# The Hawk-Dove game: why is the average payoff half of the difference between reward and cost?

My question is about the well known Hawk-Dove model used in game theory. It concerns two strategies: the Hawk, which always fights the opponent, and the Dove, which does not fight and will either retreat or share. The payoffs for each of the possible encounters are presented in a matrix. Now, say that the reward (R) is 10 units and the cost of fighting (C) is 5 units. When a Dove meets a Hawk, it will retreat: Dove gets 0 and Hawk gets R=10. Vice versa, when a Hawk meets a Dove, Hawk gets R=10 and Dove gets 0 because it retreats. When two Doves meet, they will share the benefits; both Doves get R/2, in this case 5. These three, I have no problem understanding.

My issue is with the payoff when two Hawks meet. I understand that, under the assumptions of the model, both Hawks have a 50% probability of winning. I also understand that the winner gets R and loser pays C. But I'm completely stuck at why the average payoff is given as (R-C)/2. When you input the numbers above, it gives you a value of 2.5. How is the average payoff in an encounter between two Hawks 2.5 if one receives 10 and the other loses 5?

• I'm voting to close this question as off-topic because it is not about biology but about game theory. Jan 25, 2019 at 18:44
• $\frac{(+10)+(-5)}{2}$, isn't that how an average is calculated? Jan 26, 2019 at 8:05
• It's about evolutionary game theory and it is considered a part of evolutionary biology. It cannot be considered off-topic. Feb 5, 2019 at 14:33