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Questions › JNU › JNU SIS 2021 › Q12
0 marksGame Theory › Game theory and strategic behaviour › Pure-strategy Nash equilibriumModerateabout 2 min

JNU SIS 2021 Question 12: Game theory and strategic behaviour

Two managers can invest effort in creating a better working relationship. Each invests ei≥0e_i \geq 0ei​≥0, and if both invest more then both are better off, but it is costly for each manager to invest. The payoff function for player iii from effort levels (ei,ej)(e_i, e_j)(ei​,ej​) is vi(ei,ej)=(a+ej)ei−ei2v_i(e_i, e_j) = (a + e_j)e_i - e_i^2vi​(ei​,ej​)=(a+ej​)ei​−ei2​. The Nash equilibrium of this game is

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Two managers can invest effort in creating a better working relationship. Each invests eᵢ ≥ 0, and if both invest more then both are better off, but it is costly for each manager to invest. The payoff function for player i from effort levels (eᵢ, eⱼ) is vᵢ(eᵢ, eⱼ) = (a + eⱼ)eᵢ - eᵢ². The Nash equilibrium of this game is (A) eᵢ = eⱼ = a (B) eᵢ = eⱼ = a/2 (C) eᵢ = eⱼ = 2a (D) eᵢ = a, eⱼ = 2a

Also written as: Two managers can invest effort in creating a better working relationship. Each invests e_i >= 0, and if both invest more then both are better off, but it is costly for each manager to invest. The payoff function for player i from effort levels (e_i, e_j) is v_i(e_i, e_j) = (a + e_j)e_i - e_i^2. The Nash equilibrium of this game is

Game theory and strategic behaviour has come up 61 times in 6 exams since 2008.

What this question tests

This question is on Pure-strategy Nash equilibrium, part of Game theory and strategic behaviour in Game Theory.

Outcomes from which no player wants to deviate, and classic games that illustrate them.

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