[baha_man]

i) "Isn't it a winner/loser pair for each game?"

Yes, if both players chose the same side, the 'matcher' wins. If they chose different sides, the 'mismatcher' wins.

"How can a pair "outperform" another?"

A player is better at the game the closer to a game theory optimal strategy they use. This would presumably be to chose left or right at random. The worst strategy would be to always chose the same side, the matcher would then be able to predict your next move with 100% accuracy.

Randomizing choices to be unpredictable is something humans aren't good at. Poker players sometimes use tricks like checking the position of the second hand of their watch to do this (e.g. if it's between 10 and 12, bet, if not, check). The study suggests chimps may be better at it than us.

"Nash equilibrium is about an overall better situation for both sides..."

No, this is not correct.

ii) "...chimps can read numbers and understand their order?"

It sounds like it from this Wikipedia entry:

http://en.wikipedia.org/wiki/Chimpanzee#Memory

"A 30-year study at Kyoto University’s Primate Research Institute has shown chimps are able to learn to recognize the numbers 1 through 9 and their values... jumbled digits are flashed onto a computer screen for less than a quarter of a second, after which the chimp, Ayumu, is able to correctly and quickly point to the positions where they appeared in ascending order."

[soneca]

If random is better so you might as well say that raindrops falling on a monitor also outperform a human, as the issue seems to be that humans always looks for a pattern, even when randomness is better. It is irrelevant that they are chimps.

Would you care to explain what is the correct Nash equilibrium?

[baha_man]

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.

[TheEzEzz]

In a two player game, a Nash is a "stable" pair of strategies (S1, S2), where player 1 uses S1 and player 2 uses S2. "Stable" means that if one of the player's uses their Nash pair, then it is always in the best interest of the other player to use their pair. Assuming they are "rational" then the second player is "forced" to play a certain way if they know the other play is following the Nash.

A Nash is not necessarily good for either player. For example, in the Prisoners' Dilemma, the Nash is for both prisoners to defect, which leads to a long prison term for both prisoners.