Strategy choices for Bright and Sparkle

A dominant strategy is best for a player no matter what the other does. Check each firm separately.

Bright is the first number. If Sparkle plays Strategy 1, Bright earns $3,000 with Strategy 1 and $500 with Strategy 2, so Strategy 1 is better. If Sparkle plays Strategy 2, Bright earns $2,000 with Strategy 1 and $2,500 with Strategy 2, so Strategy 2 is better. Bright's best choice depends on Sparkle, so Bright has no dominant strategy.

Sparkle is the second number. If Bright plays Strategy 1, Sparkle earns $6,000 with Strategy 1 and $4,000 with Strategy 2. If Bright plays Strategy 2, Sparkle earns $3,000 with Strategy 1 and $0 with Strategy 2. Strategy 1 wins either way, so it is Sparkle's dominant strategy.

Each choice

• A. Sparkle's half is right. Bright does best with Strategy 1 only when Sparkle plays Strategy 1; when Sparkle plays Strategy 2, Bright does better with Strategy 2.
• B. Bright's Strategy 1 holds the largest payoff Bright can get, $3,000, but a dominant strategy has to win against each of Sparkle's moves, and it loses when Sparkle plays Strategy 2. Strategy 2 pays Sparkle less in both rows, $4,000 against $6,000 and $0 against $3,000. Choosing it means looking for the move that holds down Bright's profit instead of the one that raises Sparkle's own.
• C. Strategy 2 is better for Bright only when Sparkle plays Strategy 2. A dominant strategy has to win against every choice the other firm makes.
• D. This swaps the roles of the two firms. It is Bright whose best move depends on the other firm, so Bright has no dominant strategy, and Sparkle whose Strategy 1 pays more in both rows. A student who finds that one firm lacks a dominant strategy but attaches that finding to the wrong firm, then gives Bright its better reply to Sparkle's Strategy 2, lands here.
• E (correct). Bright's best choice switches with Sparkle's move, while Sparkle does better with Strategy 1 whatever Bright does.