A refinement of the concept of equilibrium in multiple objective continous games.
R. INFANTE AND F. R. FERNÁNDEZ J. PUERTO (1999)
Revista de la Real Academia de Ciencias Exactas Físicas y Naturales
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R. INFANTE AND F. R. FERNÁNDEZ J. PUERTO (1999)
Revista de la Real Academia de Ciencias Exactas Físicas y Naturales
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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.
Tadeusz Radzik, Piotr Więcek (2015)
Applicationes Mathematicae
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This review paper gives a characterization of non-coalitional zero-sum and non-zero-sum games with finite strategy spaces and payoff functions having some concavity or convexity properties. The characterization is given in terms of the existence of two-point Nash equilibria, that is, equilibria consisting of mixed strategies with spectra consisting of at most two pure strategies. The structure of such simple equilibria is discussed in various cases. In particular, many of the results...
Anton Stefanescu (1996)
Kybernetika
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Torres-Martínez, Juan Pablo (2006)
Fixed Point Theory and Applications [electronic only]
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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...
Witold Rzymowski
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CONTENTSIntroduction...........................................................................51. Preliminaries.....................................................................6 1.1. Notation........................................................................6 1.2. Control systems. Strategies..........................................72. Main lemma......................................................................93. Avoidance of many pursuers..........................................14 3.1....
Tomasz Bielecki (1997)
Applicationes Mathematicae
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The purpose of this paper is to prove existence of an ε -equilib- rium point in a dynamic Nash game with Borel state space and long-run time average cost criteria for the players. The idea of the proof is first to convert the initial game with ergodic costs to an ``equivalent" game endowed with discounted costs for some appropriately chosen value of the discount factor, and then to approximate the discounted Nash game obtained in the first step with a countable state space game for which...
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...
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. ...