Hi please help me on this question, thank you!

Question 1 game theory: Let's think ahead to a time with less social distancing. Suppose you are at least 21 years old, you own a car, and you want to drive to a party in Waltham. At the party, you decide whether you want to drink beer or soda before driving back home. At the same time, a police ofcer decides whether they want to check for drunk drivers between Waltham and Boston at night. Suppose you get 1 more unit of utility from drinking beer at the party than from drinking soda if the police officer does NOT check you. However, if the officer DOES check you, you get 4 fewer units of utility than if you drink soda. The police officer has some opportunity cost of checking for drunk drivers, for a utility of -1 (regardless of your drinking decisions). However, if she does NOT check you and you DO drink beer, her utility is much lower (because of the guilt for letting you risk your life and that of others). If the ofcer does NOT check you, and you do NOT drink beer, the officer gets zero utility. These payoffs are summarized below: Police Check Don't check Beer 1 -3 You 4 1 Soda -1 0 a) What (if any) are the purestrategy Nash eq uilibria in this game? Then find the mixed-strategy Nash equilibrium: b) What is your optimal strategy (probability ofdri nki ng beer) as a function of the officer's probability of checking you? c) What is the officer's optimal strategy (probability of checking you) as a function of your probability of drinking beer? d) What is the Nash equilibrium in mixed strategies in this game? e) What is your expected payoff? What is the officer's expected payoff? Disclaimer: This is a hypothetical example. There obviously are huge risks to drinking and driving beyond getting pulled over. Please don't drink and drive! Please also note that I believe one can have fun at a party without drinking alcohol