Game Theory

Question 3 Consider the following discrete choice game in which two coffee shops must simultaneously choose their pricing strategy. There are two coffee shops in a nearby business district, with owners labeled A and B, who must choose whether to charge $2, $4, or $5 for a cup of coffee. Assume their payoff is equal to their revenue, i.e., the number of cups purchased multiplied by the price. There are two types of consumers in this market. There are 6000 convenience shoppers who do not concern themselves with price and will randomize across the two shops - i.e., 3000 go to each, regardless of pricing strategy. In addition to convenience shoppers, there are 4000 bargain hunters, who will always go to the shop with the cheapest coffee and randomize evenly if two shops are equally cheap. (a) Fill out the payoffs for the above game in a 3x3 matrix. Hint: payoffs are equal to the number of consumers multiplied by the price charged. For example, UA($2,$2)= (3000+2000)$2=$10,000 and UA($2,$4)=(3000+4000)$2=$14,000. (b) Identify an equilibrium via iterated elimination of strictly dominated strategies. Question 3 Consider the following discrete choice game in which two coffee shops must simultaneously choose their pricing strategy. There are two coffee shops in a nearby business district, with owners labeled A and B, who must choose whether to charge $2, $4, or $5 for a cup of coffee. Assume their payoff is equal to their revenue, i.e., the number of cups purchased multiplied by the price. There are two types of consumers in this market. There are 6000 convenience shoppers who do not concern themselves with price and will randomize across the two shops - i.e., 3000 go to each, regardless of pricing strategy. In addition to convenience shoppers, there are 4000 bargain hunters, who will always go to the shop with the cheapest coffee and randomize evenly if two shops are equally cheap. (a) Fill out the payoffs for the above game in a 3x3 matrix. Hint: payoffs are equal to the number of consumers multiplied by the price charged. For example, UA($2,$2)= (3000+2000)$2=$10,000 and UA($2,$4)=(3000+4000)$2=$14,000. (b) Identify an equilibrium via iterated elimination of strictly dominated strategies