On Braided Linear Gr-categories

We provide explicit and unified formulae for the normalized 3-cocycles on arbitrary finite abelian groups. As an application, we compute all the braided monoidal structures on linear Gr-categories.Comment: 14 pages; typos correcte

Graded elementary quasi-Hopf algebras of tame representation type

The class of graded elementary quasi-Hopf algebras of tame type is classified. Combining with our previous work [19], this completes the trichotomy for such class of algebras according to their representation types. In addition, new examples of genuine elementary quasi-Hopf algebras, and accordingly finite pointed tensor categories, are provided.Comment: 20 page

Evolution of cooperation in spatial traveler's dilemma game

Traveler's dilemma (TD) is one of social dilemmas which has been well studied in the economics community, but it is attracted little attention in the physics community. The TD game is a two-person game. Each player can select an integer value between $R$ and $M$ ($R < M$) as a pure strategy. If both of them select the same value, the payoff to them will be that value. If the players select different values, say $i$ and $j$ ($R \le i < j \le M$), then the payoff to the player who chooses the small value will be $i+R$ and the payoff to the other player will be $i-R$. We term the player who selects a large value as the cooperator, and the one who chooses a small value as the defector. The reason is that if both of them select large values, it will result in a large total payoff. The Nash equilibrium of the TD game is to choose the smallest value $R$. However, in previous behavioral studies, players in TD game typically select values that are much larger than $R$, and the average selected value exhibits an inverse relationship with $R$. To explain such anomalous behavior, in this paper, we study the evolution of cooperation in spatial traveler's dilemma game where the players are located on a square lattice and each player plays TD games with his neighbors. Players in our model can adopt their neighbors' strategies following two standard models of spatial game dynamics. Monte-Carlo simulation is applied to our model, and the results show that the cooperation level of the system, which is proportional to the average value of the strategies, decreases with increasing $R$ until $R$ is greater than the threshold where cooperation vanishes. Our findings indicate that spatial reciprocity promotes the evolution of cooperation in TD game and the spatial TD game model can interpret the anomalous behavior observed in previous behavioral experiments