Chapter 10 - Game Theory: Inside Oligopoly
Chapter 10 Game Theory: Inside Oligopoly Multiple Choice Questions
1. Consider the following information for a simultaneous move game: If you advertise and your rival advertises, you eah will earn !" million in profits. If neither of you advertise, you will eah earn !10 million in profits. #owever, if one of you advertises and the other does not, the firm that advertises will earn !1" million and the non advertising firm will earn !1 million. If you and your rival plan to $e in $usiness for only one year, the %ash e&uili$rium is A. 'or eah firm to advertise (. 'or (. 'or neither firm to advertise C. 'or C. 'or your firm to advertise and the other not to advertise ). %one ). %one of the statements assoiated with this &uestion are orret
Difficulty: Medium
*. Consider the following information for a simultaneous move game: If you advertise and your rival advertises, you eah will earn !" million in profits. If neither of you advertise, you will eah earn !10 million in profits. #owever, if one of you advertises and the other does not, the firm that advertises will earn !1" million and the non advertising firm will earn !1 million. If you and your rival plan to $e in $usiness for 10 years, then the %ash e&uili$rium is A. 'or eah firm to advertise every year (. 'or (. 'or neither firm to advertise in early years, $ut to advertise in later years C. 'or C. 'or eah firm to not advertise in any year ). 'or ). 'or eah firm to advertise in early ea rly years, $ut not advertise in later years
Difficulty: Medium
10-1
Chapter 10 - Game Theory: Inside Oligopoly
+. Consider the following information information for a simultaneous move move game: If you advertise and your rival advertises, you eah will earn !" million in profits. If neither of you advertise, you will eah earn !10 million in profits. #owever, if one of you advertises and the other does not, the firm that advertises will earn !1" million and the non advertising firm will earn !1 million. If you and your rival plan to hand your $usiness down to your hildren and this $e&uest goes on forever then a %ash e&uili$rium when the interest rate is /ero is advertise until the rival rival does, and then to advertise forever forever A. 'or eah firm to not advertise (. 'or your firm to never advertise C. 'or your firm to always advertise when your rival rival does ). 'or eah firm to advertise advertise until the rival does not advertise, and then not advertise advertise forever
Difficulty: Medium
. If you advertise and your rival advertises, you eah will earn ! million in profits. If neither of you advertise, you will eah earn !10 million in profits. #owever, if one of you advertises and the other does not, no t, the firm that advertises will earn !1 million and the non advertising firm will earn !" million. If you and your rival plan to $e in $usiness for only one on e year, the %ash e&uili$rium is . 'or . 'or eah firm to advertise B. 'or neither firm to advertise C. 'or C. 'or your firm to advertise and the other not to advertise ). %one ). %one of the statements assoiated with this &uestion are orret
Difficulty: Medium
". If you advertise and your rival advertises, you eah will earn ! million in profits. If neither of you advertise, you will eah earn !10 million in profits. #owever, if one of you advertises and the other does not, no t, the firm that advertises will earn !1 million and the non advertising firm will earn !" million. If you and your rival plan to $e in $usiness for 10 years, then the %ash e&uili$rium is . 'or . 'or eah firm to advertise every year (. 'or (. 'or neither firm to advertise in early years, $ut to advertise in later years a dvertise in any year C. 'or eah firm to not advertise ). 'or ). 'or eah firm to advertise in early ea rly years, $ut not advertise in later years
Difficulty: Medium
10-*
Chapter 10 - Game Theory: Inside Oligopoly
+. Consider the following information information for a simultaneous move move game: If you advertise and your rival advertises, you eah will earn !" million in profits. If neither of you advertise, you will eah earn !10 million in profits. #owever, if one of you advertises and the other does not, the firm that advertises will earn !1" million and the non advertising firm will earn !1 million. If you and your rival plan to hand your $usiness down to your hildren and this $e&uest goes on forever then a %ash e&uili$rium when the interest rate is /ero is advertise until the rival rival does, and then to advertise forever forever A. 'or eah firm to not advertise (. 'or your firm to never advertise C. 'or your firm to always advertise when your rival rival does ). 'or eah firm to advertise advertise until the rival does not advertise, and then not advertise advertise forever
Difficulty: Medium
. If you advertise and your rival advertises, you eah will earn ! million in profits. If neither of you advertise, you will eah earn !10 million in profits. #owever, if one of you advertises and the other does not, no t, the firm that advertises will earn !1 million and the non advertising firm will earn !" million. If you and your rival plan to $e in $usiness for only one on e year, the %ash e&uili$rium is . 'or . 'or eah firm to advertise B. 'or neither firm to advertise C. 'or C. 'or your firm to advertise and the other not to advertise ). %one ). %one of the statements assoiated with this &uestion are orret
Difficulty: Medium
". If you advertise and your rival advertises, you eah will earn ! million in profits. If neither of you advertise, you will eah earn !10 million in profits. #owever, if one of you advertises and the other does not, no t, the firm that advertises will earn !1 million and the non advertising firm will earn !" million. If you and your rival plan to $e in $usiness for 10 years, then the %ash e&uili$rium is . 'or . 'or eah firm to advertise every year (. 'or (. 'or neither firm to advertise in early years, $ut to advertise in later years a dvertise in any year C. 'or eah firm to not advertise ). 'or ). 'or eah firm to advertise in early ea rly years, $ut not advertise in later years
Difficulty: Medium
10-*
Chapter 10 - Game Theory: Inside Oligopoly
2. If you advertise and your rival advertises, you eah will earn ! million in profits. If neither of you advertise, you will eah earn !10 million in profits. #owever, if one of you advertises and the other does not, no t, the firm that advertises will earn !1 million and the non advertising firm will earn !" million. If you and your rival plan to hand your $usiness down to your hildren and this $e&uest goes on forever then a %ash e&uili$rium is for eah firm to . %ot . %ot advertise until the rival does, and then to advertise for ever B. %ever advertise C. lways C. lways advertise ). dvertise ). dvertise until the rival does not advertise, and then not advertise forever
Difficulty: Medium
3uestions 4, 5, and 6 are $ased on the following game, where firms one and two must independently deide whether to harge high or low pries.
4. 7hih of the following are %ash e&uili$rium e& uili$rium payoffs in the one-shot game8 . 0, . 0, 0 (. ", (. ", -" C. -", C. -", " D. 10, 10
Difficulty: Medium
10-+
Chapter 10 - Game Theory: Inside Oligopoly
5. 7hih of the following are the %ash e&uili$rium payoffs eah period if the game is repeated 10 times8 . 0, . 0, 0 (. ", (. ", -" C. -", C. -", " D. 10, 10
Difficulty: Medium
6. 9uppose the game is infinitely repeated. Then the $est the firms ould do in a %ash e&uili$rium is to earn per period. . 0, . 0, 0 (. ", (. ", -" C. -", C. -", " D. 10, 10
Difficulty: Medium
10. Consider the following entry game. #ere, firm ( is an eisting firm in the mar;et, and firm is a potential entrant. 'irm must deide whether to enter the mar;et play enter or stay out of the mar;et play not enter. If firm deides to enter the mar;et, firm ( must deide whether to engage in a prie war play hard, or not play soft. (y playing hard, firm ( ensures that firm ma;es a loss of !1 million, $ut firm ( only ma;es !1 million in profits. On the other hand, if firm ( plays soft, the the new entrant ta;es half of the mar;et, and eah firm earns profits of !" million. If firm stays stays out, it earns /ero while firm ( earns !10 million. 7hih of the following are %ash e&uili$rium strategies8 .
