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The pursuer-evader (PE) game is recognized as an important domain in which to study the coevolution of robust adaptive behavior and protean behavior (Mifier and Cliff, 1994). Nevertheless, the potential of the game is largely unrealized due to methodological hurdles in coevolutionary simulation raised by PE; versions of the game that have optimal solutions (Isaacs, 1965) are closed-ended, while other formulations are opaque with respect to their solution space, for the lack of a rigorous metric of agent behavior. This inability to characterize behavior, in turn, obfuscates coevolutionary dynamics. We present a new formulation of PE that affords a rigorous measure of agent behavior and system dynamics. The game is moved from the two-dimensional plane to the one-dimensional bitstring; at each time step, the evader generates a bit that the pursuer must simultaneously predict. Because behavior is expressed as a time series, we can employ information theory to provide quantitative analysis of agent activity. Further, this version of PE opens vistas onto the communicative component of pursuit and evasion behavior, providing an open-ended serial communications channel and an open world (via coevolution). Results show that subtle changes to our game determine whether it is open-ended, and profoundly affect the viability of arms-race dynamics.