GATE 2025 Question 57: Game theory and strategic behaviour

There are two firms in an industry producing a homogeneous product. The market demand function is given by $P = 1 - (q_1+q_2)$, where $q_1$ and $q_2$ are the output levels of Firm 1 and Firm 2, respectively.

Firm 1's cost function is common knowledge and equals zero. Firm 2's cost function is private information. Firm 1 believes that Firm 2's cost function is $0.5q_2$ with probability 0.5 and that Firm 2's cost function is $0.25q_2$ with probability 0.5. The firms choose their quantities simultaneously.

Let $q_1^*$ denote the quantity produced by Firm 1 in the Bayesian Nash equilibrium of this game. Then, the value of $24q_1^*$ is ______ (round off to one decimal place)