Mathematics for self-modifying games with variable numbers of players

Develop a mathematical framework for game-theoretic models in which the number of individuals (players) changes in real time as a consequence of the players’ actions, including operations such as Merge and Split that add or remove selves during the dynamics.

Background

The paper describes biological scenarios (e.g., slime mold and embryogenesis) where the boundary of the self is dynamic and can split or merge, altering the number of interacting agents and thus changing the payoff landscape.

They outline an extension of spatialized, iterated Prisoner’s Dilemma to include Merge and Split moves but note that existing mathematical tools do not capture systems whose number of agents changes endogenously as part of the game dynamics.