McNamara et al. (2004) Variation in Behavior Promotes Cooperation

McNamara, J. M., Barta, Z., & Houston, A. I. (2004). Variation in behaviour promotes cooperation in the Prisoner's Dilemma game. Nature, 428, 745-748.

This is a really elegant little paper.

Evolutionary model of iterated PD game.

Major assumptions:
1. A player's strategy is n, defined as the number of rounds he will cooperate before defecting.
2. An iterated game ends after either player defects.
3. Games last a maximum of N rounds.

If players reproduce purely, than the only ESS is always defect. To show this, imagine if everyone plays n. Then the best strategy is to play n – 1.
However, what now imagine that the average strategy is n, but there is variation around this. Since mutual cooperation is better than mutual defection, if there is Normal variance around this mean, then the optimal strategy can be larger than n (Fig. 1).

They ran simulation models with agents, and a mutation rate e. The probability of a parent with strategy n reproducing an offspring with strategy n was 1 - 2e, with mutation equally likely to produce n + 1 or n – 1. This mutation could maintain variation in the population, and a threshold value of e drove the population to cooperation (Fig 2a).

Other results: 

• Variation could also be maintained by error in addition to mutation, and error lowered the threshold mutation rate (Fig 2b). 
• Weaker selection on cooperation (the smaller effect payoffs had on reproduction rate) helped maintain variation, and so lowered the threshold mutation rate (Fig. 3a).
• The transition to cooperation is largely independent of the maximum number of games, N, provided N > 2 (Fig. 3b). 

Campbell (1960) Blind variation and selective retention in creative thought

Campbell, D. T. (1960). Blind variation and selective retention in creative thought as in other knowledge processes. Psychological Review, 67, 380-400. 

The basic idea is that most thought, of the problem-solving variety, acts on existing knowledge. To generate knowledge, as in creativity, there needs to be a blind variation process. This is not necessarily purely random, but it means that "correct" solutions are no more or less likely than "incorrect" solutions. There is then a selective retention process.

The whole thing is explicitly analogous to Darwinian natural selection.

The paper is kind of clunkily written, with lots of block quotes from fairly philosophical writings, but the underlying idea seems pretty solid.

Summary:
     This paper has attempted to make the psychological and epistemological point that all processes leading to expansions of knowledge involve a blind-variation-and-selective-retention process. Processes, such as vision and thought, substituting for an overt trial and error are of couse acknowledged. But each of these are interpreted as containing in its very workability wisdom about the environment obtained originally by the blind variation of mutation and natural selection. In addition, each contains a blind-variation-and-selective-retention process at its own level. Supporting the effort to interpret all knowledge processes in this light has been an emphasis upon the tremendous gain in knowledge in the course of evolution and history, a gain which can only be explained by a continual breakout from the bounds of what was already known, a breakout for which blind variation provides the only mechanism available.

     The application of this perspective to the process of creative thought antedates its application to trial-and- error learning in animals and to organic evolution, and is illustrated through quotations from Bain, Souriau, Mach, and Poincaré. The model is not in disagreement with the bulk of the Gestalt description of problem solving, nor the work on heuristically programed problem-solving computers. However, there is an effort to root out a prevailing implicit belief in the possibility of "direct" or "insightful" creative thought processes.