Hawks and Doves

Tastes In economics we largely take the tastes and preferences of the consumer to be a given piece of information. Within that context, the consumer attempts to maximize utility also given prices and income. We have spent some time thinking about how the consumer changes their actions when income or prices change. But we leave preferences stable. Biologists assume (I am told) an organism’s tastes are forged by the pressure of natural selection to help the organism solve important problems in their environment. Please read the book example about out tastes for sweets.

Strategic Preference A strategic preference helps the individual solve important problems of social interaction and the usefulness of having the preference depends on the fraction of the population who share them. What we will look at next is a model of preference formation. The example is taken from biology, but put into the language of economics. Note how there are basic assumptions and then conclusions are reached. On to the example of hawks and doves – a model of the taste for aggressive behavior.

The Model Say people are all the same except for some are hawks (have a strong preference for aggressive behavior) and some are doves (prefer to avoid aggressive behavior). Whenever two individuals come into conflict over an important resource (food, a mate, and so on) the hawk’s strategy will be to always fight for it while the dove’s strategy will be to never fight. Remember economics is about using scare resources. Hawks may kill doves and get the resources, but hawks might kill each other for the resource. Doves do not fight each other, but share resources.

The Model Say a food unit has 12 calories. When two doves meet close to a food unit they share it and each gets 6 calories. When a hawk and a dove meet close to a food unit the dove defers and the hawk gets all 12 calories. When two hawks meet close to a food unit there is a battle. The winner gets the 12 calories and the loser gets none. Also, each spends 10 calories in the fight. So, the winner has a net gain of 2 calories and the loser has a net gain of -10 (sometimes called a lose). If over time a hawk wins half of the encounters with other hawks and loses the other half the average payoff is -4.

The Model The average payoffs can be put in tabular form as: Individual Y hawkdove Individual X hawk -4 each12 for X, 0 for Y dove 0 for X, 12 for Y6 each. So you can see, for example, if 2 doves meet each will get 6 calories on average. Say h is the proportion of the population that is hawk and thus 1- h is the proportion that is dove. Then a hawk would meet another hawk h of the time and the payout would be -4 and would meet a dove 1-h of the time and the payout would be 12 for an average payoff of Ph = h(-4) + (1-h)12.

The Model Similarly, the dove would have an average payoff of Pd = h(0) + (1-h)6. Whenever we consider a value for h, if hawk has a higher average payoff then hawks will flourish and doves will diminish and h will grow. For example, if h =.5, Ph =.5(-4) +.5(12) = 4 and Pd =.5(0) +.5(6) = 3 and thus hawks will get most of the calories and thus they will have larger families and that trait will grow. But, if at an h doves have a higher average payoff then their families will grow and h will fall. For example, if h =.75, Ph =.75(-4) +.25(12) = 0 and Pd =.75(0) +.25(6) = 1.53 and thus doves will get most of the calories and thus they will have larger families and that trait will grow.

Conclusion Now, if the average payoff is the same at an h that h will remain and the family sizes will stabilize. We find this h by setting Ph = Pd and solving for h. We have h(-4) + (1-h)(12) = h(0) + (1-h)(6) and solving for x we get -4h + 12 – 12h = h, or 12 – 6 = 4h + 12h – 6h, or h = 6/10, or.6 The average payoff is 2.4 for each.