{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

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

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

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

View Full Document

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

View Full Document
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

{[ snackBarMessage ]}

### 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
Ask a homework question - tutors are online