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# Game theory

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1. Hi, I'm doing some work on a simplified 2 game of poker.
Up to now, I've defined a pure strategy for each player, where Player 1 has 2 thresholds, x_1 and x_2 which allows them to make a decision.
Similarly Player 2 also has a threshold, y which allows them to make a decision.
Up to now, I've been able to find the Nash equilibria by plotting 3 separate 2D plots between [0,1], for x_1<y<x_2, x_1<x_2<y ect where x_2>x_1. This allowed me to get payoff equations. I could then find where the minimum point occurs by fixing the values of x_1 and x_2 and plotting the 3 payoff equations.

The problem i have now is that I have 4 variables, x_1,x_2,y_1,y_2, therefore my previous method of fixing values won't work. If I fix both my x values, then it won't fit a 2D plot, and I'm assuming as y_1 and y_2 depend on each other, a 3D plot wouldn't work either.
Any ideas on how I can find minimum points would be appreciated.

2. (Original post by Snedss)
Hi, I'm doing some work on a simplified 2 game of poker.
Up to now, I've defined a pure strategy for each player, where Player 1 has 2 thresholds, x_1 and x_2 which allows them to make a decision.
Similarly Player 2 also has a threshold, y which allows them to make a decision.
Up to now, I've been able to find the Nash equilibria by plotting 3 separate 2D plots between [0,1], for x_1<y<x_2, x_1<x_2<y ect where x_2>x_1. This allowed me to get payoff equations. I could then find where the minimum point occurs by fixing the values of x_1 and x_2 and plotting the 3 payoff equations.

The problem i have now is that I have 4 variables, x_1,x_2,y_1,y_2, therefore my previous method of fixing values won't work. If I fix both my x values, then it won't fit a 2D plot, and I'm assuming as y_1 and y_2 depend on each other, a 3D plot wouldn't work either.
Any ideas on how I can find minimum points would be appreciated.

I know zip-all about game theory, so the language you're using is unfamiliar. If no game theorists come along, would it be possible to re-express the problem in more general terms? It sounds as if the problem might be translated into one of finding the minima of functions subject to some constraints; if it is, I might be able to help!

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