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.

Support Set Invariancy for Interval Bimatrix Games

2019 ◽  
Vol 27 (02) ◽  
pp. 225-237
Author(s):  
Milan Hladík
Keyword(s):  
Mixed Integer ◽  
Necessary Condition ◽  
Linear Programs ◽  
Bimatrix Games ◽  
Bimatrix Game ◽  
Integer Programs ◽  
Mixed Integer Programs ◽  
Support Set ◽  
First Case ◽  
Pure Strategies

Traditionally, game theory problems were considered for exact data, and the decisions were based on known payoffs. However, this assumption is rarely true in practice. Uncertainty in measurements and imprecise information must be taken into account. The interval-based approach for handling such uncertainties assumes that one has lower and upper bounds on payoffs. In this paper, interval bimatrix games are studied. Especially, we focus on three kinds of support set invariancy. Support of a mixed strategy consists of that pure strategies having positive probabilities. Given an interval-valued bimatrix game and supports for both players, the question states as follows: Does every bimatrix game instance have an equilibrium with the prescribed support? The other two kinds of invariancies are slight modifications: Has every bimatrix game instance an equilibrium being a subset/superset of the prescribed support? It is computationally difficult to answer these questions: the first case costs solving a large number of linear programs or mixed integer programs. For the remaining two cases a sufficient condition and a necessary condition are proposed, respectively.

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.

scholarly journals Cauchy matrix and Liouville formula of quaternion impulsive dynamic equations on time scales

2020 ◽  
Vol 18 (1) ◽  
pp. 353-377 ◽  
Author(s):  
Zhien Li ◽  
Chao Wang
Keyword(s):  
Time Scales ◽  
Quaternion Algebra ◽  
Matrix Exponential ◽  
Dynamic Equations ◽  
Necessary Condition ◽  
Quaternion Matrix ◽  
Exponential Functions ◽  
Cauchy Matrix ◽  
Adjoint Matrix ◽  
Sufficient And Necessary Condition

Abstract In this study, we obtain the scalar and matrix exponential functions through a series of quaternion-valued functions on time scales. A sufficient and necessary condition is established to guarantee that the induced matrix is real-valued for the complex adjoint matrix of a quaternion matrix. Moreover, the Cauchy matrices and Liouville formulas for the quaternion homogeneous and nonhomogeneous impulsive dynamic equations are given and proved. Based on it, the existence, uniqueness, and expressions of their solutions are also obtained, including their scalar and matrix forms. Since the quaternion algebra is noncommutative, many concepts and properties of the non-quaternion impulsive dynamic equations are ineffective, we provide several examples and counterexamples on various time scales to illustrate the effectiveness of our results.

scholarly journals Sufficient and necessary conditions for oscillation of linear fractional-order delay differential equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Qiong Meng ◽  
Zhen Jin ◽  
Guirong Liu
Keyword(s):  
Differential Equation ◽  
Fractional Order ◽  
Sufficient Conditions ◽  
Necessary Condition ◽  
Multiple Delays ◽  
All Solutions ◽  
Sufficient And Necessary Conditions ◽  
Delay Differential ◽  
T Tau ◽  
Sufficient And Necessary Condition

AbstractThis paper studies the linear fractional-order delay differential equation $$ {}^{C}D^{\alpha }_{-}x(t)-px(t-\tau )= 0, $$ D − α C x ( t ) − p x ( t − τ ) = 0 , where $0<\alpha =\frac{\text{odd integer}}{\text{odd integer}}<1$ 0 < α = odd integer odd integer < 1 , $p, \tau >0$ p , τ > 0 , ${}^{C}D_{-}^{\alpha }x(t)=-\Gamma ^{-1}(1-\alpha )\int _{t}^{\infty }(s-t)^{- \alpha }x'(s)\,ds$ D − α C x ( t ) = − Γ − 1 ( 1 − α ) ∫ t ∞ ( s − t ) − α x ′ ( s ) d s . We obtain the conclusion that $$ p^{1/\alpha } \tau >\alpha /e $$ p 1 / α τ > α / e is a sufficient and necessary condition of the oscillations for all solutions of Eq. (*). At the same time, some sufficient conditions are obtained for the oscillations of multiple delays linear fractional differential equation. Several examples are given to illustrate our theorems.

scholarly journals Research on the Relationship between Shared Leadership and Individual Creativity-Qualitative Comparative Analysis on the Basis of Clear Set

2021 ◽  
Vol 13 (10) ◽  
pp. 5445
Author(s):  
Muyun Sun ◽  
Jigan Wang ◽  
Ting Wen
Keyword(s):  
Comparative Analysis ◽  
Environmental Factors ◽  
Shared Leadership ◽  
Management Practices ◽  
Qualitative Comparative Analysis ◽  
Necessary Condition ◽  
The Individual ◽  
The Impact ◽  
The Relationship ◽  
Sufficient And Necessary Condition

