# Consider the following incomplete information game between Firm 1 (potential entrant) and Firm 2 (incumbent). Firm 1 has undertaken an R&D project for developing a new product. The outcome of the

Consider the following incomplete information game between Firm 1 (potential entrant) and Firm 2 (incumbent). Firm 1 has undertaken an R&D project for developing a new product. The outcome of the project is uncertain and private information of Firm 1. The new product is good with probability p and bad with probability 1-p. After learning the quality of the product, Firm 1 decides whether or not to enter the market. If Firm 1 does not enter, the payoffs are (0,4) (Firm 1 gets 0 and Firm 2 gets 4). If Firm 1 enters, payoffs depend on the quality of the product and the response of Firm 2. Firm 2 can start a price war (F-fight) or can accommodate the entry (A-accommodate). If the product is good, F leads to payoffs of (1,-2) while A generates payoffs of (2,-1). If the product is bad, F leads to payoffs of (-1,2) while A generates payoffs of (1,1).

This game has a pooling equilibrium in which Firm 1 always enters (with a good and a bad product) if p>= x, where:Option 1 : 2/3Option 2: 1/2

Option 3: 3/2

Option 4: 1/4

Provide step by step explanation

Consider the following incomplete information game between Firm 1 (potential entrant) and Firm 2 (incumbent). Firm 1 has undertaken an R&D project for developing a new product. The outcome of the
30/6/2021 Final Exam (pàgina 3 de 4) https://aulaglobal.upf.edu/mod/quiz/attempt.php?attempt=988797&cmid=739442&page=2#question-1072128-15 1/3 In fo rm ació P re g unta 1 1 No s’h a r e sp os t e n ca ra P u ntu at s ob re 1 ,0 0 P re g unta 1 2 No s’h a r e sp os t e n ca ra P u ntu at s ob re 1 ,0 0 In ic i / E ls m eu s c u rs os / C urs 2 020-2 021 / 3r T rim estr e / 2 020-2 0854-T 1 In for mation E con om ic s / Ge nera l / Fi nal E xa m Pro bl em 3. C on sid er t h e f ol lowi ng in com ple te in fo rm ation g am e b etwe en Fi rm 1 ( p ot en tia l e n tr a n t) a n d Fi rm 2 ( in cu m ben t). Fi rm 1 h as u nd erta ke n a n R& D p roj ect f or d eve lop in g a n ew prod uct. T h e ou tc om e of t h e p roj ect is u nce rta in a n d p riv a te in for mation of Fi rm 1 . T h e new prod uct is g ood wi th p rob ab ilit y p a n d b ad wi th p rob ab ilit y 1 -p . A ft e r le arn in g t h e q ualit y of t h e p rod uct, Fi rm 1 d ecid es wh eth er or n ot t o en te r t h e m ark e t. If Fi rm 1 d oe s n ot e n te r, t h e p ayof fs a re ( 0 ,4 ) ( Fi rm 1 g ets 0 a n d Fi rm 2 g ets 4 ). If Fi rm 1 e n te rs , p ayof fs d ep en d on t h e q ualit y of t h e p rod uct a n d t h e r e sp on se of Fi rm 2 . Fi rm 2 c a n s ta rt a p ric e wa r ( F- fig ht) or c a n a ccom mod ate t h e e n tr y ( A – accom mod ate ). If t h e p rod uct is g ood , F le ad s t o payof fs of ( 1 ,- 2 ) wh ile A g en era te s p ayof fs of ( 2 ,- 1 ). If t h e p rod uct is b ad , F le ad s t o payof fs of ( – 1 ,2 ) wh ile A g en era te s p ayof fs of ( 1 ,1 ).  C on sid er t h e f ol lowi ng s ta te m en ts     I.    T h is g am e d oe s n ot h ave s e p ara tin g e q uilib ria .      II.   T h is g am e h as on ly on e s e p ara tin g e q uilib riu m in wh ic h t h ere is n o en tr y wh en t h e p rod uct is b ad .     III.   E n tr y is a d om in an t s tr a te g y wh en t h e p rod uct is g ood .      Which of the above statements is correct?      S ta te m en t II is c or re ct. O nly s ta te m en t I is c or re ct. S ta te m en ts I an d III are c or re ct. O nly s ta te m en t II is c or re ct. T h is g am e h as a p ool in g e q uilib riu m  in wh ic h Fi rm 1 a lwa ys e n te rs ( wi th a g ood a n d a b ad p rod uct) if p ≥ x , wh ere x = 2 3 x = 1 2 x = 3 2 x = 1 4 30/6/2021 Final Exam (pàgina 3 de 4) https://aulaglobal.upf.edu/mod/quiz/attempt.php?attempt=988797&cmid=739442&page=2#question-1072128-15 2/3 Pre g unta 1 3 No s’h a r e sp os t e n ca ra P u ntu at s ob re 1 ,0 0 P re g unta 1 4 No s’h a r e sp os t e n ca ra P u ntu at s ob re 1 ,0 0 This game has a semi-pooling equilibrium in which if the product is good, Firm 1 enters for sure, and if the product is bad, Firm 1 enters with probability r , where       I.    If  p = 1 4  then  r= 1 3     II.   If   p = 1 4  t h en   r= 1 2     III.     r is in cre asin g in   p        W hic h of t h e a b ov e s ta te m en ts is c or re ct?      S ta te m en t I an d II S ta te m en t II S ta te m en ts I an d III S ta te m en ts II an d III R eg ard in g t h e In tu it iv e C rit e rion ( IC ) wh en a p plie d t o th is g am e, wh ic h s ta te m en t is c or re ct? O nly t h e p ool in g s a tis fie s IC . Bot h t h e s e m i- p ool in g a n d t h e p ool in g e q uilib ria s a tis fy IC . No eq uilib ria of t h e g am e s a tis fy IC . Only t h e s e m i- p ool in g e q uilib riu m s a tis fie s IC . 30/6/2021 Final Exam (pàgina 3 de 4) https://aulaglobal.upf.edu/mod/quiz/attempt.php?attempt=988797&cmid=739442&page=2#question-1072128-15 3/3 Pre g unta 1 5 No s’h a r e sp os t e n ca ra P u ntu at s ob re 1 ,0 0 U ploa d a p ag e e xp la in in g y ou r a n swe rs or t y p e in t h e t e xt f or m b elow. M id a m àxi m a p er a ls f it xe rs n ou s: 5 00M B               Fitxe rs    P od eu a rros se g ar i d eixa r a n ar f it xe rs a q uí p er a a fe g ir – los -h i. ◄ O nlin e C la ss L in k ( Z oom ) Salt a a … S lid es C la ss 1 ►