So we have the following matching penny game

$\begin{bmatrix} \ & L & R \\ T & (1,-1) & (-1,1)\\ B & (-1,1) & (1,-1) \end{bmatrix}$

Let $p_1$ denote the row player, $p_2$ denote the column player.

Now suppose there is an event, $D$, which players assess with distinct subjective probabilities: $p_1(D) = 2/3; p_2(D) = 1/3$. Suppose players bindingly agree to the following strategies: $2$ plays $L$ and $1$ plays $T$ if $D$ occurs and they play $(B,R)$ otherwise. What is the expected payoff for both players in this case. I am expecting it to be $1/3$, but I cant figure it out.

Any helps or insight is appreciated.

  • $\begingroup$ Why is this tagged with nash-equilibrium? The question doesn't seem to have anything to do with that. $\endgroup$ – joriki Feb 17 at 20:53

Since $(T,L)$ and $(B,R)$ yield the same payoffs $(1,-1)$, the probabilities are irrelevant – a strategy pair with payoffs $(1,-1)$ is certain to be played, so the payoffs will be $(1,-1)$.

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