The preferred outcome is initially where both players hunt the stag and yield 3 utiles each from this action. However the scenario where they both decide to hunt hares and thus non-cooperate with each other is also a Nash equilibrium. In both these scenarios neither player has a unilateral incentive to defect.
PB = Probability Player B will hunt the stag.
EUA(STAG) = 3 PB + (0) P’B = 3 PB
EUB(HARE) = (1) PB + (1) P’B = PB + (1- PB ) = 1
Player (A) will do better playing stag is he is certain that (B ) is also going to play stag, but since there is uncertainty towards what B’s actions might be it is less risky for A to play hare, as no matter what B does in this scenario A has 1 utile secured. It therefore follows that A should only hunt the stag when EUA(STAG)≥ EUB(HARE).
(A) needs to be certain that PB is at least 1/3 in order for it to be confident enough to play stag.
The need for the actors involved in a situation to hold a set of beliefs concerning the behavior of the other actors is illustrated by this game. In this case player (A) needs to trust that the set of beliefs regarding (B) that it holds, defined by PB, are indeed PB ≥ 1/3 in order to motivate it to engage in cooperation and hunt the stag. That is to say that (A) needs to be able to assess the predictability of (B’s) actions before carrying out a rational action. Without this trust there is no incentive for either player to engage in cooperation. 2. A coordination problem
Basketball Movies
Basketball 3,1 0,0
Movies 0,0 1,3
This scenario has two Nash equilibria, firstly where both players agree to play basketball and secondly where both players agree to go to the movies. In order to obtain a benefit both player have to attend the actions of the other, so there is no scenario where either player ends
