Computation Problems for Envy Stable Solutions of Allocation Problems with Public Resources

We consider generalizations of TU games with restricted cooperation in partition function form and propose their interpretation as allocation problems with several public resources. Either all resources are goods or all resources are bads. Each resource is distributed between points of its set and permissible coalitions are subsets of the union of these sets. Each permissible coalition estimates each allocation of resources by its gain/loss function, that depends only on the restriction of the allocation on that coalition. A solution concept of "fair" allocation (envy stable solution) was proposed by the author in (Naumova, 2019). This solution is a simplification of the generalized kernel of cooperative games and it generalizes the equal sacrifice solution for claim problems. An allocation belongs to this solution if there do not exist special objections at this allocation between permissible coalitions. For several classes of such problems we describe methods for computation selectors of envy stable solutions.

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.

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.

A fair tax (system) or an ethical taxpayer?

An interpretation of fairness based on the equal sacrifice principle is not clear; three taxation rules can be derived from it. Instead of searching for a fair tax system, ethical behavior of the taxpayer should be expected and set as a target. Ethical taxation can be encouraged and the propensity to pay taxes could be reinforced by abolishing the secrecy of individual and family tax returns, setting restrictions on cash operations which are associated with corruption, and gradually eliminating tax havens and offshore areas.