Suppose that, in an ultimatum game, the proposer may not propose less than $1 nor fractional amounts, and therefore must propose $1, $2, …, or $10 (see image attached below). The responder must Accept (A) or Reject (R). Suppose, first, that this game is played by two egoists, for whom u(x,y)=x. Find all subgame-perfect equilibria in this game. Suppose, second, that this game is played by two altruists, for whom u(x,y) = ⅔(x)1/2 + ⅓(y)1/2. Find all subgame-perfect equilibria in this game.
Suppose that, in an ultimatum game, the proposer may not propose less than $1 nor fractional amounts, and therefore must propose $1, $2, …, or $10 (see image attached below). The responder must Accept (A) or Reject (R). Suppose, first, that this game is played by two egoists, for whom u(x,y)=x. Find all subgame-perfect equilibria in this game. Suppose, second, that this game is played by two altruists, for whom u(x,y) = ⅔(x)1/2 + ⅓(y)1/2. Find all subgame-perfect equilibria in this game.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Suppose that, in an ultimatum game, the proposer may not propose less than $1 nor fractional amounts, and therefore must propose $1, $2, …, or $10 (see image attached below). The responder must Accept (A) or Reject (R).
Suppose, first, that this game is played by two egoists, for whom u(x,y)=x. Find all subgame-perfect equilibria in this game.
Suppose, second, that this game is played by two altruists, for whom u(x,y) = ⅔(x)1/2 + ⅓(y)1/2. Find all subgame-perfect equilibria in this game.
![$1
II
$4
$5
$6
$7
$8
$9
$10
A
($6,$4)
($0,$0)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa550ff16-be18-4c5b-b3ad-8a1f02d33310%2Fe18f3906-4865-4671-825e-2144332d7dc5%2F8hcaag2p_processed.png&w=3840&q=75)
Transcribed Image Text:$1
II
$4
$5
$6
$7
$8
$9
$10
A
($6,$4)
($0,$0)
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