An evolutionarily stable strategy (ESS) was originally defined as a static concept but later given a dynamic characterization. A well known theorem in evolutionary game theory says that an ESS is an attractor of replicator dynamic but not every attractor is an ESS. We search for a dynamic characterization of ESSs in quantum games and find that in certain asymmetric bi-matrix games evolutionary ...

In bi-matrix games the Bishop-Cannings theorem of the classical evolutionary game theory does not permit pure evolutionarily stable strategies (ESSs) when a mixed ESS exists. We find the necessary form of twoqubit initial quantum states when a switch-over to a quantum version of the game also changes the evolutionary stability of a mixed symmetric Nash equilibrium. PACS: 02.50.Le, 03.67.-a, 87....

These notes are largely based on a survey on learning, regret minimization and equilibria written by Avrim Blum and Yishay Mansour, and appearing as Chapter 4 of [NRTV07]. The main difference are in the presentation rather than in the content, and in the inclusion of Section 1.5. The notes correspond to two 2-hour lectures in the course on algorithmic game theory given in the Weizmann Institute...

In fact the Shapley value is the unique efficient semivalue. This motivated Ruiz et al. to do additive efficient normalization for semivalues. In this paper, by matrix approach we derive the relationship between the additive efficient normalization of semivalues and the Shapley value. Based on the relationship, we axiomatize the additive efficient normalization of semivalues as the unique solut...

An evolutionarily stable strategy (ESS) was originally defined as a static concept but later given a dynamic characterization. A well known theorem in evolutionary game theory says that an ESS is an attractor of replicator dynamics but not every attractor is an ESS. We search for a dynamic characterization of ESSs in quantum games and find that in certain asymmetric bi-matrix games evolutionary...

The basic concept of the fuzzy matrix theory is very simple and can be applied to social and natural situations. A branch of fuzzy matrix theory uses algorithms and algebra to analyse data. It is used by social scientists to analyse interactions between actors and can be used to complement analyses carried out using game theory or other analytical tools. The concepts of fuzzy matrix have been d...

By defining a special differential Nash game with an open-loop information structure scheme, a simple and direct method to obtain non-uniform multiple pole shifting for linear multivariable systems is presented. The approach is based on exploiting some properties of nonsymmetric algebraic Riccati equations associated with the Nash game. Combining solutions of such equations gives, in a single s...

In this paper we study some relations between the optimal strategies, the characteristic roots and the characteristic vectors of a positive square matrix whose rows and columns correspond to the pure strategy spaces of players in a zero-sum two-person game. Further we study a property of the game values of positive matrices that commute. The results are extended to infinite games on the unit sq...