Title: On the Endogenous Order of Play in Sequential Games

Abstract: Cases abound in political or industrial competition where it is not reasonable to assume that agents will passively wait for their turn to act. We formalize, under the name of games of addition, the strategic interaction between agents who sequentially take actions, but may also agree unanimously to stop taking further actions and collect the payoffs associated with the given sequence of moves. Our formalization differs from that of extensive form games in that the order of the agents’ moves is not predetermined but emerges endogenously when applying an adapted version of a solution concept proposed by Dutta, Jackson, and Le Breton (2004). We provide results regarding the properties of solutions to games of addition, and we also demonstrate that the predicted outcomes may significantly differ from those obtained if using extensive form

games and subgame perfection as alternative tools of analysis.