Behavioral Ecology

In contests modeled after the hawk-dove game, when the benefit is greater than the cost, the best strategy is to always play hawk.

The Prisoner's Dilemma, when repeated, offers a maximum reward if you mix up your strategy. It is true that cheating offers a better reward no matter what your opponent does, however, by mimicking your partner's behavior, you will obtain the maximum reward. When your partner cheats, you should cheat in the next game. When your partner cooperates, you should cooperate in the next game.

Figure %: Payoff Matrix for Woozle Mating Strategies

If a dominator meets another dominator, he has a 50% chance of winning and producing 10 offspring, and a 50% chance of losing which means a cost of 10 offspring. Therefore the average payoff for a dominator/dominator encounter is zero. Dominators who meet sharers will win the territory and produce 10 offspring. Sharers who meet sharers will produce 5 offspring each. Sharers who meet dominators will always produce 3 offspring at their new territory. Since these are the only two mating strategies Woozles can choose from, we know that the proportion of dominators (p) and sharers (q) will equal the entire population. We then use our equations to estimate the relative payoffs for the dominator strategy and the sharer strategy. We end up with the following two equations: p + q = 1
p(0) + q(10) = p(3) + q(5)
Solving for p and q yields:
p=5/8
q=3/8

5/8 of the population will be dominators and 3/8 will be sharers.