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Respond to the question: Continous games with symmetric players?

10/31/2016 04:38 AM by EstEst;

I think the answers to both questions are negative. Consider a two-player game where two players (1 and 2) choose the numbers x_1, x_2 from the set [0,2], and the payoff of each player is given by u_i(x_1,x_2)=x_i+(x_1-x_2)^2. Then (x_1,x_2)=(0,2) (or (2,0)) is a Nash equilibrium of this game and the payoffs in this equilibrium are (4,6) (or (6,4)). [Manage messages]

10/24/2016 05:59 AM by Paul; Add-On

Do we know that each nash equlibrium strategy in such a game is symmetric, too? [View full text and thread]

10/24/2016 05:15 AM by Paul; Continous games with symmetric players

Hi, is there some theorem stating, that in every continuous game with symmetric players every nash equlibrium will yield the same utility to all players? Or something like this for special cases? The theorem seems quite natural to [View full text and thread]