  We study a Stackelberg game to examine how two agents determine to cooperate
while competing with each other. Each selects an arrival time to a destination,
the earlier one fetching a higher reward. There is, however, an inherent
penalty in arriving too early as well as a risk in traveling alone. This gives
rise to the possibility of the agents cooperating by traveling together while
competing for the reward. In our prior work [1] we studied this problem as a
sequential game among a set of $N$ competing agents in continuous time, and
defined the formation of a group traveling together as arriving at exactly the
same time. In the present study, we relax this definition to allow arrival
times within a small window, and study a 2-agent game in both continuous and
discrete time, referred to as the flock formation game. We derive and examine
the properties of the subgame perfect equilibrium (SPE) of this game.
