Gaming Temporal Networks

Temporal networks are composed of individuals with on-and-off interactions. In the study of human dynamics, a typical interaction is interpreted as a coincidental or forced concurrence of two events. Since human beings' rationality is bounded, the interaction between sentient individuals is normally investigated under the framework of game theory in the past half a century. In this brief, a game model on social networks is introduced, in which individuals play a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2\times2$ </tex-math></inline-formula> divide-and-conquer game with their neighbors, which is a specific symmetric game based on the type of their interactions. The individuals in a network play with the game with a certain strategy. The duration of a continuous interaction is defined to be the number of the continuous rounds in which at least one of them receives a non-zero payoff. On the contrary, the inter-event time is measured by the number of the continuous rounds in which both players do not receive any payoff. A detailed analytical and numerical study of the model's dynamical properties is presented, showing that it reproduces the burstiness of the human coordinating system. The findings reveal that the burstiness is inducible by rational interactions of humans. The new model and analysis shed some new lights on the origin of the burstiness of human activities.