Difficulty: Hard
10-
Chapter 10 - Game Theory: Inside Oligopoly
11. Consider the following entry game. #ere, firm ( is an eisting firm in the mar;et, and firm is a potential entrant. 'irm must deide whether to enter the mar;et play enter or stay out of the mar;et play not enter. If firm deides to enter the mar;et, firm ( must deide whether to engage in a prie war play hard, or not play soft. (y playing hard, firm ( ensures that firm ma;es a loss of !1 million, $ut firm ( only ma;es !1 million in profits. On the other hand, if firm ( plays soft, the the new entrant ta;es half of the mar;et, and eah firm earns profits of !" million. If firm stays stays out, it earns /ero while firm ( earns !10 million. 7hih of the following are perfet e&uili$rium strategies8 A.
Difficulty: Hard
nswer &uestions 1*-1" $ased on the following information for a one-shot game:
1*. 7hat are dominant strategies for 'irm and 'irm ( respetively8 . =ow . =ow prie, high prie (. #igh (. #igh prie, low prie C. #igh C. #igh prie, high prie D. =ow prie, low prie
Difficulty: Medium
10-"
Chapter 10 - Game Theory: Inside Oligopoly
1+. 7hat are seure strategies for firm and firm ( respetively8 . =ow prie, high prie (. #igh prie, low prie C. #igh prie, high prie D. =ow prie, low prie
Difficulty: Medium
1. 7hat are the %ash e&uili$rium strategies for firm and ( respetively8 . =ow prie, high prie (. #igh prie, low prie C. #igh prie, high prie D. =ow prie, low prie
Difficulty: Medium
1". If this one-shot game is repeated 100 times, the %ash-e&uili$rium payoffs of the players will $e >>>>>>>>>>>>>>>> eah period. A. *, * (. 10, -5 C. -5, 10 ). 2, 2
Difficulty: Easy
12. 7hih of the following are important determinants of ollusion in priing games8 . The num$er of firms (. 'irm si/e C. #istory D. ll of the statements assoiated with this &uestion are orret
Difficulty: Easy
10-2
Chapter 10 - Game Theory: Inside Oligopoly
nswer &uestions 14-*0 $ased on the following payoff matri:
14. 7hat are the seure strategies for 'irm and 'irm ( respetively8 A. =ow prie, high prie (. #igh prie, low prie C. #igh prie, high prie ). =ow prie, low prie
Difficulty: Medium
15. 7hih of the following is true8 . dominant strategy for 'irm is high prie (. There does not eist a dominant strategy for 'irm C. dominant strategy for 'irm ( is low prie D. %one of the statements assoiated with this &uestion are orret
Difficulty: Hard
10-4
Chapter 10 - Game Theory: Inside Oligopoly
16. 7hat are the %ash e&uili$rium strategies for 'irm and 'irm ( respetively in a one-shot game8 A. =ow prie, low prie (. #igh prie, high prie C. =ow prie, high prie ). =ow prie, low prie and high prie, high prie
Difficulty: Medium
*0. If this one-shot game is repeated three times, the %ash e&uili$rium payoffs for 'irm and ( will $e >>>>>> eah period A. 10, 6 (. 11, 11 C. -10, 4 ). 1", 5
Difficulty: Medium
*1. 7hih of the following is true8 . In a one-shot game, a ollusive strategy always represents a %ash e&uili$rium (. perfet e&uili$rium ours when eah player is doing the $est he an regardless of what the other player is doing C.
Difficulty: Medium
10-5
Chapter 10 - Game Theory: Inside Oligopoly
nswer &uestions **-*+ $ased on the following payoff matri:
**. 7hih of the following is true8 . dominant strategy for 'irm is high prie B. There does not eist a dominant strategy for 'irm C. dominant strategy for 'irm ( is low prie ). %one of the statements assoiated with this &uestion are orret
Difficulty: Medium
*+. 7hat are the %ash e&uili$rium strategies for 'irm and 'irm ( respetively8 . =ow prie, low prie B. #igh prie, high prie C. =ow prie, high prie ). =ow prie, low prie and high prie, high prie
Difficulty: Medium
10-6
Chapter 10 - Game Theory: Inside Oligopoly
*. 7hih of the following is true8 . In an infinitely repeated game, ollusion is always a %ash e&uili$rium B. In a finitely repeated game with a ertain end period, ollusion is unli;ely $eause effetive punishments annot $e used during any time period C. ll of the statements assoiated with this &uestion are orret ). %one of the statements assoiated with this &uestion are orret
Difficulty: Easy
*". 7hih of the following is true8 . 'or a finitely repeated game, the game is played enough times to effetively punish heaters and therefore ollusion is li;ely (. In an infinitely repeated game with a low interest rate, ollusion is unli;ely $eause the game unravels so that effetive punishment annot $e used during any time period C. seure strategy is the optimal strategy for a player no matter what the op ponent does D. %one of the statements assoiated with this &uestion are orret
Difficulty: Medium
*2. 7hih of the following enhanes the a$ility of waste ompanies to ollude8 A. )eals on waste reeptales (. #igh interest rates C. )ifferentiated nature of produts ). =arge num$er of firms
Difficulty: Hard
*4. Collusion is: . =egal in the ?nited 9tates (. %ot possi$le when firms interat repeatedly forever C. @ore li;ely in industries with a large num$er of firms D. %one of the statements assoiated with this &uestion are orret
Difficulty: Easy
10-10
Chapter 10 - Game Theory: Inside Oligopoly
Aefer to the following payoff matri for &uestions *5-+0:
*5. The dominant strategy for Blayer * is: . T1 (. T1 and t* C. T+ D. %one of the statements assoiated with this &uestion are orret
Difficulty: Easy
*6. The dominant strategy for Blayer 1 is: . 91 (. 9* C. 91 and 9* D. %one of the statements assoiated with this &uestion are orret
Difficulty: Easy
+0. 7hih of the following strategies onstitutes a %ash e&uili$rium of the game: A. 91, t1 (. 9*, t* C. 9*, t+ ). 91, t*
Difficulty: Medium
10-11
Chapter 10 - Game Theory: Inside Oligopoly
+1. 7hih of the following onditions are neessary for the eistene of a %ash e&uili$rium8 . The eistene of dominant strategies for $oth players (. The eistene of a dominant strategy for one player and the eistene of seure strategy for another player C. The eistene of seure strategy for $oth players D. %one of the statements assoiated with this &uestion are orret
Difficulty: Hard
Aefer to the following payoff matri for &uestions +* and ++:
+*. The dominant strategy of Blayer 1 is: A. 91 (. 9* C. 91 and 9* ). dominant strategy does not eist
Difficulty: Medium
++. 7hih of the following pair of strategies onstitute a %ash e&uili$rium of the game8 . 91, t1 (. 91, t* C. 9*, t1 D. 91, t* and 9*, t1
Difficulty: Hard
10-1*
Chapter 10 - Game Theory: Inside Oligopoly
+. (ased on the following game, what are the seure strategies for Blayer One and Blayer Two8
A. 91 and t* (. 91 and t1 C. 9* and t* ). 9* and t1
Difficulty: Medium
+". 7hih of the following is true for a %ash e&uili$rium of a two-player game8 . The oint payoffs of the two players are highest ompared to other strategy pairs B. Given another playerDs strategy stipulated in that %ash e&uili$rium, a player annot improve his welfare $y hanging his strategy C. %ash e&uili$rium is always uni&ue in real world pro$lems ). Given another playerDs strategy stipulated in that %ash e&uili$rium, a player annot improve his welfare $y hanging his strategy and a %ash e&uili$rium is always uni&ue in real world pro$lems
Difficulty: Medium
+2. Game theory is espeially useful for analysis in the following types of mar;ets: . Berfet ompetition (. @onopolisti ompetition C. Oligopoly ). @onopoly
Difficulty: Easy
10-1+
Chapter 10 - Game Theory: Inside Oligopoly
+4. <onomists use game theory to predit the $ehavior of oligopolists. 7hih of the following is ruial for the suess of the analysis8 . @a;e sure the payoffs reflet the true payoffs of the oligopolists (. @a;e sure whether the oligopolists move simultaneously or se&uentially C. @a;e sure the pro$lem onsidered is of a one-shot or repeated nature D. ll of the a$ove
Difficulty: Medium
?se the following information to answer &uestions +5 and +6: 9uppose that you are a manager. Eou are onsidering whether or not to monitor employees with the payoffs in the following normal form game.
