Consider the following two-stage entry-pricing game between an incumbent firm and a potential entrant:

2 players: {incumbent, entrant}

Two-stage game:

Stage-1: Potential entrant makes its entry decision by choosing from {Enter, Do not enter};

Stage-2: The incumbent and the new entrant engage in simultaneous-move pricing game.

If the potential entrant chooses to enter, she must incur a one-time fixed cost of entry, f, prior to engaging in price competition. This cost includes the advertising and marketing expenses which must be incurred prior to entry to guarantee a degree of customer loyalty that can match the incumbent's.

The stage-2 price competition has the following structure:The market that opens for competition has three types of consumers:

Type-1 consumers locked into the incumbent firm's product;

Type-2 consumers locked into the new entrant's product;

Type-3 consumers with no loyalty to either firm.

Each firm can choose a price from {PH (high price), PL (low price)}.

Profit margins per unit of output are:

$10 if price = PH;

$6 if price = PL.

The demand has the following structure:

If entry takes place, each firm has a loyal captive customer base demanding 2,000 units per year regardless of the price, and the floating demand for 6,000 units per year (price-conscious consumers buying from the lower-priced firm).

If entry does not take place, the incumbent firm has the monopoly over the entire market demand for 10,000 units per year.

Given that entry takes place, if both firms charge the same price, PH or PL, the floating demand will be divided equally between the two firms (hence, 3,000 units each). If the firms charge different prices, the firm charging the lower price will capture the entire floating demand of 6,000 units.

Hence, if entry occurs in the first stage, the payoff table for the second stage post-entry game would look as follows (remember the entry cost is already sunk at this stage and, and thus it should not enter into the stage-2 payoff consideration -- it will be relevant in stage-1, however):

		Entrant
		PH	PL
Incumbent	PH	(50, 50)	(20, 48)
	PL	(48, 20)	(30, 30)

Entry cost must be 0 < F < 50 if both firms charge price high.

(g) Now suppose the firms play a "mixed strategy" game in stage-2 price competition. Again, derive the condition for the entry cost, f, that would support entry as part of the rollback equilibrium, given the mixed strategy equilibrium in stage 2. (10 pts)