scholarly journals Credibilistic Loss Aversion Nash Equilibrium for Bimatrix Games with Triangular Fuzzy Payoffs

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-16 ◽  
Author(s):  
Chunsheng Cui ◽  
Zhongwei Feng ◽  
Chunqiao Tan
Keyword(s):  
Loss Aversion ◽  
Nash Equilibria ◽  
Necessary Conditions ◽  
Existence Theorems ◽  
Bimatrix Games ◽  
Bimatrix Game ◽  
Fuzzy Variables ◽  
Confidence Levels ◽  
Sufficient And Necessary Conditions ◽  
The Relationship

Inspired by Shalev’s model of loss aversion, we investigate the effect of loss aversion on a bimatrix game where the payoffs in the bimatrix game are characterized by triangular fuzzy variables. First, we define three solution concepts of credibilistic loss aversion Nash equilibria, and their existence theorems are presented. Then, three sufficient and necessary conditions are given to find the credibilistic loss aversion Nash equilibria. Moreover, the relationship among the three credibilistic loss aversion Nash equilibria is discussed in detail. Finally, for2×2bimatix game with triangular fuzzy payoffs, we investigate the effect of loss aversion coefficients and confidence levels on the three credibilistic loss aversion Nash equilibria. It is found that an increase of loss aversion levels of a player leads to a decrease of his/her own payoff. We also find that the equilibrium utilities of players are decreasing (increasing) as their own confidence levels when players employ the optimistic (pessimistic) value criterion.

Protagoras Unbound

1975 ◽  
Vol 1 (1) ◽  
pp. 1-9
Author(s):  
F. C. White
Keyword(s):  
Necessary Conditions ◽  
Sufficient And Necessary Conditions ◽  
The Relationship

In this paper I want to do the following things. First I want to show that in the part of the Theaetetus where the relationship between knowledge and perception is examined, the concept of knowledge that is in question is very clearly characterized. We are left in no doubt as to what is to count as knowing. Secondly I want to unravel in some detail the case that Socrates puts on Protagoras’ behalf where he draws on what Protagoras actually wrote (151 E-152C); as opposed to what he may have taught secretly to his pupils (152C-160D). Thirdly I wish to argue that if we let the dialogue speak for itself, it is manifest that this case put up on Protagoras’ behalf at 151 E-152C is not overthrown; it is not even shaken.In that part of the dialogue (151 D-186E) where the question is under examination whether or not knowledge and perception are the same, Socrates uses an idealized concept of knowledge. That is, he restricts the use of the word by setting down what he will consider to be the essential characteristics of knowledge, the sufficient and necessary conditions of its being instantiated. An excellent piece of philosophical procedure.

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.

Nash Equilibria of Co-Operative Advertising Programs with Advertising Threshold Effects

2014 ◽  
Vol 16 (04) ◽  
pp. 981-1004 ◽  
Author(s):  
Qinglong Gou ◽  
Juzhi Zhang ◽  
Juan Zhang ◽  
Liang Liang
Keyword(s):  
Nash Equilibria ◽  
Necessary Conditions ◽  
Marketing Research ◽  
Threshold Effect ◽  
Cooperative Advertising ◽  
Threshold Effects ◽  
Response Model ◽  
Nash Game ◽  
Sufficient And Necessary Conditions ◽  
The Impact

As an important advertising phenomenon which has been proven by previous empirical marketing research, the advertising threshold effect implies that advertising has little effect on sales when advertising investment is beneath a certain level. In this paper, we focus on a cooperative advertising program, in which a manufacturer shares part of its retailer’s advertising cost, to illustrate the impact of the advertising threshold effect. Dividing the advertisement efforts into national and local advertising, we propose a new advertising response model which can describe the advertising threshold effect well. Based on the advertising response function, we derive the manufacturer’s and the retailer’s equilibrium advertising investments when they play a Nash game. From the analysis we find that there are four possible Nash equilibria when we take the advertising threshold effect into account. We derive the sufficient and necessary conditions under which each of the four possible equilibria is a Nash equilibrium, and explain these conditions with examples from practice. Another interesting result is that there are two different equilibria when certain conditions are satisfied.

scholarly journals Chaotic and hypercyclic properties of the quasi-linear Lasota equation

2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Cheng-Hung Hung
Keyword(s):  
Explicit Solution ◽  
Necessary Conditions ◽  
Sufficient And Necessary Conditions ◽  
Relationship Of ◽  
The Relationship

AbstractIn this paper we describe an explicit solution semigroup of the quasi-linear Lasota equation. By constructing the relationship of this solution semigroup with the translation semigroup we obtain some sufficient and necessary conditions for the solution semigroup of the quasi-linear Lasota equation to be hypercyclic or chaotic respectively.

scholarly journals A study on strongly convex hyper S-subposets in hyper S-posets

