The Lahore Metro Bus is crowded for travel during peak hours. During such travel hours two daily passengers ‘Usman’ and ‘Ibrahim’ enter the Metro. Luckily, two adjacent seats are free in the bus. Each of them must decide whether to sit or stand. For both, sitting alone is more comfortable than sitting next to the other person, which in turn is more comfortable than standing, a) Model the situation as a strategic game, assuming both ‘Usman’ and ‘Ibrahim’ care only about their own comfort. Find the Nash equilibrium (equilibria) if it exists. Also, does a dominant strategy exist for either ‘Usman’ or ‘Ibrahim’?
b) Now assume that both ‘Usman’ and ‘Ibrahim’ are altruistic, ranking outcomes according to the other person’s comfort and, out of politeness, prefer to stand than to sit if the other person stands. Model the situation as a strategic game and find any Nash equilibrium (equilibria) if it exists. Does a dominant strategy exist for either ‘Usman’ or ‘Ibrahim’ with these preferences?