Suppose that the proposer in the ultimatum game may not propose fractional amounts, and therefore must propose $0, $1, $2, or $10 (see figure below). As always, the responder must Accept (A) or Reject (R). 11 $0 $1 $2 $3 A $4 ($6,$4) ***** 1 $5 R ($0,$0) $6 $7 $8 $9 $10 (a) Suppose, first, that this game is played by two egoists, for whom u(x,y)=x. What is the Nash equilibrium? (b) Suppose, second, that this game is played by two altruists, for whom u(x, y) = 2/3√x + 1/3√y. Find the new Nash Equilibrium.

ENGR.ECONOMIC ANALYSIS
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Author:NEWNAN
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Chapter1: Making Economics Decisions
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A1
Suppose that the proposer in the ultimatum game may not propose fractional amounts,
and therefore must propose $0, $1, $2, .. or $10 (see figure below). As always, the
responder must Accept (A) or Reject (R).
XX
$0
%3D
$1
$2
$3
$4
$5
$6
$7
$9
$10
$8
R.
($6,$4)
($0,$0)
(a) Suppose, first, that this game is played by two egoists, for whom u(x,y)%3Dx. What is
the Nash equilibrium?
(b) Suppose, second, that this game is played by two altruists, for whom
u(x, y) = 2/3x+ 1/3Vy. Find the new Nash Equilibrium.
Transcribed Image Text:Suppose that the proposer in the ultimatum game may not propose fractional amounts, and therefore must propose $0, $1, $2, .. or $10 (see figure below). As always, the responder must Accept (A) or Reject (R). XX $0 %3D $1 $2 $3 $4 $5 $6 $7 $9 $10 $8 R. ($6,$4) ($0,$0) (a) Suppose, first, that this game is played by two egoists, for whom u(x,y)%3Dx. What is the Nash equilibrium? (b) Suppose, second, that this game is played by two altruists, for whom u(x, y) = 2/3x+ 1/3Vy. Find the new Nash Equilibrium.
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