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Chapter 10: Answers to Questions and Problems

1.
a. Player 1’s dominant strategy is B. Player 2 does not have a dominant strategy.
b. Player 1’s secure strategy is B. Player 2’s secure strategy is E.
c. (B, E).

2.
a.

Player 2
Strategy A B
A $500, $500 $0, $650
Player 1
B $650, $0 $100, $100

b. B is dominant for each player.
c. (B, B).
d. Joint payoffs from (A, A) > joint payoffs from (A, B) = joint payoffs from (B, A)
> joint payoffs from (B, B).
e. No; each firm’s dominant strategy is B. Therefore, since this is a one-shot game,
each player would have an incentive to cheat on any collusive arrangement.

3.
a. Player 1’s optimal strategy is B. Player 1 does not have a dominant strategy.
However, by putting herself in her rival’s shoes, Player 1 should anticipate that
Player 2 will choose D (since D is Player 2’s dominant strategy). Player 1’s best
response to D is B.
b. Player 1’s equilibrium payoff is 5.

4.
a. (A, C).
b. No.
c. If firms adopt the trigger strategies outlined in the text, higher payoffs can be
 Cheat   Coop 1
achieved if  . Here, πCheat = 60, πCoop = 50, πN = 10, and the
 Coop
 N
i
 Cheat   Coop 60  50 1 1 1
interest rate is i = .05. Since    0.25 <   20
 Coop
 N
50  10 4 i .05
each firm can indeed earn a payoff of 50 via the trigger strategies.
d. Yes.

Managerial Economics and Business Strategy, 4e Page 1

x > 2. $15) and ($10. ($10. See the accompanying figure. This is the subgame perfect equilibrium. The (5. $15) is a Nash equilibrium is because Player 2 threatens to play left if 1 plays left. x < 2. (4) X if A and Z if B. Player 2 would choose Y and player 1 would follow by choosing B. There are two Nash equilibria: (5. $8) b. $15) Right Right ($10. 6. a. 8. a. a. (2) X if A and Y if B. (60. 5) equilibrium would seem most likely since the other equilibrium entails considerable risk if the players don’t coordinate on the same equilibrium. (3) W if A and Z if B. a. ($0. and therefore permit the players to coordinate on the (20.5. b. c. $10) is the only subgame perfect equilibrium. c. ($0. b. b. x < 2. 5) and (20. 7. 150). Baye . $10) Left 2 Left (-$10. 120) and (100. 150). 20). Player 2 has four feasible strategies: (1) W if A and Y if B. (100. c. the only reason ($0. Page 2 Michael R. This would signal to player 2 that player 1 is going to use strategy B. $10). 20) equilibrium. “B”. Player 1 has two feasible strategies: A or B. This threat isn’t credible. c.

-$1 No Airbags -$1. 3) and ($3. there is not a clear-cut pricing strategy for either firm. respectively. $5 $3. The extensive form game looks like this: ($200.5. your rival’s best response would be to charge the regular price and your firm would earn profits of $5 million. $275) Notice that Coca-Cola’s best response if Pepsi introduces is to acquiesce to earn $275 million rather than to start a price war and earn $100. $3 Regular Price $3. 1 $5. $3 Notice that there are two Nash equilibria: (Sale. Sale) with profits of ($5. Thus.5 The dominant strategy. Managerial Economics and Business Strategy. this threat isn’t credible. $300) Not Introduce Price War ($100. in this case. would be to offer airbags. 11. while Coca-Cola might threaten to start a price war in an attempt to keep you out of the market. The normal form game looks like this: Ford Strategy Airbags No Airbags GM Airbags $1. One mechanism that might solve this problem is to advertise your sales on alternate weeks. Another mechanism might be to guarantee “everyday low prices” (so that you effectively commit to always charge the sale price). The savings from letting the union use its own pen and ink to craft the document are most likely small compared to the advantage you would gain by making a take-it-or- leave-it offer. 12.9. $2 $0. $5).5 $2. Thus. 1. $0. your best option is to introduce. 4e Page 3 . In this case. The normal form game looks like this: Kmart Strategy Sale Price Regular Price Target Sale Price $1.5. 10. $100) Introduce C2 Acquiesce ($227. Regular) and (Regular.

. Now suppose you and your rival compete year after year but there is a 50 percent chance the Jeep is discontinued. $8 -$1. 14. $9 $7. Baye .13. or  Coop   N i $48  $8 1  $5  . A firm that cheats Coop . $7 The one-shot Nash equilibrium is for both firms to charge a low price to earn zero profits. your optimal strategy in the finitely repeated pricing game with a known endpoint is to reduce price (defect) from the implicit collusive agreement between you and your rival. Another requirement includes the ability of firms to monitor (observe) potential deviations by rivals.. The profits of a firm that conforms to the collusive strategy (high price) under the usual trigger strategies (firms agree to charge the high price so long as no player deviated in the past. one requirement is for the interest rate to be less than 20 $8  0 i percent. Since you know for certain that the game will end in 1 month. The normal form of this game looks as follows: Rival Strategy: Price Low High You Low $0. Page 4 Michael R. Since  Coop   Cheat .-$1 $0.-$1 High -$1. Thus.5  $7  1  0. $48 Yes $48. $0 $9.5   .  2 are   $14 million. The normal form game looks like this: Rival Advertise No Yes Kellogg’s No $8. otherwise charge a low price) $7  $7  $7  1  0. $0  Cheat   Coop 1 Collusion is profitable under the usual trigger strategies if  .5 earns $9 million today and zero forever after. the collusive outcome can be sustained as a Nash equilibrium. 15.

000.16. Managerial Economics and Business Strategy.000 in fixed costs. The key is to note that if each firm produces 250 units. the market price is $90.500 and ($100 .000 toward its $20.$70) x 500 = $15.000 (since $20. and the contributions of each firm are ($90 . and is therefore irrelevant to the decision (the firms’ fixed costs are $20. In this case. The payoff matrix (normal form) below shows the relevant payoffs (contributions) towards paying the $20. You should not invest the $2 million because the ability to move first does not result in a payoff advantage. $10000 Each firm’s dominant strategy in a one-shot game is to produce 500 units. NetWorks Strategy 250 Units 500 Units GearNet 250 Units $12500. 17. the firm’s contributions are ($100 . The payoff matrix (normal form) below shows the relevant contributions toward paying the fixed costs of $20. Depreciation is a fixed (or sunk) cost. $15000 500 Units $15000.000. since that strategy is a dominant strategy. Since depreciation is a fixed cost and must be paid regardless of the firm’s output. the market price is $100. 16 15.000/250 = $80 and $20. 4e Page 5 . If each firm produces 500 units.18 Arglye $10 10. or $40 + $30 = $70. Each firm’s contributions in this case are ($120 .000. it is irrelevant to the decision.$70) x 250 = $7. since they are variable costs.$70) x 500 = $10. The firm’s marginal cost (which equals its average variable cost in this case) is thus the sum of unit labor and materials costs. If one firm produces 250 units and the other firm produces 500 units.000/500 = $40. These later numbers are the reported unit depreciation costs).000 in fixed costs for alternative levels of output by the two firms. $12500 $7500. 16 10.$70) x 250 = $12. Direct labor and direct materials are the only relevant costs. $7500 $10000. The normal form looks like this: Baker Price $10 $20 $5 15.18 Your optimal price is $5.500. In equilibrium each firm contributes $10. total market output is 500 units and the price is $120.