Stable Set

This article uncovers dynamic properties of the von Neumann–Morgenstern solution in weak tournaments and majoritarian games. We propose a new procedure for the construction of choice sets from weak tournaments, based on dynamic stability criteria. The idea is to analyze dynamic versions of tournament games. The exploration of a specific class of Markov perfect equilibria in these “dynamic tournament games” yields a new solution concept for weak tournaments—the A-stable set. The alternatives in an A-stable set constitute persistent, long-run policy outcomes in the corresponding dynamic tournament games. We find that, in any weak tournament, the class of A-stable sets coincides with that of von Neumann–Morgenstern stable sets.

The evolutionary selection of outcomes (modelled using the replicator dynamics) in games with costless communication depends crucially on the structural assumptions made on the underlying population. (1) In conflicts between two interacting populations, common interest implies that the set of efficient outcomes is the unique evolutionarily stable set. Lack of common interest prevents sets with minimal stability properties to exist.

We apply three axioms adapted from decision theory to refinements of the Nash equilibria of games with perfect recall that select connected closed sub- sets called solutions. No player uses a weakly dominated strategy in an equilibrium in a solution. Each solution contains a quasi-perfect equilibrium and thus a sequential equilibrium in strategies that provide conditionally admissible optimal continuations from

This paper gives a combinatorial approach to solving the student exam scheduling problem. The problem is to generate sched- ules that satisfy hard constraints while minimizing soft constraint voilations. This problem is NP-Hard. The problem is decomposed into stages that include nding stable sets, weighted bipartite match- ings, maximum o w, and pathnding in hypergraphs. We describe our method and

We present an algorithm for computing both upper and lower bounds on the Chvátal-rank of antiwebs, starting from the edge constraint stable set polytope. With the help of this algorithm we have been able to compute the exact values of the Chvátal-rank for all antiwebs containing up to 5,000 nodes. Moreover, the algorithm can be easily adapted to start from