Creativity is the key to obtaining and maintaining competitiveness of modern organizations, and it has attracted much attention from academic circles and management practices. Shared leadership is believed to effectively influence team output. However, research on the impact of individual creativity is still in its infancy. This study adopts the qualitative comparative analysis method, taking 1584 individuals as the research objects, underpinned by a questionnaire-based survey. It investigates the influence of the team’s shared leadership network elements and organizational environmental factors on the individual creativity. We have found that there are six combination of conditions of shared leadership and organizational environmental factors constituting sufficient combination of conditions to increase or decrease individual creativity. Moreover, we have noticed that the low network density of shared leadership is a sufficient and necessary condition of reducing individual creativity. Our results also provide management suggestions for practical activities during the team management.

scholarly journals A nonlocal game for witnessing quantum networks

2019 ◽  
Vol 5 (1) ◽  
Author(s):  
Ming-Xing Luo
Keyword(s):  
Computational Complexity ◽  
Main Idea ◽  
Bell Inequalities ◽  
Theoretical Computer Science ◽  
Graph Representation ◽  
Necessary Condition ◽  
Quantum Networks ◽  
Theoretical Computer ◽  
Sufficient And Necessary Condition ◽  
Unified Method

Abstract Nonlocal game as a witness of the nonlocality of entanglement is of fundamental importance in various fields. The well-known nonlocal games or equivalent linear Bell inequalities are only useful for Bell networks consisting of single entanglement. Our goal in this paper is to propose a unified method for constructing cooperating games in network scenarios. We propose an efficient method to construct multipartite nonlocal games from any graphs. The main idea is the graph representation of entanglement-based quantum networks. We further specify these graphic games with quantum advantages by providing a simple sufficient and necessary condition. The graphic games imply a linear Bell testing of the nonlocality of general quantum networks consisting of EPR states. It also allows generating new instances going beyond CHSH game. These results have interesting applications in quantum networks, Bell theory, computational complexity, and theoretical computer science.

New characterizations of g-frames and g-Riesz bases

2018 ◽  
Vol 16 (06) ◽  
pp. 1850053 ◽  
Author(s):  
Dongwei Li ◽  
Jinsong Leng ◽  
Tingzhu Huang
Keyword(s):  
Riesz Basis ◽  
Riesz Bases ◽  
Gram Matrix ◽  
Necessary Condition ◽  
Topological Properties ◽  
Bessel Sequence ◽  
Bessel Sequences ◽  
Sufficient And Necessary Condition

In this paper, we give some new characterizations of g-frames, g-Bessel sequences and g-Riesz bases from their topological properties. By using the Gram matrix associated with the g-Bessel sequence, we present a sufficient and necessary condition under which the sequence is a g-Bessel sequence (or g-Riesz basis). Finally, we consider the excess of a g-frame and obtain some new results.

A SUFFICIENT AND NECESSARY CONDITION FOR CREDIBILITY MEASURES

2006 ◽  
Vol 14 (05) ◽  
pp. 527-535 ◽  
Author(s):  
XIANG LI ◽  
BAODING LIU
Keyword(s):  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Extension Theorem ◽  
The Self ◽  
Necessary Condition ◽  
Self Duality ◽  
Duality Property ◽  
Sufficient And Necessary Condition

Possibility measures and credibility measures are widely used in fuzzy set theory. Compared with possibility measures, the advantage of credibility measures is the self-duality property. This paper gives a relation between possibility measures and credibility measures, and proves a sufficient and necessary condition for credibility measures. Finally, the credibility extension theorem is shown.

scholarly journals Formation behaviors of networks with antagonistic interactions of agents

2017 ◽  
Vol 13 (8) ◽  
pp. 155014771772629 ◽  
Author(s):  
Wen-Lu Zou ◽  
Gun Li
Keyword(s):  
Time Delay ◽  
Frequency Domain Analysis ◽  
Necessary Condition ◽  
Multi Agent System ◽  
Multi Agent Systems ◽  
Formation Behavior ◽  
Multi Agent ◽  
Group Form ◽  
Sufficient And Necessary Condition ◽  
Antagonistic Interactions

In this study, a new formation behavior problem for second-order multi-agent systems with time delay is investigated in the presence of antagonistic interactions. We first proposed a formation behavior protocol with time delay for each agent in the antagonistic network. Then, by a frequency-domain analysis, a sufficient and necessary condition is derived to guarantee the consensus stability of the multi-agent system. It is shown that the agents in the same group form their own desired formation while keeping a desired relative position with other groups. Finally, numerical simulations are provided to illustrate the obtained results.

Consensus Problem of Singular Multi-Agent Systems with Continuous-Time and Fixed Topology

2013 ◽  
Vol 278-280 ◽  
pp. 1687-1691
Author(s):  
Tong Qiang Jiang ◽  
Jia Wei He ◽  
Yan Ping Gao
Keyword(s):  
Continuous Time ◽  
Spanning Tree ◽  
Undirected Graph ◽  
Necessary Condition ◽  
Multi Agent Systems ◽  
Agent Systems ◽  
Multi Agent ◽  
Fixed Topology ◽  
The Stability ◽  
Sufficient And Necessary Condition

The consensus problems of two situations for singular multi-agent systems with fixed topology are discussed: directed graph without spanning tree and the disconnected undirected graph. A sufficient and necessary condition is obtained by applying the stability theory and the system is reachable asymptotically. But for normal systems, this can’t occur in upper two situations. Finally a simulation example is provided to verify the effectiveness of our theoretical result.

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