+5. 7hih of the following pair of strategies onstitute a %ash e&uili$rium8 . @anager monitors and wor;er wor;s (. @anager does not monitor and wor;er wor;s C. @anager monitors and wor;er shir;s D. %one of the statements assoiated with this &uestion are orret
Difficulty: Easy
10-1
Chapter 10 - Game Theory: Inside Oligopoly
+6. 7hat should the manager do to solve the shir;ing pro$lem8 . lways monitor (. %ever monitor C. 9inerely tell wor;ers not to shir; D.
Difficulty: Easy
0. @anagement and a la$or union are $argaining over how muh of a !"0 surplus to give to the union. The !"0 is divisi$le up to one ent. The players have one-shot to reah an agreement. @anagement has the a$ility to announe what it wants first, and then the la$or union an aept or reet the offer. (oth players get /ero if the total amounts as;ed for eeed !"0. 7hih of the following is true8 . There are multiple %ash e&uili$ria (. !*", !*" is a %ash e&uili$rium C. %ash e&uili$rium is also a perfet e&uili$rium D. There are multiple %ash e&uili$ria and !*", !*" is a %ash e&uili$rium
Difficulty: Medium
1. @anagement and a la$or union are $argaining over how muh of a !"0 surplus to give to the union. The !"0 is divisi$le up to one ent. The players have one-shot to reah an agreement. @anagement has the a$ility to announe what it wants first, and then the la$or union an aept or reet the offer. (oth players get /ero if the total amounts as;ed for eeed !"0. 7hih of the following is not a %ash e&uili$rium8 . @anagement re&uests !"0 and the la$or union aepts !0 B. @anagement re&uests !+0 and the la$or union aepts !10 C. @anagement re&uests !*" and the la$or union aepts !*" ). %either management re&uesting !"0 and the la$or union aepting !0 nor management re&uesting !+0 and the la$or union aepting !10 are %ash e&uili$ria
Difficulty: Hard
10-1"
Chapter 10 - Game Theory: Inside Oligopoly
*. @anagement and a la$or union are $argaining over how muh of a !"0 surplus to give to the union. The !"0 is divisi$le up to one ent. The players have one-shot to reah an agreement. @anagement has the a$ility to announe what it wants first, and then the la$or union an aept or reet the offer. (oth players get /ero if the total amounts as;ed for eeed !"0. 7hih of the following is a perfet e&uili$rium8 A. @anagement re&uests !6.66, and the la$or union aepts !0.01 (. @anagement re&uests !*", and the la$or union aepts !*" C. @anagement re&uests !0, and the la$or union aepts !"0 ). %one of the statements assoiated with this &uestion are orret
Difficulty: Medium
+. @anagement and a la$or union are $argaining over how muh of a !"0 surplus to give to the union. The !"0 is divisi$le up to one ent. The players have one-shot to reah an agreement. @anagement has the a$ility to announe what it wants first, and then the la$or union an aept or reet the offer. (oth players get /ero if the total amounts as;ed for eeed !"0. If you were the la$or union, whih type of rules of play would you prefer to divide the !"0 surplus8 . One-shot simultaneous-move game (. One-shot se&uential-move game with management as the first mover C. One-shot se&uential-move game with la$or union as the first mover ). One-shot simultaneous-move game and one-shot se&uential-move game with management as the first mover
Difficulty: Easy
. 7hih of the following is true8 . %ash e&uili$rium is always perfet B. perfet e&uili$rium is always %ash C. %ash e&uili$rium is always perfet in a multistage game ). Berfet e&uili$rium and %ash e&uili$rium are the same onept $ut with different names
Difficulty: Medium
10-12
Chapter 10 - Game Theory: Inside Oligopoly
Aefer to the following normal form game of prie ompetition for &uestions "-4.
". 9uppose the game is infinitely repeated, and the interest rate is 10F. (oth firms agree to harge a high prie, provided no player has harged in low prie in the past. If $oth firms sti; to this agreement, then the present value of 'irm Ds payoffs are: A. **0 (. 110 C. ++0 ). ""0
Difficulty: Medium
2. 9uppose that 'irm deviates from a trigger strategy to support a high prie. 7hat is the present value of Ds payoff from heating8 . 40 B. "0 C. +0 ). *0
Difficulty: Medium
10-14
Chapter 10 - Game Theory: Inside Oligopoly
4. 7hat is the maimum interest rate that an sustain ollusion8 . +0F (. 1"F C. 22.4F ). *0F
Difficulty: Hard
5. It is easier to sustain tait ollusion in an infinitely repeated game if: . The present value of heating is higher (. There are more players in the game C. The interest rate is lower ). The present value of heating is higher and the interest rate is lower
Difficulty: Medium
6. 7hen a wor;er announes that he plans to &uit, say net month, the threat of $eing fired has no $ite. The wor;er may find it in his interest to shir;. 7hat an the manager do to overome this pro$lem8 . 'ire the wor;er as soon as he announes his plans to &uit B. Brovide the wor;er some rewards for good wor; that etend $eyond the termination of employment with your firm C. @onitor the wor;er more fre&uently than usual and fire him when he is aught shir;ing ). Bay the wor;er some rewards when he announes his plan to &uit
Difficulty: Medium
"0. finitely repeated game differs from an infinitely repeated game in that: . The former needs a lower interest rate to support ollusion than the latter needs B. There is an end-of-period pro$lem for the former C. ollusive outome an usually $e sustained in the former $ut n ot the latter ). ll of the statements assoiated with this &uestion are orret
Difficulty: Hard
10-15
Chapter 10 - Game Theory: Inside Oligopoly
"1. 7hih of the following is a fators affeting ollusion in an infinitely repeated priing game8 . %um$er of firms (. 'irm si/e C. #istory D. ll of the statements assoiated with this &uestion are orret
Difficulty: Easy
"*. oordination pro$lem arises whenever there: . Is no %ash e&uili$rium in a game (. Is a uni&ue %ash e&uili$rium $ut it is not very desira$le C. re multiple %ash e&uili$riam ). re no dominant strategies for $oth players
Difficulty: Medium
"+. 7hih of the following is the maor means to signal good &uality of goods $y firms8 . 9ales (. dvertisement C. 7arrantiesguarantees ). (oth a and $
Difficulty: Medium
". 7hih of the following is not true8 . n etensive form representation usually provides more information than a normal form representation of a game B. normal form game is most useful for se&uential-move games C. The notion of perfet e&uili$rium is more useful in analy/ing etensive form games than normal form games ). The notion of redi$le threats ma;es more sense in etensive form representations than in normal form representations of a game
Difficulty: Hard
10-16
Chapter 10 - Game Theory: Inside Oligopoly
"". %ash e&uili$rium with a non-redi$le threat as a omponent is: . perfet e&uili$rium B. %ot a perfet e&uili$rium C. se&uential e&uili$rium ). somewhat perfet e&uili$rium
Difficulty: Medium
"2. 7hih of the following is a valid riti&ue of the use of game theory in eonomis8 . Bayoffs to players may $e diffiult to measure (. Blayers may not have omplete information a$out eah otherDs payoffs C. Game theory assumes rational players D. ll of the statements assoiated with this &uestion are orret
Difficulty: Hard
?se the following information to answer &uestions "4-"6: There are two eisting firms in the mar;et for omputer hips. 'irm ;nows how to redue the prodution osts for the hip and is onsidering whether to adopt the innovation or not. Innovation inurs a fied set-up ost of C, while inreasing the revenue. #owever, one the new tehnology is adopted, another firm, (, an adopt it with a smaller set-up ost of C*. If innovates and ( does not, earns !*0 in revenue while ( earns !0. If innovates and ( does li;ewise, $oth firms earn !1" in revenue. If neither firm innovates, $oth earn !".