2020 ◽  
Vol 18 (1) ◽  
pp. 1935-1951
Author(s):  
Jian Tang ◽  
Xiang-Yun Xie ◽  
Bijan Davvaz
Keyword(s):  
Necessary Conditions ◽  
Decomposition Theorem ◽  
Strongly Convex ◽  
Unique Decomposition ◽  
Sufficient And Necessary Conditions ◽  
The Relationship

Abstract In this paper, we study various strongly convex hyper S-subposets of hyper S-posets in detail. To begin with, we consider the decomposition of hyper S-posets. A unique decomposition theorem for hyper S-posets is given based on strongly convex indecomposable hyper S-subposets. Furthermore, we discuss the properties of minimal and maximal strongly convex hyper S-subposets of hyper S-posets. In the sequel, the concept of hyper C-subposets of a hyper S-poset is introduced, and several related properties are investigated. In particular, we discuss the relationship between greatest strongly convex hyper S-subposets and hyper C-subposets of hyper S-posets. Moreover, we introduce the concept of bases of a hyper S-poset and give out the sufficient and necessary conditions of the existence of the greatest hyper C-subposets of a hyper S-poset by the properties of bases.

scholarly journals On the Commitment Value and Commitment Optimal Strategies in Bimatrix Games

2018 ◽  
Vol 20 (03) ◽  
pp. 1840001
Author(s):  
Stefanos Leonardos ◽  
Costis Melolidakis
Keyword(s):  
Nash Equilibrium ◽  
Nash Equilibria ◽  
Sufficient Conditions ◽  
Solution Concept ◽  
Optimal Strategies ◽  
Payoff Matrix ◽  
Matrix Game ◽  
Bimatrix Games ◽  
Equilibrium Payoff ◽  
The Relationship

Given a bimatrix game, the associated leadership or commitment games are defined as the games at which one player, the leader, commits to a (possibly mixed) strategy and the other player, the follower, chooses his strategy after being informed of the irrevocable commitment of the leader (but not of its realization in case it is mixed). Based on a result by Von Stengel and Zamir [2010], the notions of commitment value and commitment optimal strategies for each player are discussed as a possible solution concept. It is shown that in nondegenerate bimatrix games (a) pure commitment optimal strategies together with the follower’s best response constitute Nash equilibria, and (b) strategies that participate in a completely mixed Nash equilibrium are strictly worse than commitment optimal strategies, provided they are not matrix game optimal. For various classes of bimatrix games that generalize zero-sum games, the relationship between the maximin value of the leader’s payoff matrix, the Nash equilibrium payoff and the commitment optimal value are discussed. For the Traveler’s Dilemma, the commitment optimal strategy and commitment value for the leader are evaluated and seem more acceptable as a solution than the unique Nash equilibrium. Finally, the relationship between commitment optimal strategies and Nash equilibria in [Formula: see text] bimatrix games is thoroughly examined and in addition, necessary and sufficient conditions for the follower to be worse off at the equilibrium of the leadership game than at any Nash equilibrium of the simultaneous move game are provided.

scholarly journals Oscillation of Second-Order Differential Equations with Multiple and Mixed Delays under a Canonical Operator

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1323
Author(s):  
Shyam Sundar Santra ◽  
Rami Ahmad El-Nabulsi ◽  
Khaled Mohamed Khedher
Keyword(s):  
Differential Equations ◽  
Necessary Conditions ◽  
Second Order ◽  
Multiple Delays ◽  
Mixed Delays ◽  
Neutral Differential Equations ◽  
Canonical Operator ◽  
Second Order Differential Equations ◽  
The Future ◽  
Sufficient And Necessary Conditions

In this work, we obtained new sufficient and necessary conditions for the oscillation of second-order differential equations with mixed and multiple delays under a canonical operator. Our methods could be applicable to find the sufficient and necessary conditions for any neutral differential equations. Furthermore, we proved the validity of the obtained results via particular examples. At the end of the paper, we provide the future scope of this study.

scholarly journals Properties of Certain Subclass of Meromorphic Multivalent Functions Associated with q-Difference Operator

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1035
Author(s):  
Cai-Mei Yan ◽  
Rekha Srivastava ◽  
Jin-Lin Liu
Keyword(s):  
Difference Operator ◽  
Necessary Conditions ◽  
Partial Sums ◽  
Coefficient Estimates ◽  
Radius Of Starlikeness ◽  
Closure Theorems ◽  
Sufficient And Necessary Conditions ◽  
Distortion Theorems ◽  
Growth And Distortion Theorems

A new subclass Σp,q(α,A,B) of meromorphic multivalent functions is defined by means of a q-difference operator. Some properties of the functions in this new subclass, such as sufficient and necessary conditions, coefficient estimates, growth and distortion theorems, radius of starlikeness and convexity, partial sums and closure theorems, are investigated.

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