Maurice Koster

Serial cost sharing methods for multi-commodity situations

Abstract We consider ways to extend the serial cost sharing method (Moulin, H., Shenker, S., Serial cost sharing, Econometrica 60 (1992) 1009–1037; Moulin, H., Shenker, S., Average cost pricing versus serial cost sharing: An axiomatic comparison, Journal of Economic Theory 64 (1992) 178–201) to a setting where agents have a demand for bundles of heterogeneous goods. We introduce a class of serial extensions which is based on the use of preorderings. The class is characterized by the properties of Equal Treatment of Preordering Equivalents and the Radial Serial Principle. The preordering that judges agents on their stand alone costs leads us to a serial extension that is a generalization of the axial rule (Sprumont, 1996). A characterization of this Radial Serial Rule is provided. As a consequence we find that, in contrary to the more restrictive model of Sprumont (1996), in our setting the properties of Independence of Null Agents, Rank Independence of Irrelevant Agents together with Ordinality and the Serial Principle are incompatible.

Sharing the cost of a network: Core and core allocations

Abstract. This paper discusses the core of the game corresponding to the standard fixed tree problem. We consider the weighted adaptation of the constrained egalitarian solution of Dutta and Ray (1989). The core of the standard fixed tree game equals the set of all weighted constrained egalitarian solutions. Each weighted constrained egalitarian solution is determined (in polynomial time) as a home-down allocation, which creates further insight in the local behaviour of the weighted constrained egalitarian solution. The constrained egalitarian solution is characterized in terms of a cost sharing mechanism.

Cost Allocation in a Bank ATM Network

Abstract.We consider a situation in which a group of banks consider connecting their Automated Teller Machines (ATMs) in a network, so that the banks’ customers may use ATMs of any bank in the network. The problem studied is that of allocating the total transaction costs arising in the network, among the participating banks. The situation is modeled as a cooperative game with transferable utility. We propose two allocations, and discuss their relation to the core and other well-known solution concepts, as well as to population monotonicity.

General aggregation of demandand cost sharing methods

This paper extends the notion of cost sharing to models with general demand aggregation rules. In the process, aggregated serial cost sharing mechanisms are defined and characterized. A framework for a dynamic view on cost sharing is provided, introducing the notion of consistency to the generalized cost sharing model. Corresponding optimistic and pessimistic cooperative cost games are defined and their cores are studied. In particular, we show that the class of bankruptcy problems can be seen as a special class of cost sharing problems. It is seen that the serial mechanism in this specific case is closely related to the Constrained Equal Award rule.

Communication and Cooperation in Public Network Situations

This paper focuses on sharing the costs and revenues of maintaining a public network communication structure. Revenues are assumed to be bilateral and communication links are publicly available but costly. It is assumed that agents are located at the vertices of an undirected graph in which the edges represent all possible communication links. We take the approach from cooperative game theory and focus on the corresponding network game in coalitional form which relates any coalition of agents to its highest possible net benefit, i.e., the net benefit corresponding to an optimal operative network. Although finding an optimal network in general is a difficult problem, it is shown that corresponding network games are (totally) balanced. In the proof of this result a specific relaxation, duality and techniques of linear production games with committee control play a role. Sufficient conditions for convexity of network games are derived. Possible extensions of the model and its results are discussed.

Weighted Allocation Rules for Standard Fixed Tree Games

Abstract.In this paper we consider standard fixed tree games, for which each vertex unequal to the root is inhabited by exactly one player. We present two weighted allocation rules, the weighted down-home allocation and the weighted neighbour-home allocation, both inspired by the painting story in Maschler et al. (1995) . We show, in a constructive way, that the core equals both the set of weighted down-home allocations and the set of weighted neighbour allocations. Since every weighted down-home allocation specifies a weighted Shapley value (Kalai and Samet (1988)) in a natural way, and vice versa, our results provide an alternative proof of the fact that the core of a standard fixed tree game equals the set of weighted Shapley values. The class of weighted neighbour allocations is a generalization of the nucleolus, in the sense that the latter is in this class as the special member where players have all equal weights.

Voluntary Contributions to Multiple Public Projects

The problem of financing a set of public goods (facilities, projects) by private contri- butions is studied. The corresponding cooperative game, the realization game, is shown to be convex. For the noncooperative setting we study a realization scheme that induces a strategic game. This contribution game is shown to be best-response equivalent with a coordination game in which the payoff to all players is the utilitarian collective welfare function, i.e., the sum of the utility functions of the players. Several equilibrium proper- ties are derived: no money is wasted in an equilibrium; a player whose necessary projects are not all realized does not contribute. Strategy profiles maximizing utilitarian welfare are strong Nash equilibria of the contribution game. Each strong Nash equilibrium corre- sponds to a core element of the realization game in a natural way. It is shown that there is a one-to-one correspondence between the set of strong Nash equilibria of the contribution game and the largest set of core elements of the realization game, that is consistent with maximizing the number of players with non-zero payoffs. It is precisely the subset of the core according to which rewards zero indicate null players

Networks and Collective Action

This paper proposes a new measure for a groups ability to lead society to adopt their standard of behavior, which in particular takes account of the time the group takes to convince the whole society to adopt their position. This notion of a groups power to initiate action is computed as the reciprocal of the resistance against it, which is in turn given by the expected absorption time of a related finite state partial Markov chain that captures the social dynamics. The measure is applicable and meaningful in a variety of models where interaction between agents is formalized through (weighted) binary relations. Using Percolation Theory, it is shown that the group power is monotonic as a function of groups of agents. We also explain the differences between our measure and those discussed in the literature on Graph Theory, and illustrate all these concerns by a thorough analysis of two particular cases: the Wolfe Primate Data and the 11S hijackers’ network.

Hierarchical constrained Egalitarianism in TU-games

Abstract The constrained egalitarian solution of Dutta and Ray [Econometrica 57 (1989) 615] for TU-games is extended to asymmetric cases, using the notion of hierarchical systems . This hierarchical constrained egalitarian solution for TU-games is based on the hierarchical Lorenz-ordering as an inequality measure, that extends the weighted Lorenz-ordering of Ebert [Social Choice of Welfare 16 (1999) 233]. It is shown that the hierarchical constrained egalitarian solution consists of one allocation at most. An algorithm is proposed for calculating the hierarchical constrained egalitarian solution for certain classes of games, and in particular the class of convex games. By varying the hierarchical system, each core element of a positive valued convex game is shown to be a hierarchical constrained egalitarian solution.

Heterogeneous Cost Sharing, the Directional Serial Rule

The directional serial rule is introduced as a natural serial extension, generalizing the Moulin–Shenker cost sharing rule to heterogeneous cost sharing models. It is the unique regular rule compatible with the radial serial principle. In particular, this shows the incompatibility of the serial principle with differentiability of a cost sharing rule as a function of the individual demands.