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GAME THEORY QUESTION

Hilbert and Cantor simultaneously call out one of the colors 'white' or 'red'. If they have both chosen 'white' Hilbert wins the game and he receives 3 $ from Cantor. If the chosen colors are different, then Cantor wins and Hilbert pays 2 $ to Cantor. If they both choose 'red', then there are three possibilities:

- with probability 1/3, game terminates without any payement,

- with probability 1/2, game is played once more,

- with probability 1/6, players switch their roles and the game is played once more.

Find value of the game and determine the minmax strategies of players.