COU2: Constructing a Simultaneous Move Game

In COU 1, you explored the strategic interdependence that arises between persons who are each deciding whether to participate in a protest if the protest will be productive when many persons participate and counterproductive when few persons participate. In this COU, you’ll construct a simultaneous move game to depict this strategic interdependence.

Imagine an interaction between two persons labeled Person A and Person B. Imagine that each of these persons must choose whether or not to participate in a protest. Imagine that these persons are strategically interdependent in the following sense:

Person A’s Expectation about What Person B Will Do	Person A’s Preferences
participate	Person A prefers to participate instead of not participate
not participate	Person A prefers to not participate instead of participate

Person B’s Expectation about What Person A Will Do	Person B’s Preferences
participate	Person B prefers to participate instead of not participate
not participate	Person B prefers to not participate instead of participate

Part 1: Persons, Actions and Profiles of Actions

You’ll start by specifying the persons, sets of actions and set of all profiles of actions for a simultaneous move game. Start by responding to the following prompts.

Prompt 1A

As a first step in constructing a simultaneous move game to depict the above interaction, write a set of persons and a set of available actions for each of those persons.

Prompt 1B

Write the set of all profiles of actions implied by the sets of available actions you wrote in response to Prompt 1A.

Prompt 1C

Begin to specify a payoff function for the game you are constructing by writing a table with columns “Person A’s Action”, “Person B’s Action”, “Person A’s Utility Level” and “Person B’s Utility Level”. Add all the required entries to the “Person A’s Action” and “Person B’s Action” column, so that there is one row in the table for each profile of actions in the game. Leave the entries for the other two columns blank.

Part 2: The Payoff Function

Prompt 2A

Re-write your table just as you wrote it in response to Prompt 1C. Then, fill in utility levels for only for Person A in (i) the row corresponding to the profile in which Person A participates and Person B participates and (ii) the profile in which Person A does not participate and Person B participates. Assign utility levels for Person A in these two rows that are ordered relative to one another in a way that depicts the strategic interdependence described these tables:

Person A’s Expectation about What Person B Will Do	Person A’s Preferences
participate	Person A prefers to participate instead of not participate
not participate	Person A prefers to not participate instead of participate

Person B’s Expectation about What Person A Will Do	Person B’s Preferences
participate	Person B prefers to participate instead of not participate
not participate	Person B prefers to not participate instead of participate

Do not worry about the size of the gap between the utility levels you assign. All that matters for this COU is the order of these utility levels relative to one another.

Prompt 2B

In no more than one-half a page of double-spaced text (i) describe Person A’s preferences over her actions when she expects Person B to participate and (ii) explain why the utility levels you assigned in Prompt 2A depict those preferences.

Prompt 2C

Re-write your table just as you wrote it in response to Prompt 2A. Then, fill in utility levels for only for Person A in (i) the row corresponding to the profile in which Person A participates and Person B does not participate and (ii) the profile in which Person A does not participate and Person B does not participate. Assign utility levels for Person A in these two rows that are ordered relative to one another in a way that depicts the strategic interdependence described these tables:

Person A’s Expectation about What Person B Will Do	Person A’s Preferences
participate	Person A prefers to participate instead of not participate
not participate	Person A prefers to not participate instead of participate

Person B’s Expectation about What Person A Will Do	Person B’s Preferences
participate	Person B prefers to participate instead of not participate
not participate	Person B prefers to not participate instead of participate

Do not worry about the size of the gap between the utility levels you assign. All that matters for this COU is the order of these utility levels relative to one another.

Prompt 2D

In no more than one-half a page of double-spaced text (i) describe Person A’s preferences over her actions when she expects Person B to not participate and (ii) explain why the utility levels you assigned in Prompt 2C depict those preferences.

Prompt 2E

Re-write your table just as you wrote it in response to Prompt 2C. Then, fill in utility levels for only for Person B in (i) the row corresponding to the profile in which Person B participates and Person A participates and (ii) the profile in which Person B does not participate and Person A participates. Assign utility levels for Person B in these two rows that are ordered relative to one another in a way that depicts the strategic interdependence described these tables:

Person A’s Expectation about What Person B Will Do	Person A’s Preferences
participate	Person A prefers to participate instead of not participate
not participate	Person A prefers to not participate instead of participate

Person B’s Expectation about What Person A Will Do	Person B’s Preferences
participate	Person B prefers to participate instead of not participate
not participate	Person B prefers to not participate instead of participate

Do not worry about the size of the gap between the utility levels you assign. All that matters for this COU is the order of these utility levels relative to one another.

Prompt 2F

In no more than one-half a page of double-spaced text (i) describe Person B’s preferences over her actions when she expects Person A to participate and (ii) explain why the utility levels you assigned in Prompt 2E depict those preferences.

Prompt 2G

Re-write your table just as you wrote it in response to Prompt 2E. Then, fill in utility levels for only for Person B in (i) the row corresponding to the profile in which Person B participates and Person A does not participate and (ii) the profile in which Person B does not participate and Person A does not participate. Assign utility levels for Person B in these two rows that are ordered relative to one another in a way that depicts the strategic interdependence described these tables:

Person A’s Expectation about What Person B Will Do	Person A’s Preferences
participate	Person A prefers to participate instead of not participate
not participate	Person A prefers to not participate instead of participate

Person B’s Expectation about What Person A Will Do	Person B’s Preferences
participate	Person B prefers to participate instead of not participate
not participate	Person B prefers to not participate instead of participate

Do not worry about the size of the gap between the utility levels you assign. All that matters for this COU is the order of these utility levels relative to one another.

Prompt 2H

In no more than one-half a page of double-spaced text (i) describe Person B’s preferences over her actions when she expects Person A to not participate and (ii) explain why the utility levels you assigned in Prompt 2G depict those preferences.

Rubric

Prompt 1A

The answer must consist of a list of persons and a set of available actions for each of those persons. The persons must be named “Person A” and “Person B”. Each person’s available actions must be to “participate” and to “not participate”.