scholarly journals Characterization of the Equilibrium Strategy of the Bimatrix Game with Fuzzy Payoff

2000 ◽  
Vol 251 (2) ◽  
pp. 885-896 ◽  
Author(s):  
Takashi Maeda
Keyword(s):  
Equilibrium Strategy ◽  
Bimatrix Game ◽  
Fuzzy Payoff

scholarly journals Jury Verdicts and Preference Diversity

2000 ◽  
Vol 94 (2) ◽  
pp. 395-406 ◽  
Author(s):  
Dino Gerardi
Keyword(s):  
Decision Making ◽  
Equilibrium Strategy ◽  
Correct Decision ◽  
Unanimity Rule ◽  
Voting Rule ◽  
Jury Verdicts ◽  
Asymptotically Efficient

I develop a model of decision making in juries when there is uncertainty about jurors' preferences. I provide a characterization of the equilibrium strategy under any voting rule and show that nonunanimous rules are asymptotically efficient. Specifically, large juries make the correct decision with probability close to one. My analysis also demonstrates that under the unanimous rule, large juries almost never convict the defendant. The last result contrasts markedly with the literature and suggests that the unanimity rule can protect the innocent only at the price of acquitting the guilty.

CREDIBILISTIC BIMATRIX GAME WITH ASYMMETRIC INFORMATION: BAYESIAN OPTIMISTIC EQUILIBRIUM STRATEGY

2013 ◽  
Vol 21 (supp01) ◽  
pp. 89-100 ◽  
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.

On characterization of credibilistic equilibria of fuzzy-payoff two-player zero-sum game

2008 ◽  
Vol 13 (2) ◽  
pp. 127-132 ◽  
Author(s):  
Jinwu Gao ◽  
Zhi-Qiang Liu ◽  
Puchen Shen
Keyword(s):  
Fuzzy Payoff ◽  
Zero Sum

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

2009 ◽  
Vol 1 (1) ◽  
Author(s):  
Chunyan Han ◽  
Zuofeng Gao ◽  
Yongbo Yu ◽  
Hua Zhang ◽  
Suting Zhang ◽  
...  
Keyword(s):  
Equilibrium Strategy ◽  
Bimatrix Game ◽  
Zero Sum

scholarly journals Approximation of Isomorphic Infinite Two-Person Non-Cooperative Games by Variously Sampling the Players’ Payoff Functions and Reshaping Payoff Matrices into Bimatrix Game

2016 ◽  
Vol 20 (1) ◽  
pp. 5-14 ◽  
Author(s):  
Vadim V. Romanuke ◽  
Vladimir V. Kamburg
Keyword(s):  
Cooperative Games ◽  
Equilibrium Strategy ◽  
Finite Dimensional Space ◽  
Sampling Step ◽  
Bimatrix Game ◽  
Infinite Game ◽  
Consistent Solution ◽  
Unit Hypercube ◽  
Payoff Functions ◽  
Non Cooperative Games

Abstract Approximation in solving the infinite two-person non-cooperative games is studied in the paper. An approximation approach with conversion of infinite game into finite one is suggested. The conversion is fulfilled in three stages. Primarily the players’ payoff functions are sampled variously according to the stated requirements to the sampling. These functions are defined on unit hypercube of the appropriate Euclidean finite-dimensional space. The sampling step along each of hypercube dimensions is constant. At the second stage, the players’ payoff multidimensional matrices are reshaped into ordinary two-dimensional matrices, using the reversible index-to-index reshaping. Thus, a bimatrix game as an initial infinite game approximation is obtained. At the third stage of the conversion, the player’s finite equilibrium strategy support is checked out for its weak consistency, defined by five types of inequalities within minimal neighbourhood of every specified sampling step. If necessary, the weakly consistent solution of the bimatrix game is checked out for its consistency, strengthened in that the cardinality of every player’s equilibrium strategy support and their densities shall be non-decreasing within minimal neighbourhood of the sampling steps. Eventually, the consistent solution certifies the game approximation acceptability, letting solve even games without any equilibrium situations, including isomorphic ones to the unit hypercube game. A case of the consistency light check is stated for the completely mixed Nash equilibrium situation.

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