Dileme proposed by John Maynard Smith. This dileme try to explain how individuals within a population behave when they compete by resources and which conduct is the most estable evolutionary strategy.
Falcon individuals are aggressive whereas pidgeons always dialogue. Falcons fight to obtain the resource, although this can cause some damage. Pidgeons try to persude to obtain the resource and if they don't win, they retire and only lose time. Therefore, the game have these variables:
- P: benefit of wining the prey (resource)
- H: the cost of being damage
- T: losed time in an argument without fight.
In this case, we are going to consider these rules are:
- P > H
- P > T
- H > T
- Falcon vs. falcon: there will we a fight. The winner obtain the prey without damage (P), but the loser will suffer harm (-H). Therefore, the average benefit per Falcon is (P-H)/2
- Falcon vs. pidgeon: the falcon obtains the prey (P), and the pidgeon doesn't have or benefit or loses (0)
- Pidgeon vs. pidgeon: they try to dialogue. The winner obtains the prey but aldo he has lost time (P-T). The looser has lost time (-T). The average benefit per pidgeon is (P-2T)/2
The before situation is little realistic, individuals are not so much extreme. So we are going to add a new category: the Bougeois. Indiviulas with this conduct, sometimes act as Falcons and others, as a Pidgeons. In this case, one individual is the owner of the resource (prey) and the other is the thief. Each individual is owner 50% of the times. In this case, rules are:
- Individuals don't lose time (T = 0)
- H > P
- Falcon vs. bourgeois:
- If the bourgeois is the owner, he acts as a falcon. Both have a fight. The winer obtained the prey (P) and the loser will suffer damage. The average benefit will be (P-H)/2.
- If the bourdeois is the thief, he act a s a pidgeon, so the falcon wins. The benefit of the falcon will be the prey (P) and the cost of the bourgeois will be 0.
- Pidgeon vs. bourgeois:
- If the bourgeois is the owner, he acts as a falcon. Therefore, he wins the prey (P) and the pidgeon have a cost of 0.
- If the bourdeois is the thief, he act as a pidgeon, so the winner obtain the prey (P-T) and the loser have a cost of 0 (T). The average of the benefit wil be P/2
- Falcon vs. falcon: there will we a fight. The winner obtain the prey without damage (P), but the loser will suffer harm (-H). Therefore, the average benefit per Falcon is (P-H)/2
- Falcon vs. pidgeon: the Falcon obtains the prey (P), and the pidgeon doesn't have or benefit or loses (0)
- Pidgeon vs. pidgeon: they try to dialogue. The winner obtains the prey but also he has lost time (P-T). The looser has lont time (-T). The average benefit per pidgeon is P/2
- Bourgeois vs. bourgeois: one alwaiys act as a falcon since he is the owner of the resource; and the anothe act as a pidegeon becasue is the thief. So the avergae benefit is P/2