Game Theory – Falcon and Dove

The  evolutionary game theory (Evolutionäre Spieltheorie) is a late development in the field of game theory. This kind of game theory has its roots in biology. When I did some internet research on the topic, I found an LMU Munich paper written by my son Maximilian and Peter Czauderna. It was really by chance, I never knew he had been working on it. Here is where you can download the paper – which I consider well worth reading:

Tauben und Falken (412 downloads) .

Let me briefly explain the falcon/dove game:

There is a feeding place. Two players go there n times. For each meeting, every one of them must give himself a determined role. But they do not know which role the other party will have chosen. The number of meetings n is determined beforehand, just as the rewards at the feeding place, dependent on the role each one played.
The two roles are called falcon and dove. They symbolize peaceful (dove) or aggressive (falcon) behaviour. The values of the game are set as follows, or similarly:

If dove meets dove, both of them get the same amount of food.
If falcon meets dove, falcon gets more, dove gets less.
If falcon meets falcon, you get “war” and both parties get a negative result.

A short time ago, I finished the game with the following values:

Dove/Dove (1.2/1.2)
Falcon/Falcon (-10/-10)
Dove/Falcon (1/2) and vice versa
Falcon/Dove (2/1)

The number of games n was 5.

Here is an additional explanation. If both players appear at the feeding place as doves, they get each 1.2 points. If they meet as two falcons, each gets -10 (!). In case of dove/falcon, the falcon will always get twice as much as the dove. The entire affair is done five times.

You realize immediately that the model is rather plump. It will, however, not get any more challenging if you take other values used in the relevant literature.

Now let me “neutralize” the cover story, so those associations that are complex and hard to control will be reduced. Let us call the roles V1 and V2. For the set of those two roles, I introduce a transitive relation: more (>). More represents a better, nicer, greater… role. That means V1 > V2 or V2 < V1.

The task is: select a role and go to a place where you can practice a maximum of V1 + V2. If you subject the place to more than V1+V2 (for instance V2 + V2), everything will collapse.

Now that sounds far less exciting than dove and falcon. And there is no association “Israel during peaceful and aggressive years” (as in the first text).

Well, I would advise the game theoreticians to do some research on the game “paper, scissors, stone” (paper buys stone, stone blunts knife, knife cuts paper). At least, there are already three roles and a cyclical-transitive relation. You can do wonderful experiments with it and even find the world champion. And you can probably also develop sociological theories to your hearts content.

RMD
(Translated by EG)

P.S.
Here is an excerpt from the aforementioned paper. It seems to me that it gives a precise description of the problem with game theory:

…
 Please keep in mind that we are talking an extremely simplified model. Additional motives for selecting a party, such as history, social life, religious concepts and economical interests were not taken into consideration. The game theory and the dove-falcon game do not really analyse of the problem. Instead, they are supposed to make people thoughtful and provide the game with additional explanations.
5 Conclusion
The dove-falcon game is a very simple model. In complex systems, it can only be used if the specifications are strongly simplified. Each user should determine individually and taking into consideration all of the circumstances whether or not the overview gained is an advantage or a disadvantage over the probably higher representation of reality in complex models.    
…

Well, I can live with that!

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