# Hotel pricing game

On Waikiki Beach, there are two hotels, Weird and Bizarre. The practice of guaranteed price matching is illegal. If the two firms act independently (they do not engage in price fixing or any other collusive behavior), each firm will rent 50 rooms per day at a price of $50 per room and an average cost of $45 per room. Under a price-fixing or cartel arrangement, each hotel would rent 30 rooms per day at a price of $60 and an average cost of $48. If one firm charges $50 and the other firm charges $60, the low-price firm will earn a profit of $500, and the high-price firm will earn a profit of $150. Bizarre picks a price first, followed by Weird.

a. Suppose each firm must pick a price and maintain its chosen price for the remaining lifetime of the firm. Draw a payoff table and predict the outcome of this game.

b. Suppose the two firms can change their prices daily, and expect to be in business for 3 more days. Weird announces that he will start will the high price, and maintain the price as long as Bizarre does too. If Bizarre undercuts Weird, however, Weird will pick the low price for the remainder of the game. Predict the outcome of the game. Use the numbers provided.

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#### Solution Preview

a. Suppose each firm must pick a price and maintain its chosen price for the remaining lifetime of the firm. Using the Table 9.3 on p. 254 as an example, draw a payoff table and predict the outcome of this game.

We can create the payoff matrix by multiplying the profit for each room by the number of rooms. Thus we have:

50 * 5 = 250 for low price

30 * 12 = 360 for high price

This ...

#### Solution Summary

Game theory and price undercutting