please answer Q3 only by using Q1 and Q2 as a reference

Question 3 The first 2 questions posed in this assignment represent simple examples which have been analyzed with the tools used in the first half of this class. In this question you are asked to model a novel situation to demonstrate your understanding and ability to apply this material in similar manner as those questions. This task is largely one of simplification. The goal will be to construct a problem in the manner of question 1 (discrete choice with randomization) or question 2 (simultaneous continuous choice). You may choose any strategic interactions that you wish to analyze. Follow the process laid out below: a) Strategic Setting Choose a strategic setting and decide justify what model structure will work best. b) Model Develop payoffs for your strategic setting leaving some key elements as variables as has been done in the questions above. (For example, I use the variable H to represent legal costs.) Again, you are trying to simplify and distill the decisions being made into its key components or key. c) Solve Do your best to find any equilibrium in your model without replacing variables with numeric inputs. Provide any restrictions you think are necessary or meaningful. This is a challenging task and may require to rethink you initial set up in part b. If needed simplify your model by replacing variable with numbers (For example: you were asked to solve the equilibrium when H = 10 in questions 2). d) Comparative Staties For any found equilibrium consider the impact of a change to that variable. c) Reflect Write a reflection on the process you undertook. What challenges did you face and how did you overcome them? If your model failed or cannot be solved explain what challenges you faced. What issues can you identify as being problematic? If you had more time how would you attempt to fix these issues? This is a challenging task. You will receive part marks for your attempts and your reflection will be key in the grading of both successful and unsuccessful models. A functioning model without meaningful process will not get full marks while a failed model with great reflection has the potential to get full marks Question 1 Toften find myself in that awkward spot between holding the door for the next person coming through and just walking through because they are too far off. The thing that makes this a tough decision is sometimes the person following speeds up to make it through the door quicker and sometimes not. From this point forward let us use player 1 and 2. Player 1 is at the door and player 2 is following player I. Payoffs To keep things simple, we will consider payoff in terms of time (seconds) Player l's choices in this situation are to either hold the door or not. If player I does not holds the door they lose no time and consider their payoff to be neutral or a payoff of 0. If player I chooses to hold the door and player 2 doesn't speed up player I will lose y seconds of time. If player 2 chooses to speed up player I waits for half the time and loses only 0.5y seconds. Player I feels good about holding the door. This feeling is worth a seconds to them. Player 2 considers their payoff to be neutral or 0 if player I doesn't hold the door from them and they don't change their speed. If player 1 holds the door and they maintain their speed they save x seconds. If they speed up they save twice as many, 2x. Being rushed by a stranger feels bad however. That feeling is like giving up another B seconds. We assume that 0