"4. ?nder what ondition will 'irm ( have an inentive to adopt if 'irm adopts the innovation8 . C H +0 B. C +0 C. 10 H C H 0 ). +" H C H *"
Difficulty: Hard
10-*0
Chapter 10 - Game Theory: Inside Oligopoly
"5. ?nder what ondition will 'irm innovate8 . C H +0 (. C +0 C. 10 H C H 0 ). +" H C H *"
Difficulty: Hard
"6. If C J 1", whih is the perfet e&uili$rium of the game8 . innovates, ( does not (. innovates, ( innovates C. %either firm innovates ). %one of the statements assoiated with this &uestion are orret
Difficulty: Hard
20. Game theory suggests that, in the a$sene of patents, the privately motivated innovation deisions of firms might lead to: A. Too little innovation (. Too muh innovation C. The soially effiient level of innovation ). %one of the statements assoiated with this &uestion are orret
Difficulty: Easy
21. If you advertise and your rival advertises, you eah will earn !" million in profits. If neither of you advertise, you will eah earn !10 million in profits. #owever, if one of you advertises and the other does not, the firm that advertises will earn !1" million and the non advertising firm will earn !1 million. 7hih of the following is true8 . dominant strategy for 'irm is to advertise (. dominant strategy for 'irm ( is to advertise C. %ash e&uili$rium is for $oth firms to advertise D. ll of the statements assoiated with this &uestion are orret
Difficulty: Medium
10-*1
Chapter 10 - Game Theory: Inside Oligopoly
2*. If you advertise and your rival advertises, you eah will earn !" million in profits. If neither of you advertise, you will eah earn !10 million in profits. #owever, if one of you advertises and the other does not, the firm that advertises will earn !1" million and the non advertising firm will earn !1 million. 7hih of the following is true8 . seure strategy for 'irm is to not advertise (. seure strategy for 'irm ( is to not advertise C. 'irm does not have a seure strategy D. %one of the statements assoiated with this &uestion are orret
Difficulty: Medium
2+. If you advertise and your rival advertises, you eah will earn !" million in profits. If neither of you advertise, you will eah earn !10 million in profits. #owever, if one of you advertises and the other does not, the firm that advertises will earn !1" million and the non advertising firm will earn !1 million. 9uppose this game is repeated for a finite num$er of times, $ut the players do not ;now the eat date at whih the game will end. The players an earn ollusive profits as a %ash e&uili$rium to the repeated play of the game if the pro$a$ility the game terminates in any period is . 1 (. Greater than one C. Close to /ero ). %one of the statements assoiated with this &uestion are orret
Difficulty: Medium
2. If you advertise and your rival advertises, you eah will earn ! million in profits. If neither of you advertise, you will eah earn !10 million in profits. #owever, if one of you advertises and the other does not, the firm that advertises will earn !1 million and the non advertising firm will earn !" million. 7hih of the following is true8 . dominant strategy for 'irm is to advertise (. dominant strategy for 'irm ( is to advertise C. %ash e&uili$rium is for $oth firms to advertise D. %one of the statements assoiated with this &uestion are orret
Difficulty: Medium
10-**
Chapter 10 - Game Theory: Inside Oligopoly
2". If you advertise and your rival advertises, you eah will earn ! million in profits. If neither of you advertise, you will eah earn !10 million in profits. #owever, if one of you advertises and the other does not, the firm that advertises will earn !1 million and the non advertising firm will earn !" million. 7hih of the following is true8 A. seure strategy for 'irm is to not advertise (. seure strategy for 'irm ( is to advertise C. 'irm does not have a seure strategy ). %one of the statements assoiated with this &uestion are orret
Difficulty: Medium
22. If you advertise and your rival advertises, you eah will earn ! million in profits. If neither of you advertise, you will eah earn !10 million in profits. #owever, if one of you advertises and the other does not, the firm that advertises will earn !1 million and the non advertising firm will earn !" million. 9uppose this game is repeated for a finite num$er of times, $ut the players do not ;now the eat date at whih the game will end. The players an earn profits of !10 eah period as a %ash e&uili$rium to a repeated play of the game if the pro$a$ility the game terminates at the end of any period is . Close to 1 (. Close to 0 C. (etween /ero and one D. ll of the statements assoiated with this &uestion are orret
Difficulty: Medium
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Chapter 10 - Game Theory: Inside Oligopoly
3uestions 24, 25, and 26 are $ased on the following game, where firms one and two must independently deide whether to harge high or low pries.
