smidsol - 1. Solve the matrix game with payoff matrix 3...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 4
Background image of page 5
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 1. Solve the matrix game with payoff matrix 3 —2 _3 ' 1 2 —4 —2 0 72 4 3 ‘ 'fiflw Cf Cfiokmfi:@5 “St/J ,3 3 i «l ‘72 % whim/1m OED 1“ i-W‘lauéfl C‘V’QU'LM H Q‘ E500 /%uvtfltwct/£YCJ VE‘m 31 if “Ff if; )7“ Z 44) 3,555..“ #2 gmf‘5)+3._(~w7) 3 Z- -. imiéél :7 f: V '2 “Mn ' “"‘ H L H n _ M 1 g, P*3(5/HJDJUJ%) if) K: (VI/C315/2) V6 ' T“ 2 2. Extend the Cournot model to three firl'nS Where the cost per unit is c for an firms and, for quantities ql, (12, (13, the sefling price is PM] , (121 (13) z (5— Q1 77 (12 w qg. “1 ix) M “224—282”: - ‘ 2 Q; R "glitz; w CZ? \. u 1‘wa‘pw (wezflo , M; “Zr/£225) "6‘sz m?» g» Ma» 2% 3 3. Show that 39* : (1/2,1/2,0)T and q* = (2/3, 0, 1/3)T are optimal strategies for the matrix game with payoff matrix flu '55 ‘7? . ' ‘ M Ma“ yin/ax 21;? cw} 29, I 4 4. Suppose the payoff matrix A of a. matrix game is an n—by—n nonsingular matrix and there is an optimai strategy 19* 2 (pi, . . . ,p;)T for Rose such that pf > U for all Prove that the value of the game is 1 v: 1TA~11 Where 1 z (1,” .,1)T. (Hint: What do you know about the optimal strategy q* for Colin?) 35’ Given the Kuhn tree of a game bsicw, calculate the expected ‘ payoff to piayer I if player i chooses the (pure) stategy a and player Expected paycff to player I = II the strategy a y. '0 (4,1) (3, -3 r - 1/2 cm 40,3) (-2,°2)- A°°h (4,4’4)' (-22.) M4 1/2/ \1/2 0 O O > (4.4) (-1.1) a «a ~ H- <3>(Lr(“/)+T(3)) + 3K7?- TC%)<‘a2=+(%)[-w ...
View Full Document

This note was uploaded on 02/02/2012 for the course MATH 115A 262398211 taught by Professor Fuckhead during the Spring '10 term at UCLA.

Page1 / 5

smidsol - 1. Solve the matrix game with payoff matrix 3...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online