Can you name a constructive use of the Nash equilibria concept? I’m not talking about things that are covered under the von Neumann minimax result, which has had an obvious impact on multiple, disparate things (LP Duality and Yao’s Theorem, to name a couple). I’m talking about a real 3+ player game outside of the laboratory where someone is playing a Nash equilibrium strategy and doing well with it.
Give up? The only research in this line I’ve seen is my good buddy Sam’s work on poker. Many poker bots use equilibrium (or nearly equilibrium) strategies for their heads-up (two player) play (you can find out more about poker bots at Alberta’s poker bot research site). However, Sam also is interested in three-player research, which ventures beyond the minimax result into dark waters. Here’s some of his work on equilibrium play in three-person tournaments. But more significantly, in his online play (and he’s one of the best single-table tournament players in the world), Sam incorporates these Nash equilibrium calculations into how he plays his endgames.
What about poker makes it amenable to the Nash concept? Here’s a hypothesis: In complex, real-world games where collusion is not allowed, Nash equilibria coincide with “good strategies”.
Now, there’s no justification for such a result at all — it’s not like the Nash equilibria have any peculiar special power. I think that it’s a combination of three things:
That playing Nash means you won’t be directly and straightforwardly exploited.
That collusion is forbidden, meaning teams of opponents will not exploit you.
Poker is so difficult and challenging that pretty much any strategy in which you’re not being directly exploited is a reasonable one — though given the enormous state space of the problem, finding something not directly exploitable is harder than it sounds.
A concept proves its mettle by its constructive use in the real world, and in this respect I think that poker research, particularly if it’s a poker bot playing Nash that ends up being able to win no-limit multi-player tournaments, represent the best hope for the Nash concept. Do you know of any other constructive uses of Nash equilibria?
