Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Does anybody know how to interpret the sentence: For any set $T$ of mixed strategies, let $D[T]$ denote the set of probability distributions over the elements of $T$, each expressed as vector, conformable to a mixed strategy, that gives the ultimate distribution of pure strategies.

This sentence appeared at p.139 of the paper

Crawford, V.P. Equilibrium without independence, Journal of Economic Theory 50 (1990), 127-154.

The pdf is available online (just google).

In particular, what I really don't understand is the last part: What's the meaning of being conformable to a mixed strategy? More seriously: what's the ultimate distribution of pure strategies?

Many thanks in advance for any help,

Valerio

share|improve this question

2 Answers 2

Ultimately gives a distribution on pure strategies. Papers in economics can be wordy. A mixed strategy over mixed strategies of course is a mixed strategy. A probability distribution over probability distributions over a set of states induces probability distribution on those states.

share|improve this answer

My interpretation: You identify a finite set of strategies $S$ with the unit vectors in $\mathbb{R}^{|S|}$, so that the simplex spanned becomes the space of mixed strategies. So every set of mixed strategies is a subset of this simplex. A probability distribution over $T$ induces again a probability distribution over $S$, so the set of probability distributions over the elements can again be identified with a subset of the simplex.

share|improve this answer
    
Yes I think I got it! Thank you. –  Valerio Capraro Oct 18 '12 at 18:47

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.