Q1) 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. [16 marks] (Note: for parts (a) & (b) below consider Usman as ‘row player’ and Ibrahim as ‘column player’).

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?

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 is discussed below in details.

Explanation:

A) In the first position, every one of them makes more profit by resting alone than by resting together, and this is favored over standing. So the payoffs are as provided in the beneath image as (a). Here if one stands and the other sits, at that point the person who relaxes gets a bigger payoff of 4, while the other gets - 2 (Since he is standing which is difficult). If the two of them stand, at that point, the payoff is - 2 for each, and on the off chance that the two of them sit they every one of them gets a payoff of 2 (which is not exactly the payoff if the other individual stands given as 4 above). So Usman stands, Ibrahim will decide to sit, bringing about a payoff of (4,- 2). In any case, if Ibrahim sits, Usman will likewise sit since his payoff is higher by choosing to sit (2>-2). So the only Nash equilibrium is given when both choose to sit, e (Sit, Sit) given by lower right corner of the game getting the payoff of (2,2).

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