<p>We consider a game in which individual players adopt strategies of moving left, moving right, or remain motionless, according to payoffs correlated to the overall population benefit and scaled by a state dependent modulation function. This results in an evolutionary game of motion under replicator dynamics; through a variety of simple forms, linear and piecewise linear, of the modulation function, we are able to capture how players local adaptation leads to the emergence of a group motion by analyzing both the stability and dynamic properties of the game. We uncover both swarm-style behaviors as well as group behaviors that counter-balance the motion of others. This includes the appearance of a continuum of equilibria akin to an evolutionary stable set. Numerical simulations are provided to validate the model analysis claims.</p>