Lima (1989) Iterated prisoner's dilemma interdependence

Lima, S. L. (1989). Iterated prisoner's dilemma: An approach to evolutionarily stable cooperation. The American Naturalist, 134, 828-834. 

A nice little paper about cooperation and interdependence. Fits nicely in the literature along with Roberts (2005) and my 2013 Am Nat paper.

The point is this:
If simply being in a social interaction is valuable, and cooperation increases the chance that your partner will survive to play again, then cooperation can be sustained. Lima alters the game such that the PD game payoffs correspond to probabilities of survival for another round of play. If one's partner dies, then the probability of surviving alone (\alpha) is less than the probability of survival even under mutual defection. Also, if your partner dies, there is some probability (\rho) that you will find another partner.

This approach differs from previous results (circa 1989) in 2 main ways: 
1. Fixed number of rounds of play. Axelrod & Hamilton only get cooperation if the number of rounds is uncertain. With interdependence, it doesn't have to be uncertain.
2. Other models treat accumulation of payoffs during the iterative game as strictly additive. In this approach fitness is multiplicative. This, and the fact that the payoff one player gets depends on the payoff it allows the other player, makes cooperation possible even in the face of a fixed number of plays.

Some more results for varying \alpha and \rho for a 10-round game: 
1. Cooperation decreases as the iterated game nears completion. This decrease may occur steadily or abruptly.
2. An increase in the probability of survival if alone (\alpha) leads to a decrease in cooperation for any given probability of obtaining another partner (\rho).
3. An increase in the probability of obtaining another partner (\rho) also leads to a decrease in cooperation.