Exam 5: Advanced Linear Programming Applications

Correct Answer:

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To determine when a two-person, zero-sum game has a pure-strategy solution, you can follow these steps:

1. Define the game: Start by defining the game in terms of the players, their strategies, and the payoffs associated with each combination of strategies.

2. Construct the payoff matrix: Create a payoff matrix that shows the payoffs for each player for every possible combination of strategies.

3. Identify dominant strategies: Look for any dominant strategies, where one player has a strategy that is always better than any other strategy, regardless of the other player's choice.

4. Check for saddle points: A saddle point occurs when the maximum payoff for one player in a row is also the minimum payoff for the other player in the corresponding column. If a saddle point exists, the game has a pure-strategy solution.

5. Use the minimax theorem: If there is no dominant strategy and no saddle point, you can use the minimax theorem to determine if the game has a pure-strategy solution. This involves finding the maximum of the minimum payoffs for each player and checking if they are equal.

By following these steps, you can determine whether a two-person, zero-sum game has a pure-strategy solution. If a pure-strategy solution exists, it means that there is a set of strategies that both players can choose to guarantee a specific outcome, without any randomness or mixed strategies involved.