Talk:Strategy (game theory)

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[edit] Non-strategic examples

The roulette and bet-hedging stock trading strategies are not game theoretical and should go to some other article. Pete.Hurd 18:51, 17 September 2006 (UTC)

Just got rid of them. Any important information is in other articles already. Cretog8 (talk) 09:10, 1 June 2008 (UTC)

[edit] Tic Tac Toe

Just removed this: "The number of "moves" in a Tic Tac Toe game is 4 or 5, depending on whether you start or not, and considering that neither player can skip a turn; while the actual number of "strategies" is over 6 trillion."

I don't know the number of strategies for tic-tac-toe, but it's certainly not 6 trillion. To give an upper bound on the number of strategies, you can do this: There are 9 spots in tic-tac-toe and each of them can be in one of 3 states: {blank, X, O}. So, there are 3^9 = 19,683 possible states for the whole board. A strategy could be defined by a rule for what to do in every state, so 19,683 strategies would be exhaustive. (Actually that number's way too high, considering that most of the board states would be impossible in a real game or wouldn't correspond to your move, but...)

If allowing for mixed strategies, then there's an infinite number, but that's something else. Cretog8 (talk) 09:04, 1 June 2008 (UTC)

[edit] merge, planetmath and stuff

This article is a merge of its previous incarnation, mixed strategy and pure strategy. I've removed references to PlanetMath, because while there is a little bit from PlanetMath, it is very little. If this lack-of-citation is inappropriate, I'm happy to be corrected.

This article incorporates material from PlanetMath, which is licensed under the GFDL.

[edit] equilibrium

Currently, the only mixed-strategy equilibrium example given is a link to rock-paper-scissors, but neither page gives any detail. More examples would be good, particularly of stable mixed strategy equilibria. One specific example that would be very good is some kind of tacit collusion (say, it would seem that small groups of service stations price petrol below the profit maximising monopoly price but above the economic equilibrium for perfect competition, and where can one learn how to explicitly calculate this eventual price?). Cesiumfrog (talk) 05:48, 3 June 2008 (UTC)

Wow, I'm surprised at Rock paper scissors. The only concrete game theory there jumps right to a biological application. I've replaced the link to RPS with one to Matching Pennies. I hate using MP as an example, because I've never heard of it outside of its pedagogical use in game theory. Maybe if/when equilibrium stuff gets added to RPS the link can get switched back.Cretog8 (talk) 11:21, 3 June 2008 (UTC)
One of the things I wonder about this article is how much it should go into equilibrium. After all, a strategy (pure or mixed) can be used out of equilibrium. So, I'm fuzzy on how many equilibrium examples should be given. I also wonder if A disputed meaning is too equilibrium-focused. Cretog8 (talk) 11:25, 3 June 2008 (UTC)