Wardil & da Silva, 2009 - Simultaneous Different Strategies and Cooperation

Ref: Wardil, L. & da Silva, J. K. L. (2009). Adoption of simultaneous different strategies against different opponents enhances cooperation. EPL (Europhysics Letters), 86, 38001.

They analyzed a situation where agents play a prisoner's dilemma game (PDG) on a lattice with all neighbors. Each time step, each agent picks a random neighbor and changes strategy with some probability if the neighbor's cumulative payoff was greater than its own. The trick here is that each agent has a separate strategy (C or D) for each neighbor. They look at 3 possible switching rules:


A: The agent chooses for replacement the interaction that had the smallest contribution to his cumulative payoff.
B: The agent changes the strategy he uses against the same agent he chose to imitate.
C: The agent changes a random strategy.

Results: Strategy C does not do any better than the usual version of this game, where every agent has only one strategy used against all neighbors. However, both models A and B do far better, promoting cooperation for much larger values of the temptation b (the payoff for (D, C), where (C, C) = 1). Model A does the best.
They obtain similar results for a ring instead of a lattice.

Model A leaves open the possibility of neutralizing a defector and keeping old cooperation.

Robustness: The introduced a probability of misjudgement, p, where agents use Model A with probability (1 - p) and Model C with probability p. In the lattice, Model A is robust for very small values of p, but the frequency of cooperation falls off dramatically if p is even a bit large, such as p = .01 for b = 2. Model A is much more robust to error in the ring, but this is probably due to the fact that Model C still performs decently there.