Suppose that the federal government wants to temporarily offer tax cuts and fee reductions to licensed producers $($LPs$)$ of cannabis on a case$-$by$-$case basis. The government wants to greatly lower taxes for struggling LPs but merely reduce some fees for financially stable LPs$.$ It estimates that $70\%$ of the LPs are struggling and $30\%$ are financially stable. However, it cannot easily tell which LPs are in each category without auditing their financial records.

Each LP knows whether it is stable or struggling. Given this knowledge, the LP will request either lower taxes or reduced fees.

After receiving the LP$$s request, the federal government must decide whether to grant the request or audit the LP$.$ If the LP merely requests a fee reduction, the government will always grant the request. If the LP requests a tax cut, the government can choose to either grant the request or to audit the LP$.$ Auditing a company that is truly struggling is a waste of resources; but if the audit finds the LP is truly stable, the government can safely refuse its request.

The payoffs will be as follows.

a$.$ If the LP is struggling, and it requests reduced fees, then the LP payoff will be $128$ and the government payoff will be $72.$

b$.$ If the LP is struggling, and it requests lower taxes, and the government grants the request, then the LP payoff will be $168$ and the government payoff will be $52.$

c$.$ If the LP is struggling, and it requests lower taxes, and the government conducts an audit, then the LP payoff will be $148$ and the government payoff will be $32.$

d$.$ If the LP is stable, and it requests reduced fees, then the LP payoff will be $108$ and the government payoff will be $60.$

e$.$ If the LP is stable, and it requests lower taxes, and the government grants the request, then the LP payoff will be $188$ and the government payoff will be $40.$

f$.$ If the LP is stable, and it requests lower taxes, and the government conducts an audit, then the LP payoff will be $88$ and the government payoff will be $96.$ i$.$ Define the $4$ complete LP strategies and the $2$ complete government strategies.