A Method to Select Best Among Multi-Nash Equilibria

2021 ◽  
pp. 232102222110243
Author(s):  
M. Punniyamoorthy ◽  
Sarin Abraham ◽  
Jose Joy Thoppan
Keyword(s):  
Nash Equilibrium ◽  
Nash Equilibria ◽  
Equilibrium Solutions ◽  
Bimatrix Game ◽  
Jel Codes ◽  
Payoff Dominance ◽  
Nash Equilibrium Solutions ◽  
The Many ◽  
Zero Sum ◽  
Selection Of

A non-zero sum bimatrix game may yield numerous Nash equilibrium solutions while solving the game. The selection of a good Nash equilibrium from among the many options poses a dilemma. In this article, three methods have been proposed to select a good Nash equilibrium. The first approach identifies the most payoff-dominant Nash equilibrium, while the second method selects the most risk-dominant Nash equilibrium. The third method combines risk dominance and payoff dominance by giving due weights to the two criteria. A sensitivity analysis is performed by changing the relative weights of criteria to check its effect on the ranks of the multiple Nash equilibria, infusing more confidence in deciding the best Nash equilibrium. JEL Codes: C7, C72, D81

UNCERTAINTY BASED ROBUST OPTIMIZATION IN AERODYNAMICS

2009 ◽  
Vol 23 (03) ◽  
pp. 477-480 ◽  
Author(s):  
ZHILI TANG
Keyword(s):  
Nash Equilibrium ◽  
Robust Design ◽  
Single Point ◽  
Optimization Method ◽  
Equilibrium Solutions ◽  
Design Problems ◽  
Nash Equilibrium Solutions ◽  
Definition Of ◽  
Taguchi Robust Design ◽  
Statistical Definition

The Taguchi robust design concept is combined with the multi-objective deterministic optimization method to overcome single point design problems in Aerodynamics. Starting from a statistical definition of stability, the method finds, Nash equilibrium solutions for performance and its stability simultaneously.

scholarly journals An Algorithmic Procedure for Finding Nash Equilibrium

2020 ◽  
Vol 40 (1) ◽  
pp. 71-85
Author(s):  
HK Das ◽  
T Saha
Keyword(s):  
Nash Equilibrium ◽  
Nash Equilibria ◽  
Payoff Matrix ◽  
Matrix Game ◽  
Perfect Equilibrium ◽  
Repeated Use ◽  
Definition Of ◽  
Zero Sum ◽  
Mathematical Construction ◽  
Algorithmic Procedure

This paper proposes a heuristic algorithm for the computation of Nash equilibrium of a bi-matrix game, which extends the idea of a single payoff matrix of two-person zero-sum game problems. As for auxiliary but making the comparison, we also introduce here the well-known definition of Nash equilibrium and a mathematical construction via a set-valued map for finding the Nash equilibrium and illustrates them. An important feature of our algorithm is that it finds a perfect equilibrium when at the start of all actions are played. Furthermore, we can find all Nash equilibria of repeated use of this algorithm. It is found from our illustrative examples and extensive experiment on the current phenomenon that some games have a single Nash equilibrium, some possess no Nash equilibrium, and others had many Nash equilibria. These suggest that our proposed algorithm is capable of solving all types of problems. Finally, we explore the economic behaviour of game theory and its social implications to draw a conclusion stating the privilege of our algorithm. GANIT J. Bangladesh Math. Soc.Vol. 40 (2020) 71-85

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.

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