Interesting. Based on Triver's theories on cooperation and parental investment. An evolutionary ABM in the style of Axelrod (1997).
Male and female agents have conditional strategies for first move, conditional responses for the last two moves, and different strings (chromosomes) for M-M, F-F, M-F, and F-M interactions (they need all four since offspring can be either sex).
Model run:
Initialization
650 agents created with random strings and assigned a sex. Each starts with a score of zero.
The reproductive cost (RC) can be separate for males (MRC) and females (FRC).
Run
Interaction: Two agents are selected at random and play the PD game for 100 rounds. Their scores accumulate.
Reproduction: Two new agents are then selected and if (1) they are of the opposite sex, and (2) they each have enough points, they reproduce to create 2 new offspring. The RC is deducted form each players score and they are returned to the pool. The offspring are randomly assigned a sex and put into an offspring array.
This process of interaction and reproduction continues until 650 new offspring have been created. At this point, the first generation is complete, and the offspring become the new parent population. This continues for 20,000 generations. Each condition was run 30 times.
Payoff matrix is CC=3, CD=0, DC=5, DD=1. The problem here, of course, is that alternating cooperate and defect is just as profitable as playing CC all the time...
Results:
They do this weird thing where they look at the average score per individual per game. Therefore, in a population where agents mostly cooperate, you get an average score of 3.0, which in a population of mostly defectors, you get an average score of 1.0. Of course, this metric has no way of letting you know whether cooperation is conditional, or if strategies of alternating C and D evolve (a reverse TFT - since they are just as effective and could be more so if the opponent keeps cooperating). This is actually a huge problem with this model.
Anyway, they define 4 classes based on average population per-individual payoff: defectors (1.25), weak defectors (1.75), weak cooperators (2.25), and cooperators (2.75).
Baseline model: MRC = FRC
They found that, as RC increased, the average payoff per individual increased, indicating that individuals were cooperating more. When RC = 1, the reproductive cost is trivial, and defection strategies evolved. When RC was larger (≥200), they claim that "some kind of TFT strategie evolves" (p. 82).
Model 1: MRC < FRC, FRC = 1000
Females generally adopted a strategy of TFT against each other regardless of MRC.
Male-male payoffs were generally lower than in the baseline model.
Then MRC was very low, females tended to exploit males - i.e., males played COOPERATE and females played DEFECT.
This makes some sense. If males need minimal resources to reproduce, and females need a lot, then as long as males are equally likely to meet each other and get some payoff, they should let females exploit them.
The most common result in these cases was where the male always cooperates and the female alternates playing cooperate and defect. However, these females will also defect to all strategies except unconditional cooperators.
This experiment was qualitatively robust to changes in FRC, population size, interaction length, and mutation rates.
Model 2: MRC < FRC, FRC = 1000, immediate opportunity to reproduce after play.
In the previous model , there was no link between the interaction and reproduction phases. However, if males must invest in females, they would be better off ensuring that they are investing in the mother of their own infant. This link may lead males to invest even more heavily in females and their offspring.
This model is identical to Model 1, except that after a male and female have finished interacting, they can reproduce if they each have enough points.
Non-reciprocal male-female altruism evolved. For MRC = 200, in 73% of the simulations (22/30), males always cooperated while females always defected. In the other 27%, non-reciprocal altruism of the type seen in Model 1 evolved.
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