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Edge-disjoint odd cycles in graphs with small chromatic number

Claude Berge, Bruce Reed (1999)

Annales de l'institut Fourier

For a simple graph, we consider the minimum number of edges which block all the odd cycles and the maximum number of odd cycles which are pairwise edge-disjoint. When these two coefficients are equal, interesting consequences appear. Similar problems (but interchanging “vertex-disjoint odd cycles” and “edge-disjoint odd cycles”) have been considered in a paper by Berge and Fouquet.

El potencial de Hart y Mas-Colell para juegos restringidos por grafos.

J. M. Bilbao Arrese, Jorge López Vázquez (1996)

Qüestiió

This paper analyzes a model of formation of connected coalitions in a cooperative game. This model is a communication situation, and the Shapley value of this graph-restricted game is the Myerson value. The potential function for cooperative games was defined by Hart and Mas-Colell, and Winter showed that the Myerson value admits a potential function. We study a recursive procedure for computing the potential of the Myerson value. In section 3, we use the Myerson value for measuring voting power...

Embedding partially ordered sets into ω ω

Ilijas Farah (1996)

Fundamenta Mathematicae

We investigate some natural questions about the class of posets which can be embedded into ⟨ω,≤*⟩. Our main tool is a simple ccc forcing notion H E which generically embeds a given poset E into ⟨ω,≤*⟩ and does this in a “minimal” way (see Theorems 9.1, 10.1, 6.1 and 9.2).

Empirical approximation in Markov games under unbounded payoff: discounted and average criteria

Fernando Luque-Vásquez, J. Adolfo Minjárez-Sosa (2017)

Kybernetika

This work deals with a class of discrete-time zero-sum Markov games whose state process x t evolves according to the equation x t + 1 = F ( x t , a t , b t , ξ t ) , where a t and b t represent the actions of player 1 and 2, respectively, and ξ t is a sequence of independent and identically distributed random variables with unknown distribution θ . Assuming possibly unbounded payoff, and using the empirical distribution to estimate θ , we introduce approximation schemes for the value of the game as well as for optimal strategies considering both,...

Equilibria in a class of games and topological results implying their existence.

R.S. Simon, S. Spiez, H. Torunczyk (2008)

RACSAM

We survey results related to the problem of the existence of equilibria in some classes of infinitely repeated two-person games of incomplete information on one side, first considered by Aumann, Maschler and Stearns. We generalize this setting to a broader one of principal-agent problems. We also discuss topological results needed, presenting them dually (using cohomology in place of homology) and more systematically than in our earlier papers.

Equilibria in constrained concave bimatrix games

Wojciech Połowczuk, Tadeusz Radzik (2013)

Applicationes Mathematicae

We study a generalization of bimatrix games in which not all pairs of players' pure strategies are admissible. It is shown that under some additional convexity assumptions such games have equilibria of a very simple structure, consisting of two probability distributions with at most two-element supports. Next this result is used to get a theorem about the existence of Nash equilibria in bimatrix games with a possibility of payoffs equal to -∞. The first of these results is a discrete counterpart...

Equilibrium transitions in finite populations of players

J. Miękisz (2006)

Banach Center Publications

We discuss stochastic dynamics of finite populations of individuals playing symmetric games. We review recent results concerning the dependence of the long-run behavior of such systems on the number of players and the noise level. In the case of two-player games with two symmetric Nash equilibria, when the number of players increases, the population undergoes multiple transitions between its equilibria.

Equivalences and Congruences on Infinite Conway Games∗

Furio Honsell, Marina Lenisa, Rekha Redamalla (2012)

RAIRO - Theoretical Informatics and Applications

Taking the view that infinite plays are draws, we study Conway non-terminating games and non-losing strategies. These admit a sharp coalgebraic presentation, where non-terminating games are seen as a final coalgebra and game contructors, such as disjunctive sum, as final morphisms. We have shown, in a previous paper, that Conway’s theory of terminating games can be rephrased naturally in terms of game (pre)congruences. Namely, various...

Equivalences and Congruences on Infinite Conway Games∗

Furio Honsell, Marina Lenisa, Rekha Redamalla (2012)

RAIRO - Theoretical Informatics and Applications

Taking the view that infinite plays are draws, we study Conway non-terminating games and non-losing strategies. These admit a sharp coalgebraic presentation, where non-terminating games are seen as a final coalgebra and game contructors, such as disjunctive sum, as final morphisms. We have shown, in a previous paper, that Conway’s theory of terminating games can be rephrased naturally in terms of game (pre)congruences. Namely, various...

Estimating the supply chain efficiency loss when the seller has to estimate the buyer’s willingness to pay

Xavier Brusset (2014)

RAIRO - Operations Research - Recherche Opérationnelle

We study the pricing problem between two firms when the manufacturer’s willingness to pay (wtp) for the supplier’s good is not known by the latter. We demonstrate that it is in the interest of the manufacturer to hide this information from the supplier. The precision of the information available to the supplier modifies the rent distribution. The risk of opportunistic behaviour entails a loss of efficiency in the supply chain. The model is extended to the case of a supplier submitting offers to...

Estrategias óptimas de un juego bipersonal de suma cero y puntos de ensilladura del campo escalar asociado.

Josep Freixas Bosch (1993)

Qüestiió

Definimos el campo escalar asociado a un juego bipersonal de suma cero. Estudiamos la existencia y unicidad de puntos estacionarios y obtenemos la forma general de los mismos en caso de unicidad. Se establece que todo punto estacionario es de ensilladura.La importancia del estudio anterior queda reflejada al establecer la equivalencia entre las estrategias óptimas simples de un juego y los puntos estacionarios del campo escalar asociado.El Teorema de Shapley-Snow [2] proporciona un método sistemático...

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