If the mayor doesn't trust you, he won't buy your crack. If he does buy your crack, and you can get away with it, you will video and sell. Since you can't commit to not videoing, he won't buy and you're both left worse off.
How can the dealer credibly commit to not videoing the transaction?
- If the mayor can commit to violent retaliation even where such retribution would be personally costly, then that can induce performance. But it's can be hard for a mayor to make that kind of credible commitment when he's had large public disputes with the police.
- The mayor could require the dealer to provide him with his name and address. Then, the mayor could wear a big "I'm smoking Jim's crack" t-shirt during any videoing. Any released video would implicate the dealer, who could then be arrested for selling crack and would likely have any video profits seized as a proceed of crime.
- But, the mayor would know that a sufficiently canny dealer could blur out the t-shirt's incriminating details before selling the video, so that doesn't work. Further, it's really no different from committing to rat out the dealer if arrested. Where the dealer has an easier time hiding than a large and prominent Mayor (and doesn't lose much by having to hide out), it won't work.
I'm not sure there are any good feasible solutions to the problem. Since no dealer can credibly commit to not selling out the Mayor, the Mayor won't buy the crack.