24. 7hih of the following are seure strategies for players one and two, respetively8 A. #igh Brie, #igh Brie (. #igh Brie, =ow Brie C. =ow Brie, #igh Brie ). =ow Brie, =ow Brie
Difficulty: Medium
25. If player one harges a #igh Brie when player two harges a =ow Brie, then player two earns: . 10 (. " C. -" ). 0
Difficulty: Medium
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Chapter 10 - Game Theory: Inside Oligopoly
26. dominant strategy for firm one is A. #igh prie (. =ow prie C. )ifferent from firm oneDs seure strategy ). =ow prie and different from firm oneDs seure strategy
Difficulty: Medium
40. Consider the following innovation game. 'irm must deide whether or not to introdue a new produt. 'irm ( must deide whether or not to lone firm Ds produt. If firm introdues and ( lones, then firm earns !1 and ( earns !10. If introdues and ( does not lone, then earns !10 and ( earns !*. If firm does not introdue, $oth firms earn profits of 0. 7hih of the following is true. . The su$game perfet %ash e&uili$rium profits are !10,* (. It is not in Ds interest to introdue C. 'irm does not are if ( lones D. %one of the statements assoiated with this &uestion are orret
Difficulty: Hard
41. Consider the following innovation game. 'irm must deide whether or not to introdue a new produt. 'irm ( must deide whether or not to lone firm Ds produt. If firm introdues and ( lones, then firm earns !1 and ( earns !10. If introdues and ( does not lone, then earns !10 and ( earns !*. If firm does not introdue, $oth firms earn profits of 0. #ow many %ash e&uili$ria are there for this game. . 0 B. 1 C. * ). 0, $ut there are seure strategies
Difficulty: Hard
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Chapter 10 - Game Theory: Inside Oligopoly
nswer &uestions 4*-4 $ased on the following information for a one-shot game:
4*. 7hat are the dominant strategies for 'irm and 'irm ( respetively8 . =ow prie, high prie (. #igh prie, low prie C. #igh prie, high prie D. %either firm has a dominant strategy
Difficulty: Medium
4+. 7hat are seure strategies for firm and firm ( respetively8 A. =ow prie, low prie (. #igh prie, low prie C. #igh prie, high prie ). %either firm has a seure strategy
Difficulty: Easy
4. 7hat are the %ash e&uili$rium strategies for this game8 . =ow prie, low prie (. #igh prie, high prie C. =ow prie, low prie and high prie, high prie ). %one of the statements assoiated with this &uestion are orret
Difficulty: Medium
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Chapter 10 - Game Theory: Inside Oligopoly
'or &uestions 4"-44, onsider the following information for a simultaneous move game: If you advertise and your rival advertises, you eah will earn !+ million in profits. If neither of you advertise, you will eah earn !4 million in profits. #owever, if one of you advertises and the other does not, the firm that advertises will earn !10 million and the non advertising firm will earn !1 million.
4". If you and your rival plan to $e in $usiness for only one year, the %ash e&uili$rium is for your firm A. nd your rival to advertise (. nd your rival not to advertise C. To advertise and your rival not to advertise ). %ot to advertise and your rival to advertise
Difficulty: Easy
42. If you and your rival plan to $e in $usiness for 1" years, then the %ash e&uili$rium is for . Eou and your rival to not advertise in any year B. Eou and your rival to advertise every year C. %either firm to advertise in early years, $ut to advertise in later years ).
Difficulty: Medium
44. If you and your rival plan to hand your $usiness down to your hildren, and this $e&uest goes on forever, then a %ash e&uili$rium when the interest rate is /ero is for . Eour firm to never advertise (. Eour firm to always advertise when your rival does provided that the interest rate is suffiiently large C.
Difficulty: Hard
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Chapter 10 - Game Theory: Inside Oligopoly
45. 7hih of the following is a orret statement a$out a %ash e&uili$rium in a two-player game8 . The oint payoffs of the two players are highest ompared to other strategy pairs (. %ash e&uili$rium is always uni&ue in real world pro$lems C. Given another playerDs strategy, no player an improve her welfare $y un ilaterally hanging her strategy ). ll of the statements assoiated with this &uestion are orret
Difficulty: Easy
46. Game theory is $est applied to analysis of . Berfet ompetition B. Oligopoly C. @onopoly ). ll of the statements assoiated with this &uestion are orret
Difficulty: Easy
50. 7hen analy/ing the $ehavior of oligopolists, whih of the following is ruial for the suess of game theoreti analysis8 . Bayoffs do not need to reflet the true payoffs of the oligopolists, they ust need to $e greater than or e&ual to /ero (. ssume that oligopolists always move simultaneously C. )o not onstrut the payoffs of the oligopolists to $e interdependent, as the payoff of one player usually does not affet the payoff of the other players D. @a;e sure the pro$lem you are onsidering is of a one-shot or repeated nature, and you model it aordingly $eause the order in whih players ma;e deisions is important
Difficulty: Medium
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Chapter 10 - Game Theory: Inside Oligopoly
51. @anagement and a la$or union are $argaining over how muh of a !"0 surplus to give to the union. The !"0 is divisi$le up to one ent. The players have one-shot to reah an agreement. @anagement has the a$ility to announe what it wants first, and then the la$or union an aept or reet the offer. (oth players get /ero if the total amounts as;ed for eeed !"0. 7hih of the following is a %ash e&uili$rium8 A. @anagement re&uests !"0 and the la$or union aepts !0 (. @anagement re&uests !+" and the la$or union aepts !10 C. @anagement re&uests !*0 and the la$or union aepts !*0 ). @anagement re&uests !*" and the la$or union aepts !10
Difficulty: Hard
5*. 7hih of the following is a orret statement8 . %ash e&uili$rium is always perfet B. perfet e&uili$rium is always %ash C. %ash e&uili$rium is always perfet in a multistage game ). %one of the statements assoiated with this &uestion are orret
Difficulty: Medium
5+. It is easier to sustain tait ollusion in an infinitely repeated game if A. The present value of heating is lower than ollusion (. There are many players C. The interest rate is higher ). The present value of heating is lower than ollusion and the interest rate is higher
Difficulty: Easy
5. 'irms will try to signal superior &uality of their goods $y . @a;ing sales information availa$le to the pu$li (. dvertising C. Issuing warranties or guarantees ). @a;ing sales information availa$le to the pu$li and advertising
Difficulty: Easy
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Chapter 10 - Game Theory: Inside Oligopoly
5". oordination pro$lem usually ours in situations where there is . %o %ash e&uili$rium in a game (. uni&ue, $ut undesira$le %ash e&uili$rium C. uni&ue seure strategies for $oth players D. @ore than one %ash e&uili$rium
Difficulty: Medium
52. 7hih of the following is not an important determinant of ollusion in priing games8 . The num$er of firms in the industry (. The punishment mehanisms that are in plae C. The history of the partiular mar;et D. %one of the statements assoiated with this &uestion are orrets
Difficulty: Easy
Aefer to the following normal form game of prie ompetition for &uestions 54-56.
54. 9uppose the game is infinitely repeated, and the interest rate is "F. (oth firms agree to harge a high prie, provided no player has harged in low prie in the past. If $oth firms sti; to this agreement, then the present value of 'irm (Ds payoffs are: . 10" (. 160 C. *10 ). "*"
Difficulty: Medium
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Chapter 10 - Game Theory: Inside Oligopoly
55. 9uppose that 'irm deviates from a trigger strategy to support a high prie. 7hat is the present value of Ds payoff from heating8 . " (. *0 C. *" ). +"
Difficulty: Easy
56. 7hat is the maimum interest rate that an sustain ollusion8 A. 22.4F (. ++F C. *"F ). 1"F
Difficulty: Hard
Aefer to the following normal form game of prie ompetition for &uestion 60.
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Chapter 10 - Game Theory: Inside Oligopoly
60. 'irms must deide whether or not to introdue a new produt. If 'irm introdues a new produt, 'irm ( must deide whether or not to lone the produt. The payoff struture of the game is depited in the a$ove tree diagram. The su$-game perfet %ash e&uili$rium to this game is . 'irm plays IntrodueK 'irm ( plays Clone if 'irm plays Introdue B. 'irm plays )o %ot IntrodueK 'irm ( plays Clone if 'irm plays Introdue C. 'irm plays IntrodueK 'irm ( plays )o %ot Clone if 'irm plays Introdue ). 'irm plays )o %ot IntrodueK 'irm ( plays )o %ot Clone if 'irm plays Introdue
Difficulty: Medium
Aefer to the following normal form game of prie ompetition for &uestions 61-6*.
