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I stumbled upon the following symmetric two-person game. We have two objects $X,Y$ with positive value $x$ and $y$, and two persons that have to pick independently form each other simultaneous one of the objects. If a person is the only one that picks $X$, then she receives $x$ as payoff. If two persons pick $X$, then everybody gets $x/2$ as payoff. Some goes for $Y$.

This gives as payoff matrix $$\begin{pmatrix}x/2,x/2 && y,x \\ x,y && y/2,y/2\end{pmatrix}.$$

Does this kind of game have a certain name? It looks similar to Hawk-Dove or chicken, but it is different. It seems to be a very natural instance of a game (also its generalization for more players), so I wonder if this is known as a classic example in game theory.

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    A relevant (inexact) analogue might be the battle of the sexes game, with one player's strategies switched.2012-11-22

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