The hawk dove game played between relatives

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Reprints and Permissions. Desjardins, MC. The hawk-dove game played between mating partners: theoretical predictions and experimental results.

Behav Ecol Sociobiol 69, — Download citation. Received : 07 August Revised : 20 December Accepted : 24 December Published : 10 January Issue Date : April This is clearly not a very reasonable assumption, but we're juststarting out so let's keep things simple. First, we'll make a qualitative analysis of the game, then we'll usegame theory to make a much more quantitative prediction as was discussedin the introductorymaterial dealing with games.

Let's start with the following question:Are either of the two strategies by themselves impervious to invasion? Imagine a population entirely of doves.

It is probably a very nice placeto live and everyone is doing reasonably well without injuries when it comesto conflicts over resources - the worst thing that happens to you is thatyou waste time and energy displaying.

Therefore on the average, you will come outahead provided the display costs are not large compared to the resourcevalue. Now, imagine what happens if a HAWK appears by mutation or immigration. The Hawk will do extremely well relative to any dove -- winning every encounterand initially at least suffering no injuries. Thus, its frequency will increaseat the expense of dove.

Thus, Dove is not a pure ESS. If dove isnot an ESS, what about hawk? So, let's do the analysis again, this time starting with a populationmade entirely of hawks. This would be a nasty place, an asphalt junglewhere you would not want to live. Lots of injurious fights. Although thesefights don't kill you, they tend to lower everyone's fitness. Yet, justlike with the dove population, no hawk is doing better than any other andthe resources are getting divided equally. Could a DOVE possibly invade this rough place?

It might not seem so sincethey always lose fights with hawks. Yet think about it:. Thus, if a mutant appears in the form of a dove or one wanders in fromelsewhere, it will do quite well relative to hawk and increase in frequency. Thus, Hawk is also not a pure ESS. Notice that in all of the arguments above, we made implicit assumptionsabout the relative values of the resource and the costs of injury and displaythat are consistent with the behavioral descriptions.

You probably realizethat if we changed some of these assumptions of relative value, the gamemight turn out differently -- perhaps Hawk or Dove could become an ESS. Moreover, even if we stick to the qualitative values and to our conclusionthat there is no pure ESS, the technique we have just used will not allowus to predict the frequencies of Dove and Hawk at the mixed ESS.

As wasstated earlier, the best models make quantitative predictions since theseare often most easily tested to review testing of models, press here.

Thus, in the next section we will use the rules and techniques we previouslylearned to quantitatively analyze the Hawks and Doves game. The first step of our analysis is to set-up a payoff matrix. The best response functions intersect in three places, each of which is a Nash equilibrium.

However, the only symmetric Nash equilibrium, in which the players cannot condition their moves on whether they are player 1 or player 2, is the mixed-strategy Nash equilibrium.

Figure 1. Nash equilibria in the Hawk-Dove Game 3. Hawk-Dove Game among Kin Selection Kinship theory is based on the commonly observed cooperative behaviors such as altruism exhibited by parents toward their children, nepotism in human societies, etc. This rule states that altruism or less aggression is favored when the following inequality holds: where r is the genetic relatedness of two interacting agents, b is the fitness benefit to the beneficiary, and c is the fitness cost to the altruist.

This rule suggests that agents should show more altruism and less aggression toward closer kin [21]. A simple way to study games between relatives was proposed by Maynard Smith for the Hawk- Dove game. In this section, we will study the Hawk-Dove game in which there is e relationship between the players.

Consider a population where the average relatedness between players is given by r , which is a number between 0 and 1. There are two possible methods to study the games between relatives. The "inclusive fitness " method adds to the payoff of a player r times the payoff to his co-player. The personal fitness method, proposed by Grafen [28] modifies the fitness of the player by allowing for the fact that a player is more likely than other players of the population to meet co-player adopting the same strategy as himself.

We regard the inclusive fitness method to study the Hawk-Dove game [16] , [10] , [26]. Hawk-dove Game among Direct Reciprocity Direct reciprocity is considered to be a powerful mechanism for the evolution of cooperation, and it is generally assumed that it can lead to high levels of cooperation. Direct reciprocity has been studied by many authors [25], [6]. In every round the two players must choose between cooperation and defection fight of give way. With probability w there is another round.

With probability the game is over. Consequently, the average number of interactions between two individuals is. TFT starts with cooperation and then does whatever the opponent has done in the past move.

On the off chance that two hawks i. If there are adequately numerous rounds, then direct reciprocity can prompt this behavior. Direct Reciprocity with Kin Selection in Hawk-Dove Game We will now consider that individuals use direct reciprocity with their relatives.

Group Selection among the Hawk-Dove Game Selection does not only act on individuals, but also on groups. A group of cooperators might be more successful than a group of defectors. A simple model of group selection works as follows: A population is subdivided into m groups.

The maximum size of a group is n. Individuals interact with others in the same group according to a Hawk-Dove game. The payoff matrix that describes the interactions between individuals of the same group is given by: 6 Between groups there is no game dynamical interaction in our model, but groups divide at rates that are proportional to the average fitness of individuals in that group.

The multi-level selection is an emerging property of the population structure. Therefore, one can say that fighting groups have a constant payoff , while the groups which give away have a constant payoff. Hence, in a sense between groups the game can take the form as follows: 7 For a large n and m , the essence of the overall selection dynamics on two levels can be described by a single payoff matrix, which is the sum of the matrix 6 multiplied by the group size, n , and matrix 7 multiplied by the number of groups, m [21].

The result is: 8 The fighting will be stable if and hawks will invade doves if. If and respectively. Hawks are RD if and will be AD if. Conclusions Direct reciprocity can lead to the evolution of cooperative behavior give way but if it works together with kin selection it can lead to a strong cooperation between players. We found that, the necessary condition for evolution of cooperative behavior is: , the population of cooperators will be RD if:.

Where r is the average relatedness between individuals , which is a number between 0 and 1, and w is the probability of next round. When the group selection works with kin selection, then our fundamental conditions, that we derived , showed that fighting can be maintained in the population, even when the average relatedness is low, groups are large and even if the benefits of fighting are low, if , fighting between players can emerge, otherwise the cooperation give way behavior will be maintain in this situation.

Hawks strategy will be risk-dominant RD whenever , and will be advantageous AD if. For cooperation give way to prove stable, the future must have a sufficiently large shadow.

An indefinite number of interactions, therefore, is a condition under which cooperation give way can emerge. The evolution of sibling rivalry. Oxford, Oxford University Press. Roughgarden, Jonathan. Theory of population genetics and evolutionary ecology. Trivers, Robert L. Parent-offspring conflict. American Zoologist — Social evolution. Zahavi, Amotz. Mate selection: a selection for a handicap. Reliability in communications systems and the evolution of altruism.

Perrins ed. Download references. You can also search for this author in PubMed Google Scholar. Reprints and Permissions. Bergstrom, C. Does mother nature punish rotten kids?. Journal of Bioeconomics 1, 47—72 Download citation. Issue Date : January Anyone you share the following link with will be able to read this content:.

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Skip to main content. Search SpringerLink Search. Abstract The theory of parent-offspring conflict predicts that mothers and their offspring may not agree about how resources should be allocated among family members.

References cited Alexander, Richard D. Google Scholar Alexander, Richard D.