61. 'irm ( is the inum$ent faing potential entry from its rivalK 'irm . 'irm Ds strategies onsist of L
Difficulty: Medium
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Chapter 10 - Game Theory: Inside Oligopoly
6*. 'irm ( is the inum$ent faing potential entry from its rivalK 'irm . 'irm Ds strategies onsist of L
Difficulty: Hard
6+. 7hih of the following onditions orretly desri$es a %ash e&uili$rium when two firms are in the mar;et8 . π1s1N,s*N ≥ π1s1,s*N for all s1 B. π1s1N,s*N ≥ π1s1,s*N for all s 1 and π*s1N,s*N ≥ π*s1N,s* for all s * C. π1s1N,s*N ≥ π*s1,s*N for all s1 and π*s1N,s*N ≥ π1s1N,s* for all s* ). π1s1,s*N ≥ π*s1N,s*N for all s1 and π*s1N,s* ≥ π1s1N,s*N for all s*
Difficulty: Medium
Aefer to the following normal form game of prie ompetition for &uestions 6-62.
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Chapter 10 - Game Theory: Inside Oligopoly
6. 'or what values of is strategy ) stritly dominant for 'irm (8 A. ll H "0 (. ll "0 C. J "0 ). "0
Difficulty: Medium
6". 'or what values of is strategy stritly dominant for 'irm 8 . ll H "0 B. ll "0 C. J "0 ). "0
Difficulty: Medium
62. 'or what values of is strategy (, ) the only %ash e&uili$rium of the game8 A. ll H "0 (. ll "0 C. J "0 ). "0
Difficulty: Medium
Aefer to the following normal form game of prie ompetition for &uestions 64-100.
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Chapter 10 - Game Theory: Inside Oligopoly
64. 7hih of the following represents 'irm Ds full strategy spae8 . L, CM B. L, (M C. L, C, , ), (, C, (, )M ). LC, )M
Difficulty: Easy
65. 7hih of the following represents 'irm (Ds full strategy spae8 . L, CM (. L, (M C. L, C, , ), (, C, (, )M D. LC, )M
Difficulty: Easy
66. 7hih of the following represents the set of possi$le pure strategy %ash e&uili$rium8 A. L, CM (. L, (M C. L, C, , ), (, C, (, )M ). LC, )M
Difficulty: Hard
100. 7hat are the pure %ash e&uili$rium strategies for this game8 . L(, CM (. L, C and (, )M C. L, CM D. There is no pure strategy %ash e&uili$rium to this game
Difficulty: Easy
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Chapter 10 - Game Theory: Inside Oligopoly
Aefer to the following normal form game of $argaining game for &uestions 101-10*.
101. 9uppose that management and the union are $argaining over how muh of a !"00 surplus to give to the union. It is assumed that the surplus an only $e split into !*"0 inrements. 'urthermore, negotiations are set up suh that management and the union must simultaneously and independently write down the amount of surplus to alloate to the union. The payoff struture to this one-shot $argaining game is listed in the a$ove payoff matri. 'ind the %ash e&uili$riumia to this game. . ?nion write down !0 and @anagement write down !"00 (. ?nion write down !*"0 and @anagement write down !*"0 C. ?nion write down !"00 and @anagement write down !0 D. ll of the statements assoiated with this &uestion onstitute %ash e&uili$ria
Difficulty: Medium
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Chapter 10 - Game Theory: Inside Oligopoly
10*. 9uppose that management and the union are $argaining over how muh of a !"00 surplus to give to the union. It is assumed that the surplus an only $e split into !*"0 inrements. 'urthermore, negotiations are set up suh that management and the union must simultaneously and independently write down the amount of surplus to alloate to the union. The payoff struture to this one-shot $argaining game is listed in the a$ove payoff matri. The num$er of ineffiient outomes resulting from the $argaining game is . + (. " C. 2 ). 5
Difficulty: Hard
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Chapter 10 - Game Theory: Inside Oligopoly
Essay Questions
10+. In a one-shot game, if you advertise and your rival advertises, you will eah earn !" million in profits. If neither of you advertise, your rival will ma;e ! million and you will ma;e !* million. If you advertise and your rival does not, you will ma;e !10 million and your rival will ma;e !+ million. If your rival advertises and you do not, you will ma;e !1 million and your rival will ma;e !+ million. a. 7rite the a$ove game in normal form. $. )o you have a dominant strategy8 . )oes your rival have a dominant strategy8 d. 7hat is the %ash e&uili$rium for the one-shot game8 e. #ow muh would you $e willing to $ri$e your rival not to advertise8 a.
$. Eour dominant strategy is to advertise . Eour rival does not have a dominant strategy d. The only %ash e&uili$rium is for you to advertise and for your rival to advertise also e. Eou are willing to $ri$e your rival not to advertise $y an amount up to !" million. This is $eause when you $ri$e your rival $y an amount less than !" million and if your rival really ooperates, then you an get !10 million gross profit. 9u$trating the $ri$e, you still get an amount of net profit greater than what you otherwise get $y not $ri$ing. Of ourse, this ignores legal onsiderations as well as the pro$lem of ensuring that your rival does not heat on the ollusive agreement.
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Chapter 10 - Game Theory: Inside Oligopoly
10. Eou operate in a duopoly in whih you and a rival must simultaneously deide what prie to advertise in the wee;ly newspaper. If you eah harge a low prie, you eah earn /ero profits. If you eah harge a high prie, you eah earn profits of !+. If you harge different pries, the one harging the higher prie loses !" and the one harging the lower prie ma;es !". a. 'ind the %ash e&uili$rium for a one-shot version of this game. $. %ow suppose the game is infinitely repeated. If the interest rate is 10 perent, an you do $etter than you ould in a one-shot play of the game8 <plain. . <plain how history affets the a$ility of firms in this game to ah ieve an outome superior to that of the one-shot version of the game. a. (oth players harging low pries is a uni&ue %ash e&uili$rium for a one-shot version of the game.
$. The ooperative ollusive outome an $e sustained in the infinitely repeated game with the following trigger strategy: Cooperate provided no player has ever heated in the past. If any player heats, punish the player $y hoosing the one-shot %ash e&uili$rium strategy forever after. In partiular, for this game we ;now
The left-hand side of this e&uation represents the one-time gain of $rea;ing the ollusive agreement today. The right-hand-side represents the present value of what is given up in the future $y heating today. 9ine the one-time gain is less than the present value of what would $e given up $y heating, players find it in their interest to live up to the agreement. . (y definition, a trigger strategy stipulates that eah p layer uses the history of what its rival did to deide whether it should ooperate or not. #ene, whenever one player heats last period, the rival of it should hoose not to ooperate. In other words, history is very important.
