Cooperation and Competition: A Sequential Game Model of Flocking

Chenlan Wang, Shane DuBay, Mingyan Liu

Abstract: We study a sequential game model on how groups form in time. In particular, agents make asynchronous decisions on a time of arrival; those choosing the same arrival time are considered to travel together, or belong to the same flock. While flocking reduces travel costs, arriving earlier allows one to obtain a higher reward. Our model is primarily motivated by commonly observed flocking behavior among migratory birds, but it can also be applied to other areas of competition and cooperation, e.g., in the case of rideshare to a common destination with a limited supply of goods. Given the model's sequential nature, the solution concept we study is the subgame perfect equilibrium (SPE). We present in detail the nature of the SPE in a 2-agent and 3-agent game, respectively, and its properties in the more general n-agent game. Of particular interest are observations on when and what types of groups emerge in an SPE.