Not All That Glitters Revisited: Recall exercise $12\mathrm{.}5$ in Chapter $12$ and your analysis of the unique Bayesian Nash equilibrium for that game. The secretary of commerce is contemplating the introduction of a certification program. This will allow a prospector to get a certificate that exactly states and publicizes the amount of gold in the mine and eliminates the problem of asymmetric information. If the program is implemented the game would be modified as follows: The prospector first decides whether or not to get a government certificate and then decides for what price to ask. Thus each type x chooses a pair $($y$($x$),$ p$($y$)),$ where y$($x$)$ in $\{$N$,$x$\}$ denotes his choice of certificate $($N for no certificate and x for the true value on the certificate$)$