5. informativeness and off-equilibrium randomness Consider a variation on Examples 16.1 through 16.4, where everything remains as specified except the probabilities. The probabilities are partially specified by π(x2|H) = .9, and the π(x, y|L) noted below. You will notice the (x, y) combinations are utterly random under input L. Specify the remaining probabilities in such a manner that the additional measure (y) is both informative and controllable.

Verify your claim by calculating the unconditional and conditional likelihood ratios. You should also provide and interpret the optimal pay-for-performance arrangement in your specified setting.
x1/g x2/g x1/b x2/b π(x, y|H)
π(x, y|L) .25 .25 .25 .25 6. informativeness and on-equilibrium randomness Consider another variation on Examples 16.1 through 16.4, where everything remains as specified except the probabilities. The probabilities are partially specified by π(x1|L) = .9, and the π(x, y|H)
noted below. You will notice the (x, y) combinations are utterly random under input H. Specify the remaining probabilities in such a manner that the additional measure (y) is both informative and controllable.
Verify your claim by calculating the unconditional and conditional likelihood ratios. You should also provide and interpret the optimal pay-for-performance arrangement in your specified setting.
x1/g x2/g x1/b x2/b π(x, y|H) .25 .25 .25 .25 π(x, y|L)