A Perspective-Invariant Approach to Nash Bargaining

The Nash axioms lead to different results depending on whether the negotiation is framed in terms of gains relative to no agreement or in terms of sacrifices relative to an ideal. We look for a solution that leads to the same result from both perspectives. To do so, we restrict the application of Nash’s IIA axiom to bargaining sets where all options are individually rational and none exceed either party’s ideal point. If we normalize the bargaining set so that the disagreement point is (0, 0) and maximal gains are (1, 1), then any perspective-invariant bargaining solution must lie between the Utilitarian solution and the maximal equal-gain (minimal equal-sacrifice) solution. We show that a modified version of Nash’s symmetry axiom leads to the Utilitarian solution and that a reciprocity axiom leads to the equal-gain (equal-sacrifice) solution, both of which are perspective invariant. This paper was accepted by Joshua Gans, Business Strategy.

Reactive and Semi-Reactive Bargaining Sets for Games with Restricted Cooperation

Generalizations of reactive and semi-reactive bargaining sets of TU games are defined for the case when objections and counter-objections are permitted not between singletons but between elements of a family of coalitions [Formula: see text] and can use coalitions from [Formula: see text]. Necessary and sufficient conditions on [Formula: see text], [Formula: see text] that ensure existence results for generalizations of the reactive bargaining set and of the semi-reactive barganing set at each TU game [Formula: see text] with nonnegative values are obtained. The existence conditions for the generalized reactive bargaining set do not coincide with existence conditions for the generalized kernel and coincide with conditions for the generalized semi-reactive bargaining set only if [Formula: see text] and [Formula: see text]. The conditions for the generalized semi-reactive bargaining set coincide with conditions for the generalized classical bargaining set that were described in the previous papers of the author. For monotonic [Formula: see text], the condition on [Formula: see text] for existence of the generalized semi-reactive bargaining sets on the class of games with nonnegative values is also necessary and sufficient on the class of simple games, but similar result for the generalized classical bargaining sets is proved only for [Formula: see text].

Rules for Dividing a Disputed Resource in the Context of the Classical Liberal Argument for Peace

In this paper, we study alternative forms of conflict resolution, both peaceful and non-peaceful, between two countries that compete for claims to a resource used to produce potentially traded goods. Consistent with the classical liberal argument, peace supports mutually beneficial trade, whereas war preempts it. War always induces countries to allocate resources into non-contractible arming (“guns”) for superiority in conflict. Under peaceful settlement, countries might choose to arm as well for gaining leverage in negotiations, but arming is typically less than what it is under war. Building on the observation that arming itself affects the countries’ bargaining sets, we compare the efficiency properties of division rules generated by three prominent bargaining solutions – namely, splitting the surplus, equal sacrifice, and Nash bargaining – and show how they depend on the gains from trade.