“Dynamic matching pennies on networks”, published by “International Journal of Game Theory”, is a cooperative paper between Pro.CAO Zhigang of our school, Pro.QIN Chengzhong of University of California, Santa Barbara, Pro.YANG Xiaoguang of Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, and Associate Pro.ZHANG Boyu of Beijing Normal University. The original version of the paper was completed in May 2013, and it took six years before officially accepted in 2019.

The Coin Matching Game is an important model written into almost all the game theory textbooks. This model is important because it includes both cooperative and anticooperative human behaviors that are fairly universal. Cyber Coin Matching Game is the extension theory of Cyber Coin Matching Game, including three basic models: Cooperative Game, Anti-Cooperative Game and Coin Matching Game. The model can also be used to study interesting issues such as fashion phenomena and viewpoint dynamics. The main concern of this paper is the limit cycle length (LLC) of synchronous optimal reaction dynamics: this is a generalization of Nash Equilibrium, because the limit cycle of LLC=1 implies that the corresponding strategy combination must be pure strategy Nash Equilibrium. By constructing a Lyapunov function, Pro.CAO Zhigang and his collaborators proved that LLC is equal to 1 or 2 if there is only one class of individuals (that is, either all of individuals are synergies or all of individuals are anti-synergies). They then considered three special types of network structures, namely linear networks, ring networks and star networks. For linear and ring networks, they found that in almost all of cases the initial value leads to LLC=1, on the other side for star networks, the initial value results in LLC=4 in half of the time.

The paper was considered to study an "extremely important" topic by an Associate Editor of “International Journal of Game Theory”, while the research on this topic in the literature is not satisfactory. （“I believe the topic you study -- the simultaneous play of different games on a given network -- is extremely important and has not been dealt with satisfactorily in the literature.") "International Journal of Game Theory" is the flagship Journal of the International Society for Game Theory,  which is one of the most important and iconic journals in the field of game theory. Founded in 1971 by Nobel Laureate Professor Aumann, the journal is difficult to publish in. Mainland scholars publish only a handful of papers in the journal each year (Three of them in 2019).

The relevant papers：Zhigang CAO, Chengzhong QIN, Xiaoguang YANG, Boyu ZHANG, 2019, Dynamic matching pennies on networks, International Journal of Game Theory, 48: 887-920.