Cavaliere et al. (2012) Prosperity is associated with instability in dynamical networks

Cavaliere M, Sedwards S, Tarnita CE, Nowak MA, & Csikász-Nagy A (2012) Prosperity is associated with instability in dynamical networks. Journal of Theoretical Biology 299, 126-138. 

A neat little model of network dynamics based on imitation. Here's how it works:

A random network is formed and agents are either cooperators or defectors. All agents play the PD game with all neighbors and collect payoffs.  A newcomer agent enters the network. A node is chosen probabilistically from the network to serve as a role-model for the newcomer, such that agents with higher payoffs are more likely to serve as role-models. A tunable parameter delta dictates the strength of this effect, but delta is not analyzed in the main text. The newcomer then forms a link with the role model with probability p and with each of the role-model's connections with probability q. These are known as the embedding parameters.

Simulations were run out to 10^8 time steps.

The big conclusions of the model is that maximum prosperity -- caused by the right mixture of cooperation and connectivity, it associated with medium-high values of q and relatively high network instability -- in other words, there is a high likelihood of transitions between all cooperators and all defectors.

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.