There are two grocery retailers
- Save-on-foods
-Safeway
Both firms SIMULTANEOUSLY determine whether to open a store in Wesbrook Village
Demand for groceries in WV is q = 4 − p
The marginal cost for each firm is assumed to be zero for simplicity (and it is a common knowledge)
Then, the monopoly price solves the following problem max (4 − p)p
So the monopoly price is 2 and the (variable) monopoly profit is 4.
There is a fixed cost of opening a store in WV
One needs to subtract the fixed cost from the variable cost to evaluate the profit
For Save-on-foods it is 2; and this is common knowledge
However, the fixed cost for Safeway is known only to Safeway, All Save-on-foods know about Safeway’s fixed cost is: 1 with probability p, 0 < p < 1 ; 3 with probability (1 − p).When both firms enter, the price is determined in a Bertrand competition, which means... There will be a fierce competition in price, so the price will drop to the marginal cost of zero. A firm not entering the market will earn the payoff of zero.
Find ALL Bayesian Nash Equilibrium of the market entry game between Save on Foods and Safeway discussed in class. Note that the set of equilibria might depend on p (0 < p < 1), the probability that Safeway’s fixed cost is low at 1. So your answers may be, ”when p is in the range of...., the set of equilibria are..., whereas when p is in different range, the set equilibria are...”. Calculate the expected social welfare for each of the equilibria. In which equilibrium is the social welfare the highest?