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Post by Neibruoma » Thu Nov 11, 2004 10:46 am

Heretofore, all new applications must also answer one of the three questions below:

Consider a linear Cournot duopoly with the true inverse demand function P = a − Q and zero marginal costs, where P is price, a> 0,and Q = q1 + q2 is the total supply of a good. Now imagine that each firm i ∫ N = {1, 2} perceives the inverse demand function as P = a + bi − Q, where bi ∫ R is the bias in i’s perception. Let G (b1,b2) be the game in which b1 and b2 are common-knowledge.

(a) Show that G (b1,b2) has a unique rationalisable strategy profile. Compute the true payoffs u1 (b1,b2) and u2 (b1,b2) at the rationalisable strategy profile – computed by using P = a − Q.

(b) Consider the meta game Γ =(N, R, R,u1,u2) , where the strategies are choices of b1 and b2,and u1 and u2 are as in (a). Show that Γ is super-modular in a proper order, has a unique Nash equilibrium b∗ ,and that b∗ i > 0 for each i ∈ N . Show that the replicator dynamics for Γ (using the true payoffs) converges to b*

(c) Now consider an evolutionary learning process in which the agents not only develop their perceptions (i.e., b1 and b2) but also learn how to play the game G (b1,b2) given perceptions. Assume that the learning process is a “two-tieredâ€￾ replicator dynamics in which they learn how to play G (b1,b2) infinitely faster than they change their perceptions, i.e., given any perception-pair (b1,b2), the play converges to the limit of the dynamics for fixed (b1,b2) before they change their perceptions. What is the limit of this “two-tieredâ€￾ replicator dynamics?

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Post by Silly » Thu Nov 11, 2004 11:24 am

:D :shock: :lol:

Oh Neib, you just gave my hamster a heart attack!! You know, the one that turns the wheel inside my head...

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Post by Kamidari » Thu Nov 11, 2004 12:08 pm

a) 42

b) 42

c) 42
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Post by Silly » Thu Nov 11, 2004 12:19 pm

Ad astra per alia perci.

I adore words, because unfortunately figures make me feel a wee inadequate. I guess you could say I have a touch of brain-envy. :P

I'm going back to the short bus now.

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Post by Bolwyn » Thu Nov 11, 2004 3:47 pm


a) BLUE!
b) Mister Rogers was NOT a marine sniper!
c) this one I don't know /shrug

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Post by Lachaise » Thu Nov 11, 2004 6:23 pm

Man I think I am not the only CN with an Economics degree... I could answer those if I took the time and remembered some of my econometric courses.

/wave Neib

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Post by Saphirone » Thu Nov 11, 2004 6:46 pm

Man, am I glad I've been a member for a while, ROFL!!
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Post by Secksiee » Thu Nov 11, 2004 7:32 pm

I dont know what half of those words mean, and.. oie, im just confused looking at it. *holds a sign above her head reading "im stupid"*
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Post by Zoey » Fri Nov 12, 2004 6:47 pm

A) Panties!

B) Panties!

C) Panties!

Push over Silly, I wanna sit with you on the short bus. :lol:
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Post by Zatrekan » Thu Nov 18, 2004 10:35 pm


You can come ride in my Pinto with me cause who needs a fancy Jaguar. Damn smart ppl.
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Post by Jaffod » Fri Nov 19, 2004 3:37 pm

I agree with 42...altthough what was the question again?


Post by Guest » Sun Nov 21, 2004 10:13 pm

::curls into a ball and sucks her thumb::
Will feigning infancy allow me to skip all intellectually challenging questions?

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Post by Syanthia » Sun Nov 21, 2004 10:19 pm

::uses the above reply as her point well made::
Yes, well, see...I wasn't logged in when I posted it. -hangs head in shame- I tell you, if it's anything more complicated than yes or no, I'm completely lost! :P

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