Comment Re:Three person games (Score 1) 421
I have more to say. I forgot to mention another reason why I think this result is so exciting.
Assume you have a game being played by N people (N > 2, but think of N > 8 as a typical example). By what I said in the prior post, everybody is playing a BAD strategy, a strategy that is far from the Nash Equilibrium because it is IMPOSSIBLE to effectively calculate a better strategy in a reasonable amount of time.
Although it is impossible to create a perfect strategy, it is possible to create an exploiting strategy. If you can accurately predict the strategies of your opponents (where the accuracy does not have to be that great -- the strategies of your opponents are that intrinsically BAD), it is easy to create an exploiting strategy in any game of sufficient complexity involving enough players. I will give a simple example. Suppose you play poker and after a sequence of bets (with the same type of sequence occurring reasonably often), you notice that an opponent tends to fold to large bets almost all the time, you would then exploit that player by always bluffing after that sequence of events and "slow calling" (that is not raising) when you have a monster hand. In a two player game, that opponent would correct his play successfully by calling more often, but in multi-player games, the information can be more muddled because the opponent does not notice the correlation between a sequence of prior bets involving multiple players and his tendency to fold. In other words, the opponent may think that he is correctly calling big bets half the time but not notice that if a second player raises, he tends to fold more often when another player enters the pot with a big bet (there is more I can say here, but I don't want to get into the strategy of poker in great detail -- but I will say that the folding player is not being stupid).
But here is where things get interesting. In order to effectively exploit the strategies of others, you have to adopt a highly exploitable strategy yourself (for example, "always bluffing after a certain sequence of events" is a fairly exploitable strategy). In stock market terms, it would be the equivalent of going into a highly vulnerable "short position" on a stock. This brings up the issue of "counter-exploitation" and the need to disguise your actions when playing in the game.
So what happens in such games.
The games are highly unstable. People are always doing crazy exploiting moves that create great risk for themselves (and potentially for the infrastructure of the game itself).
The games are highly exploitative by colluding players (the "old boys network" as some would call it).
Getting "inside information" on the actual strategies pursued by other players is highly valuable.
Likewise, hiding what you are doing is very important.
A big danger is acting in a predictable manner that is too similar to what others are doing (the "herd" mentality problem).
There is no safe way to play the game.
Researching potential ways to exploit the current state of the game is a must, particularly to see if anybody else is pursuing such strategies against you (example: there might be an opportunity to artificially squeeze somebody else's short position on a stock that you own).
So what do I conclude from this. The more we make our "markets" (stock & other assets) more "perfect" the crazier they are going to become. Derivatives made the "market" more perfect because it allowed people to act on "risk factors" in a more precise way. It is not a surprise that they have also caused problems. Derivatives removed "frictions" in the market and made the market better. But it is the friction in the "markets" that prevents greater craziness. This is not because people are irrational. Far from it. It is the nature of game theory itself that says this will be the out come. To put it another way, cleverness and rationality are actually the enemy. If we were stupider and less rational there would be less of a problem.
Let me give an example of this "stupid irrationality". Suppose we decided to deliberately sabotage the economy by telling Big Banks that they had to hold large assets and they were barred from doing anything interesting with them. This would sabotage the economy because those assets would sit moribund and do nothing to grow the economy in an efficient fashion (as any Big Bank lobbyist would be sure to tell you). We would do this because of an "irrational" fear of economic collapse. This was how we used to treat banks and our own assets. This latest result from game theory maybe implies that this type of "paranoid thinking" may be "irrational" for any one person, but it might be "rational" thinking for the world as a whole. Though it may be heresy to some to say this, but maybe we do not want the economy and its markets to work too efficiently.