L12 - Asymmetric Information: Virtual Game

Question 1

How was the first game played?

Answer 1

• 1 buyer many sellers
  
  • Buyer demand one unit and sellers can sell different qualities of the item
  • shown in the table are the buyer’s maximum willingness to pay and sellers marginal costs
• Sellers must select a single grade to sell and a single price to sell at
• buyer aims to maximise consumer surplus by selecting which seller to trade with if any.
• Full information –> buyer can fully assess the offered grades and prices
• Seller aims to maximise profit
• No collusion and price in 1P increments only, no below-cost pricing and max price of 8.60

Case study market:

• 4 volunteers submitted prices to Chris to help us understand what was happening and we put our offers in pretending we are the fifth firm –> try and maximise our profits

Question 2

What are the results of the first game?

Answer 2

• Buyer could see grades so would never pay more than they are willing to pay
  
  • Would always go for the item that had the maximum difference between willingness to pay and price
• Always an incentive to deviate for seller undercut eat other by the marginal increment to get the sale
• Always an incentive to deviate to selling B as it maximises consumer surplus other grades cannot win if other sellers swap to it
• Buyer’s consumer surplus is maximised at grade B so over time grade B was selected and competition pressure puts price down to marginal cost = 6
  
  • Maximised buyers surplus at 1.20 (and social welfare)

Same a Bertrand competition –> driving price down to marginal cost

• Extra notes
  
  • Takes time to learn and converge on the Nash Equilibrium
    
    • Speed is different for different people
  • Even if you are hyper-rational ( known what to do straight away) my not be in your best interest to pay the NE straight away, instead it may be worth to deviate from the NE and just undercut the other players who are still playing suboptimally

Question 3

How was the second game played?

Answer 3

• Simplified from game 1 - no grade A
• NOW symmetric information
• Buyers do not see chosen grade before they choose, only the price
• Sellers must select a single grade and a single price to sell at
• Byers maximise consumer surplus by selecting which seller to trade with if any
• Sellers aim to maximise profit
• No collusion
• Price in 1p increments only, no below cos pricing a max price of 7.20

Question 4

What was the result of the second game?

Answer 4

• Prices converged to the marginal costs of the lowest quality
  
  • Sellers start to learn that the Buyer will try and pick the lowest cost in hopes that it maximises their surplus (and they arent getting scammed by a company pricing the good high but it being of low quality)
  • For a company there is always an incentive to charge an high price and then deviate and make a lower quality product to maximise their surplus –> B knows this and is weary of it
    
    • So consumer assumes this through common knowledge –> so they will assume they will be sold a grade d product and will only pay a maximum of £3 for the good
  • But there is always an incentive to undercut each other
    
    • Thus if competition is fierce enough prices are pushed down to £2
• We do assume the buyer knows the potential costs of each grade –> so knows how low the seller can go –> through common knowledge I know that for example if the seller was seller at grade C the lowest he could price is 4
  
  • Is this realistic? probably not, with repeated interactions could continue to price at 6 to take an initial loss to signal that you are a high-quality producer –> then it would be optimal to cooperative give both the seller and buyers are sufficiently patient

Because of asymmetric information we are now looking at an NE with lower social welfare