There are two players. Each player has to write down a real number greater than or...

 

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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): π₁(x, y) = x-1 ifx<y if x ≥y {} and T₂(x, y) = y-1 ifx>y if x ≤y { 1 a) Show that (x, y) = (1, 1) is a Nash equilibrium. b) Find the best response function for each player. c) Show that there is no other Nash equilibrium besides (1, 1). 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): π₁(x, y) = x-1 ifx<y if x ≥y {} and T₂(x, y) = y-1 ifx>y if x ≤y { 1 a) Show that (x, y) = (1, 1) is a Nash equilibrium. b) Find the best response function for each player. c) Show that there is no other Nash equilibrium besides (1, 1).

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aSince Player 1s payoff is always 1 when x 1 Player 1 is better off choosing 1 no matter what Player ... View the full answer