Two-Person Non Zero-Sum Bimatrix Game with Fuzzy Payoffs and Its Equilibrium Strategy

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

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CREDIBILISTIC BIMATRIX GAME WITH ASYMMETRIC INFORMATION: BAYESIAN OPTIMISTIC EQUILIBRIUM STRATEGY

International Journal of Uncertainty Fuzziness and Knowledge-Based Systems ◽

10.1142/s0218488513400072 ◽

2013 ◽

Vol 21 (supp01) ◽

pp. 89-100 ◽

Cited By ~ 11

Author(s):

JINWU GAO ◽

XIANGFENG YANG

Keyword(s):

Asymmetric Information ◽

Private Information ◽

Solution Concept ◽

Equilibrium Strategy ◽

Necessary Condition ◽

Bimatrix Games ◽

Bimatrix Game ◽

Confidence Levels ◽

Sufficient And Necessary Condition ◽

Optimistic Value

In credibilistic bimatrix games, the solution concept of (α, β)-optimistic equilibrium strategy was proposed for dealing with the situation that the two players want to optimize the optimistic value of their fuzzy objectives at confidence levels α and β, respectively. This paper goes further by assuming that the confidence levels are private information of the two players. And the so-called credibilistic bimatrix game with asymmetric information is investigated. A solution concept of Bayesian optimistic equilibrium strategy as well as its existence theorem are presented. Moreover, a sufficient and necessary condition is given for finding the Bayesian optimistic equilibrium strategy. Finally, an example is provided for illustrating purpose.

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A search game with one object and two searchers

Journal of Applied Probability ◽

10.1017/s0021900200111854 ◽

1986 ◽

Vol 23 (03) ◽

pp. 696-707 ◽

Cited By ~ 1

Author(s):

Teruhisa Nakai

Keyword(s):

Nash Equilibrium ◽

Differential Equations ◽

Equilibrium Point ◽

Explicit Solution ◽

Equilibrium Strategy ◽

Surprising Result ◽

Detection Rates ◽

Nash Equilibrium Point ◽

Search Game ◽

Zero Sum

We consider a non-zero-sum game in which two searchers (player I and II) compete with each other for quicker detection of an object hidden in one of n boxes. Let p (q) be the prior location distribution of the object for player I (II). Exponential detection functions are assumed for both players. Each player wishes to maximize the probability that he detects the object before the opponent detects it. In the general case, a Nash equilibrium point is obtained in the form of a solution of simultaneous differential equations. In the case of p = q, we obtain an explicit solution showing the surprising result that both players have the same equilibrium strategy even though the detection rates are different.

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A birth–death model of advertising and pricing

Advances in Applied Probability ◽

10.1017/s0001867800031736 ◽

1979 ◽

Vol 11 (01) ◽

pp. 134-152

Author(s):

S. Christian Albright ◽

Wayne Winston

Keyword(s):

Stochastic Game ◽

Optimal Level ◽

Competitive Environment ◽

Equilibrium Strategy ◽

Pricing Strategies ◽

Current Position ◽

Market Position ◽

Primary Focus ◽

Zero Sum ◽

Over Time

This paper employs the methods currently used to solve many queuing control models in order to investigate the behavior of a firm's optimal advertising and pricing strategies over time. Given that a firm's market position expands or deteriorates in a probabilistic way which depends upon the current position, the rate of advertising, and the price the firm charges, we present conditions which ensure that the optimal level of advertising is a monotonic function of the firm's market position, and we discuss the economic meaning of these conditions. Furthermore, although the primary focus is upon a non-competitive environment, we develop the above model as a non-zero sum, two-person stochastic game and show that an equilibrium strategy exists which is simple to compute.

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A birth–death model of advertising and pricing

Advances in Applied Probability ◽

10.2307/1426772 ◽

1979 ◽

Vol 11 (1) ◽

pp. 134-152 ◽

Cited By ~ 9

Author(s):

S. Christian Albright ◽

Wayne Winston

Keyword(s):

Stochastic Game ◽

Optimal Level ◽

Competitive Environment ◽

Equilibrium Strategy ◽

Pricing Strategies ◽

Current Position ◽

Market Position ◽

Primary Focus ◽

Zero Sum ◽

Over Time

This paper employs the methods currently used to solve many queuing control models in order to investigate the behavior of a firm's optimal advertising and pricing strategies over time. Given that a firm's market position expands or deteriorates in a probabilistic way which depends upon the current position, the rate of advertising, and the price the firm charges, we present conditions which ensure that the optimal level of advertising is a monotonic function of the firm's market position, and we discuss the economic meaning of these conditions. Furthermore, although the primary focus is upon a non-competitive environment, we develop the above model as a non-zero sum, two-person stochastic game and show that an equilibrium strategy exists which is simple to compute.

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