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Questions › GATE › GATE 2025 › Q64
2 marksGame Theory › Game theory and strategic behaviour › Mixed-strategy Nash equilibriumHardabout 3 min

GATE 2025 Question 64: Game theory and strategic behaviour

Two players AAA and BBB are playing a game. Player AAA has two available actions a1a_1a1​ and a2a_2a2​. Player BBB has two available actions b1b_1b1​ and b2b_2b2​. The payoff matrix arising from their actions is presented below.

b1b_1b1​b2b_2b2​
a1a_1a1​−1,3-1, 3−1,34,−14, -14,−1
a2a_2a2​3,−43, -43,−4−2,2-2, 2−2,2

Let ppp be the probability that player AAA plays action a1a_1a1​ in the mixed strategy Nash equilibrium of the game. Then the value of ppp is ______ (round off to one decimal place)

Answer and worked solution

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Plain-text version

Two players A and B are playing a game. Player A has two available actions a₁ and a₂. Player B has two available actions b₁ and b₂. The payoff matrix arising from their actions is presented below. | b₁ | b₂ | a₁ | -1, 3 | 4, -1 | a₂ | 3, -4 | -2, 2 | Let p be the probability that player A plays action a₁ in the mixed strategy Nash equilibrium of the game. Then the value of p is (round off to one decimal place)

Also written as: Two players A and B are playing a game. Player A has two available actions a_1 and a_2. Player B has two available actions b_1 and b_2. The payoff matrix arising from their actions is presented below. | b_1 | b_2 | a_1 | -1, 3 | 4, -1 | a_2 | 3, -4 | -2, 2 | Let p be the probability that player A plays action a_1 in the mixed strategy Nash equilibrium of the game. Then the value of p is (round off to one decimal place)

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

What this question tests

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

Equilibria where players randomise, found by making the opponent indifferent.

TestStop has 5 past-paper questions on this subtopic.

Take this paper as a timed mockMore on Mixed-strategy Nash equilibrium

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