Eric Bahel

A Discrete Cost Sharing Model with Technological Cooperation

This article proposes a setting that allows for technological cooperation in the cost sharing model. Dealing with discrete demands, we study two properties: additivity and dummy. We show that these properties are insufficient to guarantee a unit-flow representation similar to that of Wang (Econ Lett 64:187–192, 1999). To obtain a characterization of unit flows, we strengthen the dummy axiom and introduce a property that requires the cost share of every agent to be non-decreasing in the incremental costs generated by their demand. Finally, a fairness requirement as to the compensation of technological cooperation is examined.

On the core and bargaining set of a veto game

The notion of veto player was originally introduced in simple games (see Nakamura in Int J Game Theory 8:55–61, 1979), for which every coalition has a value of 0 or 1. In this paper we extend it to monotonic cooperative games with transferable utility: a player has veto power if all coalitions not containing her are worthless. We examine and characterize the core (and other solution concepts) for these “veto games”. In particular, for this class of games, we show the equivalence between the core and the bargaining set. Our work generalizes the clan games and big-boss games introduced respectively by Potters et al. (Games Econ Behav 1:275–293, 1989) and Muto et al. (Econ Stud Q 39:303–321, 1988).

Consistency Requirements and Pattern Methods in Cost Sharing Problems with Technological Cooperation

Using the discrete cost sharing model with technological cooperation, we investigate the implications of the requirement that demand manipulations must not affect the agents’ shares. In a context where the enforcing authority cannot prevent agents (who seek to reduce their cost shares) from splitting or merging their demands, the cost sharing methods used must make such artifices unprofitable. The paper introduces a family of rules that are immune to these demand manipulations, the pattern methods. Our main result is the characterization of these methods using the above requirement. For each one of these methods, the associated pattern indicates how to combine the technologies in order to meet the agents’ demands. Within this family, two rules stand out: the public Aumann–Shapley rule, which never rewards technological cooperation; and the private Aumann–Shapley rule, which always rewards technology providers. Fairness requirements imposing natural bounds (for the technological rent) allow to further differentiate these two rules.

Shapley–Shubik methods in cost sharing problems with technological cooperation

In the discrete cost sharing model with technological cooperation (Bahel and Trudeau in Int J Game Theory 42:439–460, 2013a), we study the implications of a number of properties that strengthen the well-known dummy axiom. Our main axiom, which requires that costless units of demands do not affect the cost shares, is used to characterize two classes of rules. Combined with anonymity and a specific stability property, this requirement picks up sharing methods that allow the full compensation of at most one technological contribution. If instead we strengthen the well-known dummy property to include agents whose technological contribution is offset by the cost of their demand, we are left with an adaptation of the Shapley–Shubik method that treats technologies as private and rewards their contributions. Our results provide two interesting axiomatizations for the adaptations of the Shapley–Shubik rule to our framework.

Minimum incoming cost rules for arborescences

The paper examines minimum cost arborescence (mca) problems, which generalize the well-known minimum cost spanning tree (mcst) problems by allowing the cost to depend on the direction of the flow. We propose a new family of cost sharing methods that are easy to compute, as they closely relate to the network-building algorithm. These methods are called minimum incoming cost rules for arborescences (MICRAs). They include as a particular case the extension of the folk solution introduced by Dutta and Mishra [Games Econ Behav 74(1):120–143, 2012], providing a simple procedure for its computation. We also provide new axiomatizations of (a) the set of stable and symmetric MICRAs and (b) the Dutta–Mishra solution. Finally, we closely examine two MICRAs that (unlike the Dutta–Mishra rule) compensate agents who help others connect at a lower cost. The first of these two rules relates to the cycle-complete solution for mcst problems introduced by Trudeau [Games Econ Behav 75(1):402–412, 2012].