Marc Meertens

On the Core of Routing Games with Revenues

Traveling salesman problems with revenues form a generalization of traveling salesman problems. Here, next to travel costs an explicit revenue is generated by visiting a city. We analyze routing problems with revenues, where a predetermined route on all cities determines the tours along subgroups. Corresponding routing games with revenues are analyzed. It is shown that these games have a nonempty core and a complete description of the core is provided.

Envy-free and Pareto efficient allocations in economies with indivisible goods and money

Abstract This paper investigates the existence of envy-free and Pareto efficient allocations in economies with finitely many indivisible goods and one divisible good (money). The existence of envy-free allocations is proved under very weak conditions, but the paper contains an example of an economy in which the set of envy-free allocations and the set of Pareto efficient allocations are disjoint. It contains moreover sufficient conditions for an economy in which the existence of an envy-free and Pareto efficient allocation is assured.

The nucleolus of trees with revenues

Trees with revenues are a generalization of standard trees. In a tree with revenues, players have to pay for their connections to the root, but a player can also earn some revenue from being connected to the root. In this paper, we present an algorithm for calculating the nucleolus.

Processing Games with Restricted Capacities

This paper analyzes processing problems and related cooperative games.In a processing problem there is a finite set of jobs, each requiring a specific amount of effort to be completed, whose costs depend linearly on their completion times.There are no restrictions whatsoever on the processing schedule.The main feature of the model is a capacity restriction, i.e., there is a maximum amount of effort per time unit available for handling jobs.Assigning to each job a player and letting each player have an individual capacity for handling jobs, each coalition of cooperating players in fact faces a processing problem with the coalitional capacity being the sum of the individual capacities of the members.The corresponding processing game summarizes the minimal joint costs for every coalition.It turns out that processing games are totally balanced.An explicit core element is constructed.

Bargaining sets in exchange economies with indivisibilities and money

This paper introduces and investigates the semireactive bargaining set (Sudhölter and Potters (2001)) and the reactive bargaining set (Granot (1994)), which are originally solution concepts for TU-games, in economies in which agents exchange indivisible goods and one perfectly divisible good (money). Under the assumptions that the preferences of the agents are quasi-linear and the endowments satisfy the Total Abundance condition, a condition on the amounts of money agents initially have, it is shown that the (semi)reactive bargaining set is nonempty. In addition, we prove that in such an economy the (semi)reactive bargaining set and the (strong) core coincide if and only if the (semi)reactive bargaining set and the core of the underlying TU-game coincide.

Dynamic Selection in Normal-Form Games

This paper investigates a class of dynamic selection processes for n-person normal-form games which includes the Brown-von Neumann-Nash dynamics. For (two-person) zero-sum games and for (n-person) potential games every limit set of these dynamics is a subset of the set of Nash-equilibria. Furthermore, under these dynamics the unique Nash-component of a zero-sum game is minimal asymptotically stable and for a potential game a smoothly connected component which is a local maximizer is minimal asymptotically stable.