Jeroen Kuipers

On the computation of the nucleolus of a cooperative game

Abstract. We consider classes of cooperative games. We show that we can efficiently compute an allocation in the intersection of the prekernel and the least core of the game if we can efficiently compute the minimum excess for any given allocation. In the case where the prekernel of the game contains exactly one core vector, our algorithm computes the nucleolus of the game. This generalizes both a recent result by Kuipers on the computation of the nucleolus for convex games and a classical result by Megiddo on the nucleolus of standard tree games to classes of more general minimum cost spanning tree games. Our algorithm is based on the ellipsoid method and Maschlers scheme for approximating the prekernel.

Perfect-Information Games with Lower-Semicontinuous Payoffs

We prove that every multiplayer perfect-information game with bounded and lower-semicontinuous payoffs admits a subgame-perfect e-equilibrium in pure strategies. This result complements Example 3 in Solan and Vieille [Solan, E., N. Vieille. 2003. Deterministic multi-player Dynkin games. J. Math. Econom.39 911--929], which shows that a subgame-perfect e-equilibrium in pure strategies need not exist when the payoffs are not lower-semicontinuous. In addition, if the range of payoffs is finite, we characterize in the form of a Folk Theorem the set of all plays and payoffs that are induced by subgame-perfect 0-equilibria in pure strategies.

A note on the 5-person traveling salesman game

AbstractLetN=1,2,...,n be a set of customers andG=(N ∪ {0},E) an undirected connected graph with non-negative edge lengths. 0 is the home location of a salesman who visits the customers inN. Each subset

Some characterizations of egalitarian solutions on classes of TU-games

S \subseteq N

Selecting Telecommunication Carriers to Obtain Volume Discounts

can invite the salesman to visit its members only. The costc(S) of coalitionS is the length of a shortest tour that starts in 0, visits each customer inS at least once and returns to 0. The cooperative cost game defined in this way is called a (symmetric) traveling salesman game (TSG).The core of a TSG can be empty when ¦N¦ ≥ 6 and it was proved that it always has a non-empty core when ¦N¦≤ 4. In this note we shall prove that a TSG always has a non-empty core when ¦N¦=5.

Pure subgame-perfect equilibria in free transition games

A core concept is a solution concept on the class of balanced games that exclusively selects core allocations. We show that every continuous core concept that satisfies both the equal treatment property and a new property called independence of irrelevant core allocations (IIC) necessarily selects egalitarian allocations. IIC requires that, if the core concept selects a certain core allocation for a given game, and this allocation is still a core allocation for a new game with a core that is contained in the core of the first game, then the core concept also chooses this allocation as the solution to the new game. When we replace the continuity requirement by a weak version of additivity we obtain an axiomatization of the egalitarian solution concept that assigns to each balanced game the core allocation minimizing the Euclidean distance to the equal share allocation.

Cost Allocation for a Tree Network with Heterogeneous Customers

Abstract In this paper we derive characterizations of egalitarian solutions on two subclasses of the class of balanced games. Firstly we show that the Dutta–Ray solution is the only solution that satisfies symmetry, independence of irrelevant core allocations, and continuity on the class of convex games. Secondly, together with the other two requirements, a strengthening of continuity to monotonicity in the value of the grand coalition turns out to be sufficient for the characterization of the lexicographically maximal solution on the class of large core games.

Bin packing games

We consider a class of n-player stochastic games with the following properties: (1) in every state, the transitions are controlled by one player; (2) the payoffs are equal to zero in every nonabsorbing state; (3) the payoffs are nonnegative in every absorbing state. We propose a new iterative method to analyze these games. With respect to the expected average reward, we prove the existence of a subgame-perfect e-equilibrium in pure strategies for every e > 0. Moreover, if all transitions are deterministic, we obtain a subgame-perfect 0-equilibrium in pure strategies.