Consider games where players wish to minimize the cost to reach some state. A subgame-perfect Nash equilibrium can be regarded as a collection of optimal paths on such games. Similarly, the well-known state-labeling algorithm used in model checking can be viewed as computing optimal paths on a Kripke structure, where each path has a minimum number of transitions. We exploit these similarities i...

The foundations of classical algebraic geometry and real are the Nullstellensatz Positivstellensatz. Over last two decades, basic analogous theorems for matrix operator theory (noncommutative variables) have emerged. This paper concerns commuting strategies nonlocal games, recalls NC which helpful, extends these, applies them to a very broad collection games. In process, it brings together resu...

We describe the class of games with opacity condition, as an adequate model for security aspects of computing systems. We study their theoretical properties, relate them to reachability perfect information games and exploit this relation to discuss a search approach with heuristics, based on the directing-word problem in automata theory.

It is a well known fact that in extensive form games with perfect information, there is a Nash equilibrium with support of size one. This doesn’t hold for games with imperfect information, where the size of minimal support can be larger. We present a dependency between the level of uncertainty and the minimum support size. For many games, there is a big disproportion between the game uncertaint...

Let $$\gamma (G)$$ and _{t}(G)$$ be the domination number total of a graph G, respectively, let _g(G)$$ _{tg}(G)$$ game respectively. Then, G is _g$$ -perfect (resp. _{tg}$$ -perfect) if every induced subgraph F satisfies _g(F)=\gamma (F)$$ _{tg}(F)=\gamma _t(F)$$ ). A recursive characterization graphs derived. The yields polynomial recognition algorithm for graphs. It proved that minimally -im...

We prove the existence of a subgame-perfect ε-equilibrium, for every ε > 0, in a class of multi-player games with perfect information, which we call free transition games. The novelty is that a non-trivial class of perfect information games is solved for subgameperfection, with multiple non-terminating actions, in which the payoff structure is generally not semi-continuous. Due to the lack of s...

Model-checking the alternating-time temporal logics AT L and AT L∗ with incomplete information is undecidable for perfect recall semantics. However, when restricting to memoryless strategies the model-checking problem becomes decidable. In this paper we consider two other types of semantics based on finite-memory strategies. One where the memory size allowed is bounded and one where the memory ...

We analyze several perfect-information combinatorial games played on planar triangulations. We introduce three broad categories of such games—constructing, transforming, and marking triangulations— and several specific games within each category. In various situations of each game, we develop polynomial-time algorithms to determine who wins a given game position under optimal play, and to find ...