs assigned to him by the egalitarian and utilitarian solutions. In the 2-person bargaining problem, the Nash solution is the unique scale-invariant solution satisfying this property. Additionally, a similar result, relating the weighted egalitarian and utilitarian solutions to a weighted Nash solution, is obtained. These results are related to a theorem of Shapley, which I generalize. For n>=3, there does not exist any n-person scale-invariant bargaining solution that balances fairness and efficiency.Bargaining; fairness; efficiency; Nash solution

Twofold Optimality of the Relative Utilitarian Bargaining Solution

Given a bargaining problem, the `relative utilitarian' (RU) solution maximizes the sum total of the bargainer's utilities, after having first renormalized each utility function to range from zero to one. We show that RU is `optimal' in two very different senses. First, RU is the maximal element (over the set of all bargaining solutions) under any partial ordering which satisfies certain axioms of fairness and consistency; this result is closely analogous to the result of Segal (2000). Second, RU offers each person the maximum expected utility amongst all rescaling-invariant solutions, when it is applied to a random sequence of future bargaining problems which are generated using a certain class of distributions; this is somewhat reminiscent of the results of Harsanyi (1953) and Karni (1998).relative utilitarian; bargaining solution; impartial observer

An Egalitarian Value for Cooperative Games with Incomplete Information

A bargaining solution concept generalizing the Harsanyi NTU value is defined for cooperative games with incomplete information. Our definition of a cooperative solution implies that all coalitional threats are equitable when players make interpersonal utility comparisons in terms of some virtual utility scales. In contrast, Myerson’s (1984b) generalization of the Shapley NTU value is only equitable for the grand coalition. When there are only two players, the two solutions are easily seen to coincide, however they may differ for general n-person games. By using the concept of virtual utility, our bargaining solution reflects the fact that players negotiate at the interim stage

Intergenerational Justice in the Hobbesian State of Nature

We analyse the issue of justice in the allocation of resources across generations. Our starting point is that if all generations have a claim to natural resources, then each generation should be entitled to exercise veto power on the unpalatable choices of the other generations. We analyse this situation as one of bargaining à la Rubinstein, Safra and Thomson [15], which incorporates a notion of justice as mutual advantage, rather than justice as impartiality, as in the Kantian-Rawlsian tradition. Our framework captures some key aspects of the interaction between isolated agents in a Hobbesian state of nature, in which agents are not placed behind a veil of ignorance, but none of them is sufficiently strong to impose their will against all others (state of war of all against all). We analyse some new social welfare relations emerging from this Hobbesian framework. JEL Categories: D63, Q01Intergenerational justice; bargaining; Hobbes; social choice.

Compensatory Transfers in Two-Player Decision Problems

This paper presents an axiomatic characterization of a family of solutions to two-player quasi-linear social choice problems. In these problems the players select a single action from a set available to them. They may also transfer money between themselves. The solutions form a one-parameter family, where the parameter is a nonnegative number, t. The solutions can be interpreted as follows: Any efficient action can be selected. Based on this action, compute for each player a "best claim for compensation". A claim for compensation is the difference between the value of an alternative action and the selected efficient action, minus a penalty proportional to the extent to which the alternative action is inefficient. The coefficient of proportionality of this penalty is t. The best claim for compensation for a player is the maximum of this computed claim over all possible alternative actions. The solution, at the parameter value t, is to implement the chosen efficient action and make a monetary transfer equal to the average of these two best claims. The characterization relies on three main axioms. The paper presents and justifies these axioms and compares them to related conditions used in other bargaining contexts. In Nash Bargaining Theory, the axioms analagous to these three are in conflict with each other. In contrast, in the quasi-linear social choice setting of this paper, all three conditions can be satisfied simultaneously.

Bargaining and the theory of cooperative games: John Nash and beyond

This essay surveys the literature on the axiomatic model of bargaining formulated by Nash ("The Bargaining Problem," Econometrica 28, 1950, 155-162).Nash's bargaining model, Nash solution, Kalai-Smorodinsky solution, Egalitarian solution

No Profitable Decomposition in Quasi-Linear Allocation Problems

We study the problem of allocating a bundle of perfectly divisible private goods from an axiomatic point of view, in situations where compensations can be made through monetary transfers. The key property we impose on the allocation rule requires that no agent should be able to gain by decomposing the problem into sequences of subproblems. Combined with additional standard properties, it leads to a characterization of the rule that shares the total surplus equally. Hence a traditional welfarist rule emerges as the unique consequence of our axioms phrased in a natural economic environment.Social Choice; Axiomatic Bargaining; Welfarism; Egalitarianism