Question

3 Coordinated care (9 pts.) California and Nevada are adopting electronic medical records (EMR) systems, provided by either Kareo or Praxis. Each state has a preference for using one of these systems rather than the other, but all else equal, both states would like to use the same system since doing so makes it easier to coordinate healthcare for people who commute across state lines. Nevada | Kareo Praxis Kareo 6,1 0,0 California Praxis | 0,0 3,5 a. (1 pt.) What is California's best response against Nevada choosing Praxis? b. (2 pts.) Identify any/all pure strategy Nash equilibria (in each case, list the strategies as an ordered pair). For each PSNE, also indicate the corresponding equilibrium payoffs. C. (3 pts.) Suppose that California picks Kareo with probability 3 and that Nevada picks Kareo with probability Show that this cannot be a mixed strategy Nash equilibrium. Which player is not playing a best response? d. (3 pts.) Now imagine that California makes its decision first. California's decision will be public knowledge, so Nevada will get to see what California did before making its decision. Draw the game tree corresponding to this dynamic game. What will California do? How will Nevada respond? What are the equilibrium payoffs?

Answer 1

A) california BR is Praxis

if N plays P, then C gets 0 from K & 3 from P

So it gets higher Payoff from P, thus C's BR is to play Praxis

B)

C/N	Kareo(K)	praxis (P)
Kareo(K)	(6*,1•)	(0,0)
Praxis(P)	(0,0)	(3*,5•)

PSNE : pure strategy NE

(K,K) & (P,P)

C)

O Mixed St. Ne 3 14K 43 N (611) (0o) 213 (0,0) (35) Now EU = 683x113 +0 to + Bx14 x2lz - ®/2) + 18 = -57.5 = 2 EU N = B 4xl (3) XI toto+ 5x14 1213 = -25+ 5/6 = -25+ •83 = 1.083. Let at MSNE, C plays K with Bobe, & plays p with (IP) I N Plays K " nq & nnn (19) then Euc= 6 p q toto t3 (1-P) (19) = 6pq + 3-39 tent 3 p q -3p = 9pq-39-3p-3 al4c = 99 -3 =0 q = 1/3 ap la EUN= pq+0 tot 5-58-59 +59p = 6pq-5p-5915 ADUN - 7 69 - 5=0, p= 5/6 aq l so optimal MSNE (P. 9) = (5/6, 1/3) Player California not playing POR AL

D) sequential game ;

d) Қалео Praxis Game Tree к е . К- N N P KY IP k ve. (6.1 100 000 (315) Solving The Game backwards K P 13,5 SPNE: <K, KP7 o California selects K. Nevada playsk (af c selects P, N will play P). payoff of c = 6 7 9 99 N=1 h &m eam