Journal ArticleDOI
A finite step algorithm via a bimatrix game to a single controller non-zero sum stochastic game
A. S. Nowak,T. E. S. Raghavan +1 more
Reads0
Chats0
TLDR
It is shown that any Nash equilibrium point of this bimatrix game can be used to find a Nash equilibriumpoint of the stochastic game whenever the law of motion is controlled by one player.Abstract:
Given a non-zero sum discounted stochastic game with finitely many states and actions one can form a bimatrix game whose pure strategies are the pure stationary strategies of the players and whose penalty payoffs consist of the total discounted costs over all states at any pure stationary pair. It is shown that any Nash equilibrium point of this bimatrix game can be used to find a Nash equilibrium point of the stochastic game whenever the law of motion is controlled by one player. The theorem is extended to undiscounted stochastic games with irreducible transitions when the law of motion is controlled by one player. Examples are worked out to illustrate the algorithm proposed.read more
Citations
More filters
Book ChapterDOI
Nonzero-sum Stochastic Games
TL;DR: In this article, a survey of stochastic Markov games with general state spaces is presented. But the authors focus on nonzero-sum games and provide a detailed survey of selected recent results.
Journal ArticleDOI
Homotopy methods to compute equilibria in game theory
TL;DR: A survey of the use of homotopy methods in game theory can be found in this paper, where the main ideas can be extended to compute equilibria in extensive form and dynamic games, and how homotopies can be used to compute all Nash Equilibria.
Book
Game Theory for Next Generation Wireless and Communication Networks: Modeling, Analysis, and Design
TL;DR: In this paper, game-theoretic approaches for designing, modeling, and optimizing emerging wireless communication networks and systems have been described, including matching theory and games with bounded rationality, and tutorial chapters show how to use these tools to solve current and future wireless networking problems.
Proceedings Article
Homotopy Methods to Compute Equilibria in Game Theory
TL;DR: A survey of the use of homotopy methods in game theory, which explains how the main ideas can be extended to compute equilibria in extensive form and dynamic games, and how homotopies can be used to compute all NashEquilibria.
Book ChapterDOI
Finite-Step Algorithms for Single-Controller and Perfect Information Stochastic Games
TL;DR: This work focuses on finite-step algorithms for two special classes of stochastic games, Single-Controller Stochastic Games and Perfect Information Stochastics, where the player has exactly one action in each state.
References
More filters
Journal ArticleDOI
Stochastic Games
TL;DR: In a stochastic game the play proceeds by steps from position to position, according to transition probabilities controlled jointly by the two players, and the expected total gain or loss is bounded by M, which depends on N 2 + N matrices.
Journal ArticleDOI
Discrete Dynamic Programming
TL;DR: In this paper, the authors consider a system with a finite number of states and choose an action from a finite set of possible actions to move the system to a new state with the probability of a particular new state given by a function.
Some topics in two-person games
TL;DR: In this article, several loosely-related essays on the theory of finite, two-person games are presented, with an emphasis on features of the theory that depend only on the ordering of the payoffs, as opposed to their numerical values.
Journal ArticleDOI
Equilibrium in a stochastic $n$-person game
TL;DR: In this article, the authors consider a stochastic game with a finite set of states, where a player's strategy will reflect a concern both for the game now being played and for the situation that will be probably confronted in the next period.