| From Wikipedia (http://en.wikipedia.org/wiki/Nash_equilibrium): "In game theory, the Nash equilibrium is a solution concept of a non-cooperative game involving two or more players, in which each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only their own strategy." So, it is not correct to say "Nash equilibrium is about an overall better situation for both sides" - one player wants to win at the expense of the other. Chosing sides at random is a game theory optimal strategy, that is, it is the best strategy to use when your opponent always choses the best counter-strategy. If the two players flip coins to chose their sides they will both end up winning 50% of games in the long run. Likewise if they are able to randomize their choices perfectly, they will both win 50% of games. If your opponent plays in a sub-optimal manner (e.g. they chose the left side more often than the right), then the best strategy to use is an exploitative one (e.g. I see you chose left more than right so I always chose left), however, in this case you gain by changing your strategy (so no Nash equilibrium). I can't see any way to 'beat' this simple game and win more than 50% of games in the long run without using an exploitable strategy, so it seems that chimps have somehow evolved to become better at playing this game in a game theory optimal manner than us. |