Bird's tree allocations revisited

Game Theory;Cost Allocation

Equity and economic theory: reflections on methodology and scope

This paper provides an introduction to the recent literature on ordinal distributive justice. Its objetive is to explain the process of the mathematical analysis of fairness and to consider its potential for solving real allocative problems by means of several illustrative examples

Implementing Efficient Graphs in Connection Networks

We consider the problem of sharing the cost of a network that meets the connection demands of a set of agents. The agents simultaneously choose paths in the network connecting their demand nodes. A mechanism splits the total cost of the network formed among the participants. We introduce two new properties of implementation. The first property, Pareto Nash Implementation (PNI), requires that the efficient outcome is always implemented in a Nash equilibrium, and that the efficient outcome Pareto dominates any other Nash equilibrium. The average cost mechanism (AC) and other asymmetric variations, are the only rules that meet PNI. These mechanisms are also characterized under Strong Nash Implementation. The second property, Weakly Pareto Nash Implementation (WPNI), requires that the least inefficient equilibrium Pareto dominate any other equilibrium. The egalitarian mechanism (EG), a variation of AC that meets individual rationality, and other asymmetric mechanisms are the only rules that meet WPNI and Individual Rationality. PNI and WPNI provide the first economic justification of the Price of Stability (PoS), a seemingly natural measure in the computer science literature but not easily embraced in economics. EG minimizes the PoS across all individually rational mechanisms.Cost-sharing, Implementation, Average Cost, Egalitarian Mechanism.

Implementing Efficient Graphs in Connection Networks

We consider the problem of sharing the cost of a network that meets the connection demands of a set of agents. The agents simultaneously choose paths in the network connecting their demand nodes. A mechanism splits the total cost of the network formed among the participants. We introduce two new properties of implementation. The first prop- erty, Pareto Nash Implementation (PNI), requires that the efficient out- come is always implemented in a Nash equilibrium, and that the efficient outcome Pareto dominates any other Nash equilibrium. The average cost mechanism (AC) and other assymetric variations, are the only rules that meet PNI. These mechanisms are also characterized under Strong Nash Implementation. The second property, Weakly Pareto Nash Implementation (WPNI), requires that the least inefficient equilibrium Pareto dominate any other equilibrium. The egalitarian mechanism (EG), a variation of AC that meets individual rationality, and other assymetric mechanisms are the only rules that meet WPNI and Individual Rationality. PNI and WPNI provide the first economic justification of the Price of Stability (PoS), a seemingly natural measure in the computer science literature but not easily embraced in economics. EG minimizes the PoS across all individually rational mechanisms.ntable SCFs in our environment if we add a few desirable axioms.

Communication networks with endogenous link strength

This paper analyzes the formation of networks when players choose how much to invest in each relationship. We suppose that players have a fixed endowment that they can allocate across links, and in the baseline model, suppose that link strength is an additively separable and convex function of individual investments, and that agents use the path which maximizes the product of link strengths. We show that both the stable and efficient network architectures are stars. However, the investments of the hub may differ in stable and efficient networks. Under alternative assumptions on the investment technology and the reliability measure, other network architectures can emerge as efficient and stable

Equity and economic theory: reflections on methodology and scope.

This paper provides an introduction to the recent literature on ordinal distributive justice. Its objetive is to explain the process of the mathematical analysis of fairness and to consider its potential for solving real allocative problems by means of several illustrative examples.Fairness; Equity; Distributive justice;