Displaying similar documents to “On noncooperative nonlinear differential games”

A new geometric approach to bimatrix games.

Gloria Fiestras-Janeiro, Ignacio García Jurado (1991)

Qüestiió

Similarity:

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.

Simple equilibria in finite games with convexity properties

Tadeusz Radzik, Piotr Więcek (2015)

Applicationes Mathematicae

Similarity:

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...

Equilibria in constrained concave bimatrix games

Wojciech Połowczuk, Tadeusz Radzik (2013)

Applicationes Mathematicae

Similarity:

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...

Method of construction of the evasion strategy for differential games with many pursuers

Witold Rzymowski

Similarity:

CONTENTSIntroduction...........................................................................51. Preliminaries.....................................................................6 1.1. Notation........................................................................6 1.2. Control systems. Strategies..........................................72. Main lemma......................................................................93. Avoidance of many pursuers..........................................14 3.1....

Approximations of dynamic Nash games with general state and action spaces and ergodic costs for the players

Tomasz Bielecki (1997)

Applicationes Mathematicae

Similarity:

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...

Convergence method, properties and computational complexity for Lyapunov games

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

International Journal of Applied Mathematics and Computer Science

Similarity:

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...

On two-point Nash equilibria in bimatrix games with convexity properties

Wojciech Połowczuk (2006)

Applicationes Mathematicae

Similarity:

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. ...