Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:Consider two firms who are engaged in a Research and Development (R&D) "con-
test". Both firms simultaneously expend resources to try to win the contest (which
may mean developing a superior product or developing a product before the com-
petitor). If the two firms expend bị and b2, respectively, on R&D, the probability
that firm 1 wins the contest is
if b1 = b2 =0
BE otherwise
P1(b1, b2) =
where r is some exogenous constant, r E (0, 0). If firm 1 wins the contest, it will
subsequently earn revenue of 1 (not including the cost of R&D, b1). If firm 1
loses the contest, it will earn zero revenue, and thus lose bj in total. Hence, firm
l's expected profit is n'(b1,b2) = p1(b1,b2) - b1. Everything is symmetric for
firm 2.
i. How does p1(b1,0) depend on b1? Is it an equilibrium for both firms to
spend nothing on R&D (b1 = b2 = 0)? Prove and explain your answer. For
which values of r is n' (b,b2) concave in b1 when b2 > 0?
ii. Consider the possibility of a symmetric pure-strategy equilibrium. Assum-
ing such an equilibrium exists, derive it and prove it is unique. Is the equi-
librium efficient? Under what conditions onr do a symmetric pure-strategy
equilibrium exists? Prove and explain your answers.
iii. Assume r = 1 and that firm 2 observes firm 1's expenditures before it has
to make its own investment. Derive the subgame perfect Nash equilibrium.
How does it differ from the equilibrium in the simultaneous-move game? Is
there a first-mover advantage in this game? Does firm 2 prefer the sequential
game or the simultaneous game?
iv. Assume r = 2. Does firm 2 have a unique best response to all bi E (0, 00)?
Is there an equilibrium of the sequential game in which firm 1 invests more
than in the simultaneous-move game? If firm 1 invests less than in
simultaneous game, does firm 2 invest more or less than firm 1? Describe
an equilibrium of the sequantial game and compare it to the equilibrium
of the simultanous game. Does firm 1 prefer the sequential game or the
simultaneous game? How about firm 2? Prove and explain your answers.
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