Search

Signed networks describe many real-world relations among users. Positive connections between two users or vertices generally mean good feelings between them, but negative connections mean bad feelings. A disruptor cycle in a graph is a cycle containing only one negative edge. A signed graph is known to be clusterable if and only if it does not contain a disruptor cycle. In this paper, we study the clusterability of a signed graph from the point of view of game theory introducing social disruption games on signed graphs. In these games, a coalition wins if the subgraph induced by the coalition is non-clusterable, i.e., it contains a disruptor cycle. Moreover, we study parameters and properties of players and compare them to other subclasses of simple games. In addition, we give some complexity results. In particular, we show that, unlike other subclasses of simple games, given a social disruption game, computing its length, deciding whether it is proper, or deciding whether it has a dummy player can be done in polynomial time. However, other problems, such as deciding whether the game is strong, or computing known power indices, remain computationally hard. • We introduce social disruption games on signed graphs to study clusterability. • A coalition wins if the subgraph induced by the coalition is non-clusterable. • We study parameters and properties of players and compare them to other simple games. • We provide different computational complexity results. • For this games, some problems become polynomial, while some others remain hard. [ABSTRACT FROM AUTHOR]

Based on a generalized nonlinear price function and consumer surplus, a Cournot duopoly game whose players want to maximize their profits and social welfare is introduced in this paper. Just like studies in literature, the game is modeled by a nonlinear two-dimensional discrete map. Due to the general price function, the dynamics for the model such as local and global dynamic behaviors, synchronization and multi-stability are investigated at some special cases. The studies and the formation of game in this paper generalize other studies in literature. The general forms of the equilibrium points including Nash one are calculated. Analytically, the conditions of stability for those points are investigated. Focusing on Nash point and its dynamics, it is confirmed that the map's manifold can be studied using a one-dimensional map that is similar to the famous logistic map. It is confirmed that the game's map is noninvertible and belongs to the Z 4 − Z 2 − Z 0 type. The global bifurcation is analyzed using critical curves for some attracting sets and chaotic attractors. The symmetry of the game makes the diagonal line form an invariant set and hence synchronization is discussed. • A Cournot game whose players use gradient rule and want to maximize their profits and social welfare is introduced. • The interior equilibrium point of the game can be destabilized due flip bifurcation only. • Global analysis shows that the game's map is noninvertible. [ABSTRACT FROM AUTHOR]