Suppose that you are playing the following game: you and your competitor are both holding very valuable gold coins (say near mint condition coins from the early Roman empire, so worth a million dollars to the right collector); you both put your coins in your closed hands, then simultaneously open them; if they match, i.e. both heads or both tails, then you win the other person's coin; but if they mis-match, i.e. one is heads and the other is tails, the other person wins your coin. Assuming that the dollars won or lost can be translated into utility, the representation of the game