GATE 2026 DA – Question 30

Artificial Intelligence · Search: informed, uninformed and adversarial · 1 mark · Numerical answer

Consider the game tree for a two-player turn-taking minimax game as shown in the figure. The value of a terminal node represents the utility of the game state if the game ends there. The numbers written next to the edges denote the strategies.

There are two players MAX and MIN. At any particular state of the game, MAX prefers to move to a state of maximum value. On the other hand, MIN prefers to move to a state of minimum value.

Suppose MAX starts the game at the root and has three strategies: 1, 2 and 3. Next, MIN plays and also has three strategies: 1, 2 and 3. The game ends there. Both players always take optimal strategies throughout the game.

At the root, the best strategy for MAX is ___________ . (*Answer in integer*)

A game tree. The root is a MAX node with three edges 1, 2 and 3 to three MIN nodes. The leaves under the first MIN node are 8, 6 and -1, under the second 1, 5 and 7, and under the third -4, -3 and -12.

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Correct answer: 2

Explanation

MIN picks the smallest leaf under each of its nodes: $\min(8, 6, -1) = -1$ for strategy 1, $\min(1, 5, 7) = 1$ for strategy 2 and $\min(-4, -3, -12) = -12$ for strategy 3. MAX picks the largest of $-1$, $1$ and $-12$, which is 1, reached by strategy 2.