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Respond to the question: Nash Equilibrium with sets?

11/03/2012 05:38 PM by name withheld; Nash Equilibrium (with sets!)
I have done my game theory course. But I have found some questions which are a lot more difficult to find nash equilibrium because they include sets! I just want to know how to go about doing them.

For this particular question;

Player 1 chooses strategy x1 from [-1,1] and Player 2 chooses strategy x2 from [-1,1]. Player 1 utility function is x1^2/2 + x1x2. Player 2 utility function is x2^2/2 -x1x2. Find the best response function of each player (to pure strategies). Is there a nash equilibrium?

I really would appreciate explanations so I can get around my head and apply this to the rest of the questions on sets from this textbook. Please use hide/show because it is interesting. Please be detailed as you can. Thank you. [Manage messages]