Question

Two people, 1 and 2, are engaged in a joint project. Person 𝑖∈{1,2} puts in effort 𝑥𝑖 (0≤ 𝑥𝑖 ≤ 1), and incurs cost 𝐶𝑖 (𝑥𝑖 ) = 𝑥𝑖 . The monetary outcome of the project is 4𝑥1𝑥2 which is split equally between them. Considering the situation as a strategic game, the set of all Nash Equilibria in pure strategies is

• A. {(0, 0), (1, 1)}
• B. $\\{{(0,0),(\frac{1}{4},\frac{1}{4}),(\frac{3}{4},\frac{3}{4}),(1,1)\\}}$
• C. $\\{(0,0),(\frac{1}{2},\frac{1}{2}),(1,1)\\}$
• D. a null set

Answer 1

Answer: (C)

$\\{(0,0),(\frac{1}{2},\frac{1}{2}),(1,1)\\}$

Answer 2

The correct option is (C): $\\{(0,0),(\frac{1}{2},\frac{1}{2}),(1,1)\\}$