Great Prelim Question  Cheap Talk

Great Prelim Question
Roy is coming to plant flowers in Zoe’s garden. Zoe loves flowers, her utility for a garden with flowers is Roy plants a unit mass of seeds and the fraction of these that will bloom into flowers depends on how attentive Roy is as a gardener. Roy’s attentiveness is his type . In particular when […]
http://cheaptalk.org/2013/09/08/greatprelimquestion2/ 
^ She never </observes> theta, the problem is writing in a confusing way, let me simplify it
1. Nature chooses
theta
uniformly distributed over[0,1]
. Noone observes this2. Zoe privately chooses
alpha
in[0,1]
3. The output
alpha times theta
is realized, at this point Zoe can infer theta, but Jane can't because she does not knowalpha
(assuming Zoe play's a mixed strategy)4. Finally, Zoe decides whether to hire the gardener or not

^ She never </observes> theta, the problem is writing in a confusing way, let me simplify it
1. Nature chooses theta uniformly distributed over [0,1] . Noone observes this
2. Zoe privately chooses alpha in [0,1]
3. The output alpha times theta is realized, at this point Zoe can infer theta, but Jane can't because she does not know alpha (assuming Zoe play's a mixed strategy)
4. Finally, Zoe decides whether to hire the gardener or notRoy should know his own type so noone observing theta is a bit misleading. Roy knows this.