One of these game theoretic considerations, called the Hawk/Dove Game, is due to a behavioral ecologist named John Maynard-Smith. Consider a population of birds with two strategies with regard to conflict over resources: There are doves, who will always share the resource with another but will always back down and take nothing if challenged. And there are hawks, who will always fight over the resource, gaining all the resource on winning the challenge, but will suffer an injury on losing.
Essentially the conflict over resources will result in a pay-off matrix looking something like this:
The way to read this matrix is that two players can choose two different strategies. When both players choose the Hawk strategy, each wins the resources R half the time and the other half the time it gets injured with payoff –I. If a Dove meets a Dove they both share the resource every time. On the off-diagonal entries, we show the average payoff to Player 1 in the first position, and the average payoff to Player 2 in the second position.
The question posed by Maynard-Smith is, given the parameters of the above payoff matrix, what would be the stable proportion of hawks and doves? Let H denote the proportion of hawks in the population and D = 1-H, the proportion of doves. And, without belaboring the point, the proportion is H = R / I. Observe that as long as I > R > 0, the proportion of hawks and doves will be well-defined, that is 1 > H >0.
A couple of interesting inferences are immediate. First that as long as R > 0, i.e. there is a perceived reward for fighting, there will be hawks in the population. It just seems immediate to me that sharing resources more equitably makes R smaller, and there would be less to be gained by (and therefore less need for) fighting. Second, note that as long as I > R, i.e. the cost of losing exceeds the reward of winning a fight, there will be doves in the population as well. But if it is perceived that there is more to win by fighting than there is to lose, doves will be extinguished from the population. The lesson for me in this is that if the true cost of fighting is fully accounted for, there would be more peace. George Fox declared that he "lived in the virtue of that life and power that took away the occasion of all wars". Perhaps that virtue is the spiritual insight that the parameter I >> R and that R ≈ 0, that the costs of fighting far outweigh the paltry benefits.
I feel like for myself if I think through the payoffs when I am tempted to fight, I can come to a greater realization of peace. But how do you deal with people who don't see these payoffs and are still living in the delusion that there is something to be gained by fighting? In that case the game changes to one called Prisoner's Dilemma and the dominant strategy is to always fight, since no matter what the opponent does, there is more to be gained by fighting than by cooperating. But even in this case there are some further insights from game theory.
One approach is to think about what happens when the game is played iteratively? A political scientist Robert Axelrod hosted a contest between computer algorithms playing the iterated Prisoner's Dilemma. He found that successful algorithms tended to be:
- Polite, not the first to be aggressive.
- Forbearing, slow to retaliate.
- Forgiving, quicker to cooperate again after a run of retaliation.
- Generous, not striving to score more than the opponent.
To me this suggests that such ostensibly altruistic behaviors are actually self-interested. Perhaps the right term is enlightened self-interest.
Finally, the rules of game theory are that the players do not communicate or negotiate, and that players only act rationally. Of course this is not true in real life, and this kind of analysis underscores the importance of transcending mere rationality and striving for deep connections, trust and communication.
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