A class of two-person zero-sum matrix games with rough payoffs.
Xu, Jiuping, Yao, Liming (2010)
International Journal of Mathematics and Mathematical Sciences
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Xu, Jiuping, Yao, Liming (2010)
International Journal of Mathematics and Mathematical Sciences
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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...
Natália Martins, Delfim F.M. Torres (2011)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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We present necessary conditions for linear noncooperative N-player delta dynamic games on an arbitrary time scale. Necessary conditions for an open-loop Nash-equilibrium and for a memoryless perfect state Nash-equilibrium are proved.
R. INFANTE AND F. R. FERNÁNDEZ J. PUERTO (1999)
Revista de la Real Academia de Ciencias Exactas Físicas y Naturales
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Milan Hladík (2010)
Kybernetika
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Payoffs in (bimatrix) games are usually not known precisely, but it is often possible to determine lower and upper bounds on payoffs. Such interval valued bimatrix games are considered in this paper. There are many questions arising in this context. First, we discuss the problem of existence of an equilibrium being common for all instances of interval values. We show that this property is equivalent to solvability of a certain linear mixed integer system of equations and inequalities....
Andrzej Wieczorek (2005)
Applicationes Mathematicae
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The games of type considered in the present paper (LSE-games) extend the concept of LSF-games studied by Wieczorek in [2004], both types of games being related to games with a continuum of players. LSE-games can be seen as anonymous games with finitely many types of players, their action sets included in Euclidean spaces and payoffs depending on a player's own action and finitely many integral characteristics of distributions of the players' (of all types) actions. We prove the existence...
Sylvain Sorin, Cheng Wan (2013)
RAIRO - Operations Research - Recherche Opérationnelle
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This work studies a new strategic game called delegation game. A delegation game is associated to a basic game with a finite number of players where each player has a finite integer weight and her strategy consists in dividing it into several integer parts and assigning each part to one subset of finitely many facilities. In the associated delegation game, a player divides her weight into several integer parts, commits each part to an independent delegate and collects the sum of their...
Wojciech Połowczuk, Tadeusz Radzik (2013)
Applicationes Mathematicae
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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...
Gloria Fiestras-Janeiro, Ignacio García Jurado (1991)
Qüestiió
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In this paper we study some properties concerning the equilibrium point of a bimatrix game and describe a geometric method to obtain all the equilibria of a bimatrix game when one of the players has at most three pure strategies.
Andrzej Wieczorek (2004)
Applicationes Mathematicae
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Large games of kind considered in the present paper (LSF-games) directly generalize the usual concept of n-matrix games; the notion is related to games with a continuum of players and anonymous games with finitely many types of players, finitely many available actions and distribution dependent payoffs; however, there is no need to introduce a distribution on the set of types. Relevant features of equilibrium distributions are studied by means of fixed point, nonlinear complementarity...
Wojciech Połowczuk (2006)
Applicationes Mathematicae
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This paper considers bimatrix games with matrices having concavity properties. The games described by such payoff matrices well approximate two-person non-zero-sum games on the unit square, with payoff functions F₁(x,y) concave in x for each y, and/or F₂(x,y) concave in y for each x. For these games it is shown that there are Nash equilibria in players' strategies with supports consisting of at most two points. Also a simple search procedure for such Nash equilibria is given. ...
Pedro Mariano, Luís Correia (2015)
International Journal of Applied Mathematics and Computer Science
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We analyse Give and Take, a multi-stage resource sharing game to be played between two players. The payoff is dependent on the possession of an indivisible and durable resource, and in each stage players may either do nothing or, depending on their roles, give the resource or take it. Despite these simple rules, we show that this game has interesting complex dynamics. Unique to Give and Take is the existence of multiple Pareto optimal profiles that can also be Nash equilibria, and a...
Krzysztof Krawiec, Wojciech Jaśkowski, Marcin Szubert (2011)
International Journal of Applied Mathematics and Computer Science
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We apply Coevolutionary Temporal Difference Learning (CTDL) to learn small-board Go strategies represented as weighted piece counters. CTDL is a randomized learning technique which interweaves two search processes that operate in the intra-game and inter-game mode. Intra-game learning is driven by gradient-descent Temporal Difference Learning (TDL), a reinforcement learning method that updates the board evaluation function according to differences observed between its values for consecutively...