Mysterious sentence in a paper: what's the ultimate distribution of pure strategies? - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-20T07:48:02Z http://mathoverflow.net/feeds/question/109998 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/109998/mysterious-sentence-in-a-paper-whats-the-ultimate-distribution-of-pure-strategi Mysterious sentence in a paper: what's the ultimate distribution of pure strategies? Valerio Capraro 2012-10-18T09:41:43Z 2012-10-18T11:02:23Z <p>Does anybody know how to interpret the sentence: <em>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.</em></p> <p>This sentence appeared at p.139 of the paper</p> <p>Crawford, V.P. <em>Equilibrium without independence</em>, Journal of Economic Theory 50 (1990), 127-154.</p> <p>The pdf is available online (just google).</p> <p>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?</p> <p>Many thanks in advance for any help,</p> <p>Valerio</p> http://mathoverflow.net/questions/109998/mysterious-sentence-in-a-paper-whats-the-ultimate-distribution-of-pure-strategi/110002#110002 Answer by Michael Greinecker for Mysterious sentence in a paper: what's the ultimate distribution of pure strategies? Michael Greinecker 2012-10-18T10:19:39Z 2012-10-18T10:19:39Z <p>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.</p> http://mathoverflow.net/questions/109998/mysterious-sentence-in-a-paper-whats-the-ultimate-distribution-of-pure-strategi/110005#110005 Answer by Rabee Tourky for Mysterious sentence in a paper: what's the ultimate distribution of pure strategies? Rabee Tourky 2012-10-18T11:02:23Z 2012-10-18T11:02:23Z <p><em>Ultimately</em> 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. </p>