Theoretical Population Biology 12S (2019) 38-55 ITSEVIER Contents lists available at ScienceDirect Theoretical Population Biology journal home pa go: ..vww.elscvier.comflocateApb A two-player iterated survival game John Wakeley a.*, Martin Nowak a'b'c 'Department of Organismic and Evolutionary Biology. Harvard University. Cambridge. MA, 02138. USA b Program for Evolutionary Dynamics. Harvard University. Cambridge. MA 02138. USA ' Department of Mathematics, Harvard University. Cambridge, hfA 02138, USA ARTICLE INFO Ankle history: Received 22 May 2018 Available online 12 December 2018 Keywords: Prisoner's Dilemma Survival game Iterated game Replicator equation Moran model I. Introduction ABSTRACT We describe an iterated game between two players, in which the payoff is to survive a number of steps. Expected payoffs are probabilities of survival. A key feature of the game is that individuals have to survive on their own if their partner dies. We consider individuals with hardwired, unconditional behaviors or strategies. When both players are present. each step is a symmetric two-player game. The overall survival of the two individuals forms a Markov chain. As the number of iterations tends to infinity, all probabilities of survival decrease to Zero. We obtain general, analytical results for n-step payoffs and use these to describe how the game changes as it increases. In order to predict changes in the frequency of a cooperative strategy over time, we embed the survival game in three different models of a large, well- mixed population. Two of these models are deterministic and one is stochastic. Offspring receive their parent's type without modification and (finesses are determined by the game. Increasing the number of iterations changes the prospects for cooperation. All models become neutral in the limit (ri co). Further, if pairs of cooperative individuals survive together with high probability, specifically higher than for any other