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 be detailed as you can with solutions. Thank you, and please enjoy it!
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 be detailed as you can with solutions. Thank you, and please enjoy it!