~charmaine~
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#1
Report Thread starter 11 years ago
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I am a bit confused with some part of game theory.

Suppose The expected gain for X when Y plays Y1 is 5p+ (1-p)
when Y plays Y2 is p+ 4(1-p)
when Y plays Y3 is 4p+ 3(1-p)

So X's problem is to maximise his game value v subject to
v ≤ 5p+ (1-p)
v ≤ p+ 4(1-p)
v ≤ 4p+ 3(1-p)

Can someone explain to me where these inequalities come from and how? especially the signs?

Thank you.
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DFranklin
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#2
Report 11 years ago
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Y will act to minimize X's score. So for a given value of p, v will equal min(Y1, Y2, Y3).

Or in other words, v always satisfies

v \leq Y1

v \leq Y2

v \leq Y3
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Goldenratio
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#3
Report 11 years ago
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(Original post by ~charmaine~)
I am a bit confused with some part of game theory.

Suppose The expected gain for X when Y plays Y1 is 5p+ (1-p)
when Y plays Y2 is p+ 4(1-p)
when Y plays Y3 is 4p+ 3(1-p)

So X's problem is to maximise his game value v subject to
v ≤ 5p+ (1-p)
v ≤ p+ 4(1-p)
v ≤ 4p+ 3(1-p)

Can someone explain to me where these inequalities come from and how? especially the signs?

Thank you.
Your innequalities come from player Y's pure strategies. you obviously want to minimise Y's gain, ie minimise his maximum gain. The inequalities themselves are from the matrix of gain values which i'm guessing you have there infront of you. From which you can draw your graph of strategies by doing q_1+p(q_2-q_1)
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~charmaine~
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Report Thread starter 11 years ago
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Thanks.
I am just really confused with the whole ideal of game theory. I am just learning the method by heart and don't really understand what I am doing. For mixed strategies game, what does the optimal mixed strategies tells you? Is this the one when X gain the most she can and Y loses the least he can? what does the value of the game actually mean in a mixed strategies game?
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