Talk:Mixed strategy

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[edit] Removed line

I have removed the following line from the previous entry:

A player would only use a mixed strategy when they are indifferent between several pure strategies, and when keeping the opponent guessing is desirable, that is, when the opponent can benefit from knowing the next move.

I'm worried this might be misleading. Supposing that players only play Nash equilibria, this statement is true. But an entry on mixed strategies should not assume that players only play Nash equilibria, one might play a mixed strategy which is not Nash. --Kzollman 21:14, Mar 17, 2005 (UTC)

[edit] Example optimal mixed/pure strategies

These tables represent the payoff matrices for player A along with the optimal strategies in column A_p representing the probability of each move, with the table captioning "strategy N" where N represents the minimum expected payoff for player A.

mixed strategy -0.2 Ap B1 B2 B3 A1 0.2 3 -1 2 A2 0.8 -1 0 3 A3 0.0 -4 -3 1

pure strategy -4 Ap B1 B2 B3 A1 0.0 -9 -4 8 A2 1.0 -4 7 7 A3 0.0 -5 0 1

mixed strategy 0.937 Ap B1 B2 B3 A1 0.0 6 0 -1 A2 0.188 -8 5 -8 A3 0.812 3 0 3

mixed strategy 1.681 Ap B1 B2 B3 A1 0.0 6 2 -2 A2 0.437 9 -1 0 A3 0.563 -4 8 3

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If you have any questions please ask. --ANONYMOUS COWARD0xC0DE 04:13, 2 January 2007 (UTC)

I reverted because these because they add no explanatory power to the article. Why are there four matrices? What property to the four examples illustrate that is particular to each of the four? We are to assume thes payoffs given are for player A? What are the payoffs to player B? The Ap column isn't part of a payoff matrix, so what is it, the probabilty of using that move at the mixed Nash? What is the number in table footer? Why do you expect readers to supply their own answers to these questions? Without adequate explanation these examples are incomprehensible to the reader, you cannot expect readers to decipher totally opaque material. The onus is on the writer, not the reader, to provide the thinking. Pete.Hurd 16:41, 5 February 2007 (UTC)

[edit] Meaning

I have just added the pragraph about the meaning of mixed strategies. I believe it factually correct, but I know my English is not as good as it should be to contribute to this Wikipedia. Hence, all corrections are welcome.

On a more fundamental level, I am an Industrial organization guy, not a game theorist. Rubinstein and Aumann are proeminent figures of game theory, but some of their claims about its meaning can be controversial. Hence, this paragraph may be biased. All I can describe is the impact of this insider criticism upon the use of mixed strategies in economic research at large. Again, comments and corrections welcome.--Bokken | 木刀 09:45, 10 March 2007 (UTC)