# Game theory, mixed strategies

1. Apr 29, 2010

### pawelch

1. The problem statement, all variables and given/known data
I am trying to study a mixed-strategy phenomenon form the book:
Game Theory Evolving:A Problem-Centered Introduction to Modeling Strategic Interaction (Second Edition)
by Herbert Gintis. There is an example (The Prisoner's Dilemma) which looks as follows:

[PLAIN]http://img199.imageshack.us/img199/1092/img1sh.jpg [Broken]

where P=1, R=0, T=1+t, S=-s and s,t>0.

There are two players Alice and Bob. They both play C with alpha and beta probabilities respectively.
The author claims that payoffs to Alice and Bob are:

[PLAIN]http://img696.imageshack.us/img696/3070/img1ye.jpg [Broken]

However, I think this is wrong and there should not be alpha multiplied by beta, just at the beginning of the right-hand side - it stems from the fact that since R=0 then alpha multiplied by beta and 0 is equal to 0. Am I correct? I think that, the zero factor which is at the end of right-hand side, should be next to alpha multiplied by beta right at the beginning of the RHS.

2. Relevant equations

3. The attempt at a solution

In the other example:
[PLAIN]http://img709.imageshack.us/img709/4764/img1yk.jpg [Broken]

the payoff's are following:

[PLAIN]http://img402.imageshack.us/img402/4696/img1hr.jpg [Broken]

Therefore, I think there might be a mistake in the first example.

Last edited by a moderator: May 4, 2017