Constructions of Nash Equilibria in Stochastic Games of Resource Extraction with Additive Transition Structure

2006 ◽  
Vol 63 (2) ◽  
pp. 239-260 ◽  
Author(s):  
Piotr Szajowski
Keyword(s):  
Nash Equilibria ◽  
Stochastic Games ◽  
Resource Extraction ◽  
Transition Structure

scholarly journals Existence of Nash equilibria in stochastic games of resource extraction with risk-sensitive players

Top ◽  
2019 ◽  
Vol 27 (3) ◽  
pp. 502-518
Author(s):  
Hubert Asienkiewicz ◽  
Łukasz Balbus
Keyword(s):  
Nash Equilibria ◽  
Stochastic Games ◽  
Resource Extraction ◽  
Risk Sensitive

NASH EQUILIBRIA IN UNCONSTRAINED STOCHASTIC GAMES OF RESOURCE EXTRACTION

2008 ◽  
Vol 10 (01) ◽  
pp. 25-35
Author(s):  
ŁUKASZ BALBUS ◽  
ANDRZEJ S. NOWAK
Keyword(s):  
Capital Accumulation ◽  
Nash Equilibria ◽  
Stochastic Games ◽  
Resource Extraction ◽  
Equilibrium Solutions ◽  
Resource Stock

A class of nonzero-sum symmetric stochastic games of capital accumulation/resource extraction is considered. It is shown that Nash equilibria in the games with some natural constraints are also equilibrium solutions in unconstrained games and dominate in the Pareto sense an equilibrium leading to exhausting the entire resource stock in the first period of the game.

On Nash Equilibria in Stochastic Games

2004 ◽  
pp. 26-40 ◽  
Author(s):  
Krishnendu Chatterjee ◽  
Rupak Majumdar ◽  
Marcin Jurdziński
Keyword(s):  
Nash Equilibria ◽  
Stochastic Games

DYNAMIC STOCHASTIC GAMES OF RESOURCE ALLOCATION BETWEEN PRODUCTION AND CONSUMPTION

1999 ◽  
Vol 01 (02) ◽  
pp. 149-158 ◽  
Author(s):  
VICTOR DOMANSKY
Keyword(s):  
Resource Allocation ◽  
Nash Equilibria ◽  
Stochastic Games ◽  
Public Utility ◽  
Production Functions ◽  
Multistage Processes ◽  
Production And Consumption ◽  
Dynamic Stochastic

Controlled by several agents, multistage processes of resource allocation between production and consumption with random production functions are considered as non-cooperative dynamic stochastic games. For these games, the Nash Equilibria are constructed satisfying the criteria of maximisation of some kind of "public utility". Both finite and infinite horizons of planning are examined.

scholarly journals On the existence of stationary Nash equilibria in average stochastic games with finite state and action spaces

2020 ◽  
Vol 13 ◽  
pp. 304-323
Author(s):  
Dmitrii Lozovanu ◽  
◽  
Stefan Pickl ◽  
Keyword(s):  
Nash Equilibria ◽  
Stochastic Games ◽  
Optimal Strategies ◽  
Stationary Strategies ◽  
Finite State ◽  
Optimal Stationary Strategies ◽  
Action Spaces

We consider infinite n-person stochastic games with limiting average payoffs criteria for the players. The main results of the paper are concerned with the existence of stationary Nash equilibria and determining the optimal strategies of the players in the games with finite state and action spaces. We present conditions for the existence of stationary Nash equilibria in the considered games and propose an approach for determining the optimal stationary strategies of the players if such strategies exist.

scholarly journals Nonzero-Sum Stochastic Games and Mean-Field Games with Impulse Controls

2021 ◽  
Author(s):  
Matteo Basei ◽  
Haoyang Cao ◽  
Xin Guo
Keyword(s):  
Nash Equilibria ◽  
Stochastic Games ◽  
Mean Field ◽  
Sufficient Conditions ◽  
Mean Field Games ◽  
Model Parameters ◽  
Management Problem ◽  
Player Game ◽  
The Impact ◽  
Impulse Controls

We consider a general class of nonzero-sum N-player stochastic games with impulse controls, where players control the underlying dynamics with discrete interventions. We adopt a verification approach and provide sufficient conditions for the Nash equilibria (NEs) of the game. We then consider the limiting situation when N goes to infinity, that is, a suitable mean-field game (MFG) with impulse controls. We show that under appropriate technical conditions, there exists a unique NE solution to the MFG, which is an ϵ-NE approximation to the N-player game, with [Formula: see text]. As an example, we analyze in detail a class of two-player stochastic games which extends the classical cash management problem to the game setting. In particular, we present numerical analysis for the cases of the single player, the two-player game, and the MFG, showing the impact of competition on the player’s optimal strategy, with sensitivity analysis of the model parameters.

scholarly journals Learning Nash Equilibria in Zero-Sum Stochastic Games via Entropy-Regularized Policy Approximation

2021 ◽  
Author(s):  
Yue Guan ◽  
Qifan Zhang ◽  
Panagiotis Tsiotras
Keyword(s):  
Nash Equilibrium ◽  
Nash Equilibria ◽  
Stochastic Games ◽  
Computational Cost ◽  
Q Learning ◽  
Scheduling Scheme ◽  
Speed Up ◽  
Zero Sum ◽  
Q Function ◽  
Previous Training

We explore the use of policy approximations to reduce the computational cost of learning Nash equilibria in zero-sum stochastic games. We propose a new Q-learning type algorithm that uses a sequence of entropy-regularized soft policies to approximate the Nash policy during the Q-function updates. We prove that under certain conditions, by updating the entropy regularization, the algorithm converges to a Nash equilibrium. We also demonstrate the proposed algorithm's ability to transfer previous training experiences, enabling the agents to adapt quickly to new environments. We provide a dynamic hyper-parameter scheduling scheme to further expedite convergence. Empirical results applied to a number of stochastic games verify that the proposed algorithm converges to the Nash equilibrium, while exhibiting a major speed-up over existing algorithms.

Sign in / Sign up

Export Citation Format

Share Document