COU 1: Practice Identifying Best Responses
In this COU you’ll work on developing your ability to quickly identify best responses in the matrix forms of simultaneous move games in which two persons each have three available actions.
Example Problem
Below is an example that illustrates the following problems and the prompts for each one. Watch this video to make sure you understand how to do these problems before getting started.
Here is the matrix form of a game in which there are two persons who each have three available actions:
- Prompt E1
- Name each of Person B’s three actions that are best responses to the expectation that Person A will take action a_1.
- Prompt E2
- Explain how you know the answer to Prompt E1 by stating the utility levels Person B gets from each of the profiles in which Person A takes action a_1, stating the highest utility level that Person B can get when Person A takes action a_1, and stating which of Person B’s actions result in that highest utility level for Person B when Person A takes action a_1.
- Prompt E3
- Name each of Person A’s three actions that are best responses to the expectation that Person B will take action b_2.
- Prompt E4
- Explain how you know the answer to Prompt E3 by stating the utility levels Person A gets from each of the profiles in which Person B takes action b_2, stating the highest utility level that Person A can get when Person B takes action b_2, and stating which of Person A’s actions result in that highest utility level for Person A when Person B takes action b_2.
Actual Problem
Answer Prompts 1 through 12 regarding the following matrix-form of a game between Person A and Person B:
- Prompt 1
- Name each of Person B’s three actions that are best responses to the expectation that Person A will take action ‘left’.
- Prompt 2
- Explain how you know the answer to Prompt 1 by stating the utility levels Person B gets from each of the profiles in which Person A takes action ‘left’, stating the highest utility level that Person B can get when Person A takes action ‘left’, and stating which of Person B’s actions result in that highest utility level for Person B when Person A takes action ‘left’.
- Prompt 3
- Name each of Person B’s three actions that are best responses to the expectation that Person A will take action ‘middle’.
- Prompt 4
- Explain how you know the answer to Prompt 3 by stating the utility levels Person B gets from each of the profiles in which Person A takes action ‘middle’, stating the highest utility level that Person B can get when Person A takes action ‘middle’, and stating which of Person B’s actions result in that highest utility level for Person B when Person A takes action ‘middle’.
- Prompt 5
- Name each of Person B’s three actions that are best responses to the expectation that Person A will take action ‘right’.
- Prompt 6
- Explain how you know the answer to Prompt 5 by stating the utility levels Person B gets from each of the profiles in which Person A takes action ‘right’, stating the highest utility level that Person B can get when Person A takes action ‘right’, and stating which of Person B’s actions result in that highest utility level for Person B when Person A takes action ‘right’.
- Prompt 7
- Name each of Person A’s three actions that are best responses to the expectation that Person B will take action ‘top’.
- Prompt 8
- Explain how you know the answer to Prompt 7 by stating the utility levels Person A gets from each of the profiles in which Person B takes action ‘top’, stating the highest utility level that Person A can get when Person B takes action ‘top’, and stating which of Person A’s actions result in that highest utility level for Person A when Person B takes action ‘top’.
- Prompt 9
- Name each of Person A’s three actions that are best responses to the expectation that Person B will take action ‘middle’.
- Prompt 10
- Explain how you know the answer to Prompt 9 by stating the utility levels Person A gets from each of the profiles in which Person B takes action ‘middle’, stating the highest utility level that Person A can get when Person B takes action ‘middle’, and stating which of Person A’s actions result in that highest utility level for Person A when Person B takes action ‘middle’.
- Prompt 11
- Name each of Person A’s three actions that are best responses to the expectation that Person B will take action ‘bottom’.
- Prompt 12
- Explain how you know the answer to Prompt 11 by stating the utility levels Person A gets from each of the profiles in which Person B takes action ‘bottom’, stating the highest utility level that Person A can get when Person B takes action ‘bottom’, and stating which of Person A’s actions result in that highest utility level for Person A when Person B takes action ‘bottom’.
Rubric
Each of the odd prompts (1, 3, 5 etc.) is worth 1 point. Each wholly correct answer to each of those prompts gets 1 point, with no partial credit available. This means that to get 1 point on one of these prompts, you must name every action that is a best response and not name any of the actions that are not best responses.
Each of the even prompts (2, 4, 6, etc.) is worth 3 points, with 1 point available for each of the three elements required of an explanation. For each of those elements, the point is awarded if the element is present and wholly correct (e.g. it correctly names the highest utility level, correctly names the all the relevant utility levels, correctly states which actions achieve the highest utility levels, etc. etc.)