Question

Question 3

An airline severely damages identical antiques purchased by two different travellers. The airline manager is willing to compensate them for the loss of the antiques. The manager doesn’t know the actual value of the antiques but he knows that they are individually worth at least $180 and not more than $300. He knows that they can exaggerate the antique’s value, so he decided to act as follow: He placed each one of the two travellers in a different room and asked them tell him their estimate value of the antique, as any value between $180 and $300. However, there are a couple of caveats:

• If both travellers say the same value, he will refund each one of them that amount.
• If they say different values, he will know that one of them is lying. He will pay both of them the lower value and reward the traveller who said the lower price by $5 for “honesty”, and punish the one who said the higher price with a $5 fine.

1. Describe the above game: Who are the players? What are each player’s strategies? What are the payoffs? What are each player’s preferences?
2. What is the Nash equilibrium of this game (what value will each one of them say to the airline manager in equilibrium)? Describe the process that got you to this solution in terms of Best Responses.
3. Is it an efficient solution?

Bonus Question (10 points)

In the bicycle market there are two companies A and B. Each company can sell either electric bicycles or regular bicycles.

If they both sell electric bicycles, they will get $2m each.

If one store sells electric bicycles and the other store sells regular bicycles:

• The store that sells electric bicycles will get $5m
• The store that sells regular bicycles will get $2.5m

If they both sell regular bicycles, they will get $1m each.

1. Describe the situation as a simultaneous game.
2. Do any of the stores have a dominant strategy?
3. Is there a dominant strategy equilibrium?
4. Are there Nash equilibria? If so, which one of them is better?

Answer 1