Displaying similar documents to “Distributed Nash equilibrium tracking via the alternating direction method of multipliers”

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...

Interval valued bimatrix games

Milan Hladík (2010)

Kybernetika

Similarity:

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....

Large games with only small players and strategy sets in Euclidean spaces

Andrzej Wieczorek (2005)

Applicationes Mathematicae

Similarity:

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...

Delegation equilibrium payoffs in integer-splitting games

Sylvain Sorin, Cheng Wan (2013)

RAIRO - Operations Research - Recherche Opérationnelle

Similarity:

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...

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...

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.

Large games with only small players and finite strategy sets

Andrzej Wieczorek (2004)

Applicationes Mathematicae

Similarity:

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...

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. ...

The Give and Take game: Analysis of a resource sharing game

Pedro Mariano, Luís Correia (2015)

International Journal of Applied Mathematics and Computer Science

Similarity:

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...

Evolving small-board Go players using coevolutionary temporal difference learning with archives

Krzysztof Krawiec, Wojciech Jaśkowski, Marcin Szubert (2011)

International Journal of Applied Mathematics and Computer Science

Similarity:

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...