3. There are two players. Each player has to write down a real number greater than or equal to 1; thus the strategy sets are S₁ S₂ = [1,00). Payoffs are as follows (x is the number written by Player 1 and y is the number written by Player 2): a) b) ₁(x, y) = {} fx-1 ifxy if x ≤ y Show that (x, y) = (1, 1) is a Nash equilibrium. Find the best response function for each player. Show that there is no other Nash equilibrium besides (1, 1).
3. There are two players. Each player has to write down a real number greater than or equal to 1; thus the strategy sets are S₁ S₂ = [1,00). Payoffs are as follows (x is the number written by Player 1 and y is the number written by Player 2): a) b) ₁(x, y) = {} fx-1 ifxy if x ≤ y Show that (x, y) = (1, 1) is a Nash equilibrium. Find the best response function for each player. Show that there is no other Nash equilibrium besides (1, 1).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:3.
There are two players. Each player has to write down a real number greater
than or equal to 1; thus the strategy sets are S₁ S₂ = [1,00). Payoffs are as
follows (x is the number written by Player 1 and y is the number written by
Player 2):
a)
b)
{8
fx-1 ifx<y
if x ≥y
and
72(x-3) = { 0-¹ [X²Y
y-1 ifx>y
Show that (x, y) = (1, 1) is a Nash equilibrium.
Find the best response function for each player.
Show that there is no other Nash equilibrium besides (1, 1).
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