Vladimir Gurvich

On graphs whose maximal cliques and stable sets intersect

We say that a graph G has the CIS-property and call it a CIS-graph if every maximal clique and every maximal stable set of G intersects.

On equistable, split, CIS, and related classes of graphs ☆

Abstract We consider several graphs classes defined in terms of conditions on cliques and stable sets, including CIS, split, equistable, and other related classes. We pursue a systematic study of the relations between them. As part of this study, we introduce two generalizations of CIS graphs, obtain a new characterization of split graphs, and a characterization of CIS line graphs.

Markov Decision Processes and Stochastic Games with Total Effective Payoff

We consider finite Markov decision processes with undiscounted total effective payoff. We show that there exist uniformly optimal pure and stationary strategies that can be computed by solving a polynomial number of linear programs. This implies that in a two-player zero-sum stochastic game with perfect information and with total effective payoff there exists a stationary best response to any stationary strategy of the opponent. From this, we derive the existence of a uniformly optimal pure and stationary saddle point. Finally we show that mean payoff can be viewed as a special case of total payoff.

On Nash-solvability in pure stationary strategies of the deterministic n-person games with perfect information and mean or total effective cost

We study existence of Nash equilibria (NE) in pure stationary strategies in n-person positional games with no moves of chance, with perfect information, and with the mean or total effective cost function. We construct a NE-free three-person game with positive local costs, thus disproving the conjecture suggested in Boros and Gurvich (2003). Still, the following four problems remain open: Whether NE exist in all two-person games with total effective costs such that (I) all local costs are strictly positive or (II) there are no dicycles of the total cost zero? Whether NE exist in all n-person games with the terminal (transition-free) cost functions, provided all dicycles form a unique outcome c and (III) assuming that c is worse than any terminal outcome or (IV) without this assumption? For n=3 the case (I) (and hence (II)) is answered in the negative. This is the main result of the present paper. For n=2 the case (IV) (and hence (III)) was answered in the positive earlier. We briefly survey the above and some other negative and positive results on Nash-solvability in pure stationary strategies for the games under consideration.

A convex programming-based algorithm for mean payoff stochastic games with perfect information

We consider two-person zero-sum stochastic mean payoff games with perfect information, or BWR-games, given by a digraph

Backward induction in presence of cycles

G = (V, E)

Combinatorial games modeling seki in GO

G=(V,E), with local rewards