Re: Game Theory question

Sorry, I pressed "send" a tad too soon...

Disclaimer: This is not a homework problem, I've never followed
a course on game theory (I probably should), and I am hoping
someone in the know might be able to give me some clues...

Here goes,

In a three-player game, where each playercan choose between
2 strategies S1, and S2, and one person (player 3) always plays
the mixed strategy (p0,p1) with probabilities p0=p1=0.5. The
pay-off functions for player 1, and 2 are the same (e will be
a function of three variables, the first slot being player 1's
chosen strategy, the second slot being player 2's, etc):

e(S1, S1, S1) = 1
e(S1, S1, S2) = -2
e(S1, S2, S1) = -2
e(S1, S2, S2) = -2
e(S2, S1, S1) = -2
e(S2, S1, S2) = -2
e(S2, S2, S1) = -2
e(S2, S2, S2) = 1

So, e is symmetric in its first two slots.

The question is: Is there anything we can say about player 1 and 2's
optimal solution (some sort of an equilibrium?), given that player 3
always plays with (p0,p1) ? We can assume that player 1 and 2
cannot co-operate. We can also assume perfect information.

Cheers,
Willem

"Willem H. de Boer" <wdeboer@xxxxxxxxxxxxxxxxxx> wrote in message
news:f6c8$4278d3b4$d468cfd2$12626@xxxxxxxxxxxxxxxxxxxxxxx
> Hi all.
>
> In a three-person game, where each person can choose between
> 2 strategies S1, and S2, and one person always plays the mixed strategy
with
> probability 0.5
>
>


.

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