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Chapter 10 - Game Theory: Inside Oligopoly
10". Eou are onsidering entering a mar;et servied $y a monopolist. Eou urrently earn !0 eonomi profits, while the monopolist earns !". If you enter the mar;et and the monopolist engages in a prie war, you will lose !" and the monopolist will earn !1. If the monopolist doesnDt engage in a prie war, you will eah earn profits of !*. a. 7rite out the etensive form of the a$ove game. $. There are two %ash e&uili$ria for the game. 7hat are they8 . Is there a su$game perfet e&uili$rium8 <plain. d. If you were the potential entrant, would you enter8 <plain why or why not. a. The etensive form is presented in 'igure 10-+ $elow. 'igure 10-+
$. One %ash e&uili$rium is that you stay outK your rival engages a prie war should you enter. nother %ash e&uili$rium is that you enterK your rival does not engage a prie war if you enter. . The seond one is a perfet e&uili$rium, while the first one is not. This is $eause if you enter, the inum$ent an get !* profits $y not engaging a prie war, whih is greater than !1 profits otherwise o$tained $y engaging a prie war. The threat to engage in a prie war is not redi$le. d. If you were the potential entrant, you should enter. Eou get !* profits $y entering, whih is greater than the /ero you earn $y not entering.
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Chapter 10 - Game Theory: Inside Oligopoly
102. OB
104. The %C prohi$its shools that are aught paying athletes from partiipating in $owl games, and sometimes the punishment is even more severe. <plain why shools donDt $rea; away from the %C and form a league in whih athletes an legitimately $e paid. #int: ?se hypothetial payoffs to onstrut an illustrative normal-form game in whih the strategies are pay players and donDt pay players. Then analy/e the game in one-shot and infinitely repeated ontets.
The a$ove hypothetial pay-off matri shows that, in a one-shot game, eah shool has an inentive to pay athletes, in an attempt to o$tain the $est athletes and $e assured of $owl revenues. (ut when all shools do this, athletes etrat virtually all of the profits, and the shools are left with nothing. If shools ollude and agree not to pay athletes, eah shool earns higher profits, sine less money goes to the athletes. In an infinitely repeated game, the shools threaten to punish those who pay athletes $y preluding them from partiipating in $owl games long enough to wipe out any gains to heating. This an support the e&uili$rium where shools do $etter than they would $y forming an independent league that permitted ollege athletes to $e paid larger sums.
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Chapter 10 - Game Theory: Inside Oligopoly
105. (ased on your ;nowledge of one-shot and repeated games, would you epet tipping $ehavior to differ depending on whether a person is eating in a hometown diner or in a restaurant loated in Tim$u;tu8 <plain.
106. ording to a spo;esperson for ereal ma;er ellogg, … for the past several years, our individual ompany growth has ome out of the other fellowDs hide. 9ee '.'. 9herer, The 7elfare <onomis of Brodut Pariety: n ppliation to the Aeady-to-
a. The news implies that advertising inreases the demand for a firmDs produt $y ta;ing ustomers away from other firms in the industry. The end result in a one-shot game is that ereal firms spend money on advertising, with no real hange in their demand. $. The ooperative ollusive outome an $e sustained in the infinitely repeated game with the following trigger strategy: )onDt advertise provided no player has ever heated in the past. If any player heats, punish the player $y advertising forever after. In partiular, there is no inentive to heat on this agreement if . 9olving this for i, we see that for any interest rate less than or e&ual to 20 perent, there is no inentive to heat.
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Chapter 10 - Game Theory: Inside Oligopoly
110. Eou are the manager of a firm that is $argaining with another firm over how muh to pay for a ;ey input your firm uses in prodution. 7hih type of $argaining would $e $etter from your firmDs point of view, simultaneous-move $argaining or ta;e-it-over-leave-it $argaining8 <plain arefully. 9e&uential, ta;e-it or leave-it $argaining is prefera$le for the manager if she has the first move advantage. This is $eause any proposal leaving a positive amount of money to la$or will $e aepta$le to the other firm under this setting.
111. Eou are the manager of the (C novelty store, and your only ompetitor is the QER novelty store. Eou are $oth trying to deide on whih magi tri;s and party favors to arry in sto;. The produt mies availa$le to $oth of you are low, medium, and high in variety. Eour epeted earnings in this mar;et are shown in the following ta$le.
a. 'ind the %ash e&uili$rium or e&uili$ria for a simultaneous-move, one-shot play of this game. $. 7hat outome would you epet in this one-shot game8 7hy8 a. The only %ash e&uili$rium is that 'irm (C hooses medium while 'irm QER hooses high. $. In a one-shot game, we epet the two firms to hoose medium 'irm (C and high 'irm QER to o$tain **" and 16" units of profit, respetively.
11*. Eou are the owner-operator of the (etter Gas 9tation in a small southeastern town. Over the past *0 years, you and your rival have suessfully ;ept pries at a very high level. Eou reently learned that your ompetitor is retiring and losing his station in two wee;s. 7hat should you do today8 7hy8 EouDd $etter lower your prie todayK the game is now a finitely repeated game with a ;nown end point, and ollusion will no longer $e sustaina$le with trigger strategies.
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Chapter 10 - Game Theory: Inside Oligopoly
11+. Eou are the manager of Copies re ?s. The only other opy store in town, the Car$on Copy, reently got $ids on adding a olor opier. Eou must deide whether to o$tain a olor opier, $ut you an $ase deision on what your rival does. If your rival adds a olor opier and you donDt, you epet your profits to fall $y !1,000 per wee; and its profits to rise $y !1,"00 per wee;. Conversely, if you add the olor opier and your rival does not, your profits will inrease $y !1,"00 per wee; and your rivalDs profits will fall $y !1,000 per wee;. #owever, if you $oth do the same thing add olor opies or not, you eah epet profits to stay at their urrent level. 9how the etensive form of this game, and find the %ash e&uili$rium or e&uili$ria. Is there a su$game perfet e&uili$rium8 The etensive form game is shown in 'igure 10-11. The su$game perfet %ash e&uili$rium is for $oth of you to add olor opiers, to earn /ero profits. 'igure 10-11
10-
Chapter 10 - Game Theory: Inside Oligopoly
11. Eou are the $argaining oordinator for 9un Car @anufaturers. t present you are renegotiating the la$or ontrat with the union representative. Eou are $argaining over an epeted *0 perent inrease in earnings over the net three-year ontrat period. Eou are trying to deide whether to offer one-third, one-half, or all o f the inrease in earnings to the union. The union rules are suh that all ontrats must $e voted on. The additional earnings are ontingent on getting started on the new ontrat net wee;. If an agreement isnDt reahed on the first round of negotiations, the firm will go out of $usiness. The union representative tells you that if you do not give the union all of the additional profits, the union mem$ers will not vote for the agreement. a. 9how the etensive form of this game. $. 7hat will you offer the union8 7hy8 a. 9ee 'igure 10-1*. 'igure 10-1*
$. The $argaining oordinator should offer ++F of the inrease to the union. The union laims it will vote no if you do so, $ut $y doing so, the firm will go $an;rupt and the mem$ers will lose their o$s. O$viously, a 2.4 perent pay hi;e is prefera$le for the un ionK the ?nionDs threat is not redi$le.
11". 7ould ollusion $e more li;ely in the shoe industry or in the airline industry8 7hy8 The airline industry seems to $e more li;ely to have ollusion than the shoe industry $eause the former is more onentrated, sells more homogeneous produts, has good reords of ustomers, and has an easier opportunity to o$serve and punish heaters.
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Chapter 10 - Game Theory: Inside Oligopoly
112. ording to various trade pu$liations, over *00,000 hanges are made in airfares eah day. 7hy do you thin; this is the ase8 (y randomi/ing pries it ma;es prie shopping more ostly to onsumers, and redues the a$ility of rivals to systematially underut their fares.
