Loyal Customers and Shoppers
A market has 100 consumers, each willing to pay up to 10 for one unit. Of them, 20 are loyal to firm A and 20 are loyal to firm B: a loyal consumer buys from their firm if its price is at most 10. The other 60 are shoppers who buy from the cheaper firm (splitting equally on a tie). Production is costless and the two firms choose prices in [0, 10] simultaneously. There is no pure-strategy equilibrium; in the symmetric mixed equilibrium, what is the probability that a firm charges a price below 5? Give a reduced fraction.
Related problems & prerequisites
Worth solving first
- The Unprofitable Merger 5.0/10
- Matching Pennies 5.0/10
- Selling Imperfect Substitutes 5.0/10
Source: Inspired by Hal Varian's model of sales (1980). Statement written for AxiomIQ.