CMA Final · Strategic Cost Management · Game Theory
In a zero-sum game, payoffs to A are: A1 = 6 and 2; A2 = 3 and 5 (columns B1 and B2). A publicly commits to always playing A1, and B, knowing this, chooses its best response. What is A's payoff?
A's payoff is 2. Once B knows A will play A1, B minimises A's gain by choosing B2, which pays 2 rather than 6. This is below the mixed-strategy game value of 4, showing predictability is costly.
- A2Correct
- B3
- C4
- D6
Explanation
If A plays A1, B (minimiser) chooses between 6 (B1) and 2 (B2) and picks B2, so A gets 2. The game value with optimal mixing is 4, so committing to a pure strategy loses 2 relative to the optimum. The figure 6 ignores that B responds.
Did you get it right without looking?
One question tells you little. A timed set on Game Theory shows your real accuracy, how long you take and where you lose marks.
More Game Theory questions
- In a two-person zero-sum game, the payoffs to Player A (the maximiser) are: A1: 3, 5, 4 against B1, B2, B3; A2: 6, 7, 8; A3: 2, 9, 1. Player…
- Two firms, X and Y, each choose a High or Low price. Payoffs are annual profits in ₹ crore, written as (X, Y). High-High: (10, 10) High-Low…
- Two rival firms, P and Q, each choose a High price or a Low price. Profits in Rs lakh (P, Q) are: both High (50, 50); P High and Q Low (20, …
- Two rival firms, P and Q, each choose a High price or a Low price. Profits (₹ crore) as (P, Q): both High = (10, 10); P High and Q Low = (4,…
- Payoffs to Player A in a zero-sum game are: A1: 5 against B1 and 1 against B2; A2: 2 against B1 and 4 against B2. Which is the value of the …
- Firm A (maximiser) and firm B (minimiser) have the following payoff matrix, showing A's gain in ₹ crore. A1: 8, 5, 6 A2: 7, 9, 4 A3: 6, 4, …