114. Two eeutives were arrested $y authorities for em$e//ling money from their firm. 9hort of a onfession, the proseutor only had enough evidene to put them away for 10 years. Given a onfession, however, she was ertain to put them $ehind $ars for life without parole, sine they ;illed a law enforement offier who was investigating the ase. The proseutor put the two prisoners in separate rooms, and told them the following: If you onfess and your partner does not, IDll give you a yearDs pro$ated sentene $ut put your partner in the slammer for life without parole. Of ourse, if your partner onfesses and you donDt, youDll get the life sentene without parole and heDll get one yearDs pro$ation. I must warn you, however, that if you $oth onfess IDll have enough evidene to put you $oth away for life without parole. a. )o you thin; the proseutorDs $argain will indue the two eeutives to onfess8 <plain. $. 7ould your answer hange if the life sentene arried the possi$ility of parole8 <plain. a. Ees. Given no parole, this is a one-shot game and the dominant strategy for eah eeutive is to onfess. %otie that $oth end up with life sentenes without parole. $. It might. If parole is a possi$ility, then the game is not a one shot game $ut a finitely repeated game with an unertain end-point the parole date. In this ase, the eeutives might $e a$le to suessfully ollude $y not onfessing -- provided that eah eeutive fears that his own onfession will result in a suffiiently harsh punishment if the other eeutive gets paroled.
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Chapter 10 - Game Theory: Inside Oligopoly
115. In the early 1660s, there was onsidera$le unertainty in the omputer industry a$out whether the dominant operating system for future personal omputers would $e I(@Ds O9* or @irosoftDs 7indows. ?ltimately, 7indows emerged as the dominant system despite the fat that several trade pu$liations viewed O9* as the superior system. 7hy do you thin; this outome prevailed8 The pro$lem of seleting an operating system an $e thought of as a oordination game, in whih it is often diffiult to ahieve a %ash e&uili$rium. Consider, for eample, the deision $y personal omputer users to use @irosoftDs 7indows operating system or I(@Ds O9*. If all other users deided to use 7indows, then your $est hoie would also $e to use 7indows, even if you personally li;e the O9* environment. This is $eause there would $e a muh greater seletion of software availa$le if you used the same system that everyone else uses. On the other hand, if all other users deided to use O9*, then your $est hoie would $e to use O9*, even if you personally li;e the 7indows environment. gain, the reason is that you would have a muh $etter seletion of software if you use the system everyone else is using. One reason 7indows ultimately prevailed is that onsumers pereived that everyone else was opting for 7indows.
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Chapter 10 - Game Theory: Inside Oligopoly
116. Eou are the manager of QER In. and must deide how muh output to produe to maimi/e your firmDs profit. QER and its rival, (C Corp., produe a good that onsumers view as essentially idential. These two firms ma;e up the entire industry, so the mar;et prie for the good depends on the total amount produed $y the two firms. survey reveals that the mar;et prie of the produt depends on total mar;et output as follows:
QER and (C eah use la$or, materials, and mahines to produe output. QER p urhases la$or and materials on an as-needed $asisK their mahines were purhased three years ago and are $eing depreiated aording to the straight-line method. QERDs aounting department has provided the following data a$out its unit prodution osts:
Aeports from industry eperts suggest that (CDs ost struture is similar to QERDs ost struture and that tehnologial onstraints re&uire eah firm to produe either 100 units or *00 units of output. a. (riefly eplain whih osts are relevant for your deision, and why. $. 7rite this game in normal form. . #ow many units should QER produe: 100 units or *00 units8
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Chapter 10 - Game Theory: Inside Oligopoly
a. )iret la$or and diret materials, sine they are varia$le osts. )epreiation is a fied or sun; ost, and is therefore irrelevant to the deision the firmDs fied osts are !*00, sine !*00100 J !* !*00*00 J !1. These later num$ers are the ones reported in the ta$le. $. The payoff matri normal form $elow shows the relevant ontri$utions to overall profits the sun; osts are irrelevant, remem$erS for alternative levels of output $y the two firms. The ;ey is to note that if eah firm produes 100 units, total mar;et output is *00 units and the prie is !2. QERDs ontri$utions in this ase are !2 - !" 100 J !100. If one firm produes 100 units and the other firm produes *00 units, the mar;et prie is !". In this ase, eah firms ontri$utions are /ero the prie e&uals relevant unit osts of !". If $oth firms produe *00 units, the mar;et prie is !, and the ontri$utions of eah firm are ! - " *00 J ! - *00.
. The dominant strategy for QER is to produe 100 units -- regardless of what (C does, QER is $etter off produing 100 units. Importantly, this is true regardless of whether the game is simultaneous move or se&uential move. The same is true for (C. Thus, if QER plays its dominant strategy it will ontri$ute !100 towards itDs fied osts of !*00. ny other strategy leads to lower ontri$utions and even greater losses.
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Chapter 10 - Game Theory: Inside Oligopoly
1*0. Two firms produe idential produts at /ero ost, and they ompete $y setting pries. If eah firm harges a low prie, the $oth firms earn profits of /ero. If eah firm harges a high prie, then eah firm earns profits of !+0. if one firm harges a high prie and the other firm harges a low prie, the firm that harges the lowest prie earns profits of !"0 and the firm harging the highest prie earns profits of /ero. a. 7hih oligopoly model $est desri$es this situation8 $. 7rite this game in normal form. . 9uppose the game is infinitely repeated. Can the players sustain the ollusive outome as a %ash e&uili$rium if the interest rate if "0 perent8 <plain. a. The (ertrand model Cournot and 9ta;el$erg are models of &uantity ompetition, and 9wee/y assumes differentiated produts. $.
. If it is possi$le to monitor the ations of rivals and ignoring antitrust onsiderations, the ollusive outome an $e sustained in the infinitely repeated game with the following trigger strategy: Charge a high prie provided no player has ever harged a low prie. If any player harges a low prie, punishD the player $y harging a low prie forever after. There is no inentive to heat on this agreement sine
.
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Chapter 10 - Game Theory: Inside Oligopoly
1*1. 9uppose the mar;et for omputer hips is dominated $y two firms: Intel and @). Intel has disovered how to ma;e superior hips and is onsidering whether or not to adopt the new tehnology. doption would entail a fied setup ost of C $ut would inrease revenues. #owever, if Intel adopts the new tehnology, @) an easily opy it at a lower setup ost of C *. If Intel adopts and @) does not, Intel would earn !*0 in revenues while @) would earn !0. If Intel adopts and @) does li;ewise, eah firm will earn !1" in revenues. If Intel does not adopt the new tehnology, it will earn !" and @) will earn !*. a. 7rite this game in etensive form. $. ?nder what onditions i.e., for what values of C does @) have an inentive to adopt the new tehnology if Intel introdues it8 . If C J 1*, should Intel adopt the new tehnology8 <plain. a. 'igure 10-16
$. @)Ds payoff from adopting must eeed its payoff from not adopting. This is true if 1" C* H 0. 9olving for C we find that @) has an inentive to adopt if Intel adopts whenever C +0. . %o. 7hen C J 1*, @)Ds $est strategy is to adopt if Intel dopts, whih means Intel would earn only + $y adopting. (y not adopting, Intel an earn a payoff of "K IntelDs $est option is not to adopt. This is the only %ash e&uili$rium, and it is also a su$game perfet %ash e&uili$rium.
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