Displaying similar documents to “Some heuristics in automatic theorem proving.”

Carcassonne -- description of the game

Kárná, Lucie

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This article formalizes some aspects of the board game Carcassonne. Combinatorical problems related to the number of tile types are mentioned. Then the paper describes a game map using graph theory.

A tandem version of the cops and robber game played on products of graphs

Nancy E. Clarke, Richard J. Nowakowski (2005)

Discussiones Mathematicae Graph Theory

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In this version of the Cops and Robber game, the cops move in tandems, or pairs, such that they are at distance at most one from each other after every move. The problem is to determine, for a given graph G, the minimum number of tandems sufficient to guarantee a win for the cops. We investigate this game on three graph products, the Cartesian, categorical and strong products.

A graph-theoretic characterization of the core in a homogeneous generalized assignment game

Tadeusz Sozański (2006)

Banach Center Publications

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An exchange network is a socioeconomic system in which any two actors are allowed to negotiate and conclude a transaction if and only if their positions-mathematically represented by the points of a connected graph-are joined by a line of this graph. A transaction consists in a bilaterally agreed-on division of a profit pool assigned to a given line. Under the one-exchange rule, every actor is permitted to make no more than one transaction in each negotiation round. Bienenstock and Bonacich...

Note On The Game Colouring Number Of Powers Of Graphs

Stephan Dominique Andres, Andrea Theuser (2016)

Discussiones Mathematicae Graph Theory

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We generalize the methods of Esperet and Zhu [6] providing an upper bound for the game colouring number of squares of graphs to obtain upper bounds for the game colouring number of m-th powers of graphs, m ≥ 3, which rely on the maximum degree and the game colouring number of the underlying graph. Furthermore, we improve these bounds in case the underlying graph is a forest.

Spreading mechanisms of cooperation for the evolutionary Prisoner's Dilemma games

György Szabó (2008)

Banach Center Publications

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We survey several mechanisms supporting the maintenance of cooperation for evolutionary Prisoner's Dilemma games. In these models players are located on the sites of a lattice or graph and they can follow one of the pure strategies: cooperation (C) or defection (D). Their total income comes from Prisoner's Dilemma games with their neighbors. We discuss the consequences of different evolutionary rules determining the time-dependence of the strategy distribution and compare the results...

Game list colouring of graphs.

Borowiecki, M., Sidorowicz, E., Tuza, Zs. (2007)

The Electronic Journal of Combinatorics [electronic only]

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Convergence method, properties and computational complexity for Lyapunov games

Julio B. Clempner, Alexander S. Poznyak (2011)

International Journal of Applied Mathematics and Computer Science

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We introduce the concept of a Lyapunov game as a subclass of strictly dominated games and potential games. The advantage of this approach is that every ergodic system (repeated game) can be represented by a Lyapunov-like function. A direct acyclic graph is associated with a game. The graph structure represents the dependencies existing between the strategy profiles. By definition, a Lyapunov-like function monotonically decreases and converges to a single Lyapunov equilibrium point identified...