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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

b. c. Player 2 would choose Y and player 1 would follow by choosing B. c. x < 2.5. ($10. 7. $10) Left 2 Left (-$10. 5) and (20. x < 2. The (5. 5) equilibrium would seem most likely since the other equilibrium entails considerable risk if the players don’t coordinate on the same equilibrium. This would signal to player 2 that player 1 is going to use strategy B. $10). b. 120) and (100. Player 2 has four feasible strategies: (1) W if A and Y if B. $15) and ($10. and therefore permit the players to coordinate on the (20. $15) is a Nash equilibrium is because Player 2 threatens to play left if 1 plays left. This is the subgame perfect equilibrium. 8. This threat isn’t credible. Baye . $8) b. ($0. a. (100. 20). (2) X if A and Y if B. (60. a. There are two Nash equilibria: (5. x > 2. Page 2 Michael R. “B”. 150). a. b. See the accompanying figure. ($0. 20) equilibrium. (4) X if A and Z if B. 6. c. the only reason ($0. $10) is the only subgame perfect equilibrium. c. 150). $15) Right Right ($10. a. (3) W if A and Z if B. Player 1 has two feasible strategies: A or B.

In this case. respectively.5.5 $2. The normal form game looks like this: Ford Strategy Airbags No Airbags GM Airbags $1.9. would be to offer airbags. $2 $0. $5 $3. 4e Page 3 . $100) Introduce C2 Acquiesce ($227. 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. $300) Not Introduce Price War ($100. while Coca-Cola might threaten to start a price war in an attempt to keep you out of the market. 3) and ($3. there is not a clear-cut pricing strategy for either firm. 1 $5.5 The dominant strategy. 11. $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. 10. this threat isn’t credible.-$1 No Airbags -$1. $3 Notice that there are two Nash equilibria: (Sale. Managerial Economics and Business Strategy. Thus. The extensive form game looks like this: ($200. Thus. Regular) and (Regular. 12. Sale) with profits of ($5. Another mechanism might be to guarantee “everyday low prices” (so that you effectively commit to always charge the sale price). $5). One mechanism that might solve this problem is to advertise your sales on alternate weeks. 1. The normal form game looks like this: Kmart Strategy Sale Price Regular Price Target Sale Price $1. in this case. your rival’s best response would be to charge the regular price and your firm would earn profits of $5 million.5. $0. your best option is to introduce.

. $48 Yes $48. 14. $0  Cheat   Coop 1 Collusion is profitable under the usual trigger strategies if  . Since you know for certain that the game will end in 1 month.. Baye . $7 The one-shot Nash equilibrium is for both firms to charge a low price to earn zero profits. The normal form of this game looks as follows: Rival Strategy: Price Low High You Low $0. one requirement is for the interest rate to be less than 20 $8  0 i percent. Since  Coop   Cheat .5   . The normal form game looks like this: Rival Advertise No Yes Kellogg’s No $8. otherwise charge a low price) $7  $7  $7  1  0.13. Page 4 Michael R.5 earns $9 million today and zero forever after. Another requirement includes the ability of firms to monitor (observe) potential deviations by rivals.-$1 $0. $8 -$1. A firm that cheats Coop . 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. Thus.5  $7  1  0. $9 $7.  2 are   $14 million. Now suppose you and your rival compete year after year but there is a 50 percent chance the Jeep is discontinued.-$1 High -$1. or  Coop   N i $48  $8 1  $5  . the collusive outcome can be sustained as a Nash equilibrium. $0 $9. 15. 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.

since they are variable costs.18 Arglye $10 10.000.$70) x 500 = $15. Managerial Economics and Business Strategy. and is therefore irrelevant to the decision (the firms’ fixed costs are $20. the market price is $90. or $40 + $30 = $70. NetWorks Strategy 250 Units 500 Units GearNet 250 Units $12500.000 (since $20. the firm’s contributions are ($100 . and the contributions of each firm are ($90 . total market output is 500 units and the price is $120. since that strategy is a dominant strategy.000/250 = $80 and $20. You should not invest the $2 million because the ability to move first does not result in a payoff advantage. In equilibrium each firm contributes $10. $7500 $10000. the market price is $100. The key is to note that if each firm produces 250 units. 17. The normal form looks like this: Baker Price $10 $20 $5 15. $12500 $7500. In this case.000.$70) x 500 = $10. Each firm’s contributions in this case are ($120 . $15000 500 Units $15000. 16 10. Direct labor and direct materials are the only relevant costs. 4e Page 5 . it is irrelevant to the decision. These later numbers are the reported unit depreciation costs).000.000/500 = $40. Since depreciation is a fixed cost and must be paid regardless of the firm’s output. The firm’s marginal cost (which equals its average variable cost in this case) is thus the sum of unit labor and materials costs. 16 15.16. The payoff matrix (normal form) below shows the relevant contributions toward paying the fixed costs of $20. The payoff matrix (normal form) below shows the relevant payoffs (contributions) towards paying the $20. If one firm produces 250 units and the other firm produces 500 units.18 Your optimal price is $5.000 in fixed costs for alternative levels of output by the two firms. $10000 Each firm’s dominant strategy in a one-shot game is to produce 500 units.000 toward its $20.$70) x 250 = $12.000 in fixed costs.500. If each firm produces 500 units. Depreciation is a fixed (or sunk) cost.500 and ($100 .$70) x 250 = $7.