1. **State the problem:** We have a 2x2 payoff matrix for two companies, Paramount and Disney, each choosing between two strategies. We want to find Disney's dominant strategy and the Nash equilibrium. 2. **Recall definitions:** - A **dominant strategy** is one that yields a higher payoff for a player regardless of the opponent's choice. - A **Nash equilibrium** is a strategy profile where no player can improve their payoff by unilaterally changing their strategy. 3. **Analyze Disney's payoffs:** - If Paramount chooses Strategy 1: - Disney's payoff for Strategy 1 is $75$ - Disney's payoff for Strategy 2 is $25$ - If Paramount chooses Strategy 2: - Disney's payoff for Strategy 1 is $300$ - Disney's payoff for Strategy 2 is $150$ 4. **Check for Disney's dominant strategy:** - Compare Disney's payoffs for each of Paramount's strategies: - When Paramount chooses Strategy 1, Disney prefers Strategy 1 ($75 > 25$). - When Paramount chooses Strategy 2, Disney prefers Strategy 1 ($300 > 150$). Since Disney prefers Strategy 1 regardless of Paramount's choice, **Disney's dominant strategy is Strategy 1**. 5. **Find Nash equilibrium:** - Check each cell to see if neither player can improve by changing their strategy alone. - Cell A (Paramount S1, Disney S1): Payoffs $(75,75)$ - Paramount can switch to Strategy 2 and get $25$ (less than $75$), so no incentive. - Disney can switch to Strategy 2 and get $25$ (less than $75$), so no incentive. - So, (S1, S1) is a Nash equilibrium. - Cell B (Paramount S1, Disney S2): Payoffs $(300,25)$ - Paramount can switch to Strategy 2 and get $150$ (less than $300$), no incentive. - Disney can switch to Strategy 1 and get $75$ (better than $25$), so Disney would deviate. - Not a Nash equilibrium. - Cell C (Paramount S2, Disney S1): Payoffs $(25,300)$ - Paramount can switch to Strategy 1 and get $75$ (better than $25$), so Paramount would deviate. - Not a Nash equilibrium. - Cell D (Paramount S2, Disney S2): Payoffs $(150,150)$ - Paramount can switch to Strategy 1 and get $300$ (better than $150$), so Paramount would deviate. - Not a Nash equilibrium. 6. **Conclusion:** - Disney's dominant strategy is Strategy 1. - The only Nash equilibrium is when both choose Strategy 1, with payoffs $(75,75)$. **Final answers:** - Disney's dominant strategy: Strategy 1 - Nash equilibrium: (Paramount Strategy 1, Disney Strategy 1) with payoffs $(75,75)$