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 1.

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-space text explain why ordering of the utility levels you assigned in Prompt 2A depicts Persons A’s preferences over her actions given her expectations about Person B’s action.

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-space text explain why ordering of the utility levels you assigned in Prompt 2C depicts Persons A’s preferences over her actions given her expectations about Person B’s action.

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-space text explain why ordering of the utility levels you assigned in Prompt 2E depicts Persons B’s preferences over her actions given her expectations about Person A’s action.

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-space text explain why ordering of the utility levels you assigned in Prompt 2G depicts Persons B’s preferences over her actions given her expectations about Person A’s action.

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”.

An answer gets one point if it satisfies all of the above and zero points otherwise.

Prompt 1B

The answer must consist of the set of all profiles of actions in which each profile consists of one action from Person A and one action from Person B, where each of those person’s available actions are to “participate” or to “not participate”.

An answer gets one point if it satisfies all of the above and zero points otherwise.

Prompt 1C

The answer must consist of a table with columns “Person A’s Action”, “Person B’s Action”, “Person A’s Utility Level” and “Person B’s Utility Level”. The “Person A’s Action” and “Person B’s Action” columns must be filled in, with one row for each of the profiles of actions in the set of all profiles of actions.

An answer gets one point if it satisfies all of the above and zero points otherwise.

Prompt 2A

The answer must consist of a table with columns as required for Prompt 1C. The “Person A’s Action” and “Person B’s Action” columns must be filled in, with one row for each of the profiles of actions in the set of all profiles of actions. Utility levels for Person A must be filled-in in the rows corresponding to the (1) the profile in which Person A participates and Person B participates and (2) the profile in which Person A does not participate and Person B participates. The utility level at the former profile must be larger than the utility level at the latter profile.

An answer gets one point if it satisfies all of the above and zero points otherwise.

Prompt 2B

A successful answer meets all the following criteria:

It states that Person A prefers to participate instead of not participate if she expects Person B to participate.
It states that this preference ordering can be represented by assigning a higher utility level to Person A at the profile in which both Person A and Person B participate than at the profile in which Person A does not participate and Person B participates.
It points out that the utility level assigned to Person A at the profile in which Person A participates and Person B participates in the answer to Prompt 2A is higher than the utility level assigned to Person A at the profile in which Person A does not participate and Person B participates.
It must be sufficiently free of errors of spelling, grammar and usage as to be readily and easily comprehensible.
If hand written, it must be immediately and easily legible.

An answer gets…

Four points…: if it meets all of the above criteria.
Two points…: if it meets criteria (a), (d) and (e) and meets either criterion (b) or (c) but not both.
One point…: if it meets criteria (a), (d) and (e) and meets neither criterion (b) nor (c).
Zero points…: if it misses any of criteria (a), (d) or (e).

Prompt 2C

The answer must consist of a table with columns as required for Prompt 1C. The “Person A’s Action” and “Person B’s Action” columns must be filled in, with one row for each of the profiles of actions in the set of all profiles of actions. Utility levels for Person A must be filled-in in the rows corresponding to the (1) the profile in which Person A participates and Person B does not participate and (2) the profile in which Person A does not participate and Person B does not participate. The utility level at the former profile must be smaller than the utility level at the latter profile.

An answer gets one point if it satisfies all of the above and zero points otherwise.

Prompt 2D

A successful answer meets all the following criteria:

It states that Person A prefers to not participate instead of participate if she expects Person B to not participate.
It states that this preference ordering can be represented by assigning a higher utility level to Person A at the profile in which both Person A and Person B do not participate than at the profile in which Person A participates and Person B does not participate.
It points out that the utility level assigned to Person A at the profile in which Person A and Person B do not participate in the answer to Prompt 2C is higher than the utility level assigned to Person A at the profile in which Person A participates and Person B does not participate.
It must be sufficiently free of errors of spelling, grammar and usage as to be readily and easily comprehensible.
If hand written, it must be immediately and easily legible.

An answer gets…

Four points…: if it meets all of the above criteria.
Two points…: if it meets criteria (a), (d) and (e) and meets either criterion (b) or (c) but not both.
One point…: if it meets criteria (a), (d) and (e) and meets neither criterion (b) nor (c).
Zero points…: if it misses any of criteria (a), (d) or (e).

Prompt 2E

The answer must consist of a table with columns as required for Prompt 1C. The “Person A’s Action” and “Person B’s Action” columns must be filled in, with one row for each of the profiles of actions in the set of all profiles of actions. Utility levels for Person B must be filled-in in the rows corresponding to the (1) the profile in which Person B participates and Person A participates and (2) the profile in which Person B does not participate and Person A participates. The utility level at the former profile must be larger than the utility level at the latter profile.

An answer gets one point if it satisfies all of the above and zero points otherwise.

Prompt 2F

A successful answer meets all the following criteria:

It states that Person B prefers to participate instead of not participate if she expects Person A to participate.
It states that this preference ordering can be represented by assigning a higher utility level to Person B at the profile in which both Person A and Person B participate than at the profile in which Person B does not participate and Person A participates.
It points out that the utility level assigned to Person B at the profile in which Person A participates and Person B participates in the answer to Prompt 2E is higher than the utility level assigned to Person B at the profile in which Person B participates and Person A does not participate.
It must be sufficiently free of errors of spelling, grammar and usage as to be readily and easily comprehensible.
If hand written, it must be immediately and easily legible.

An answer gets…

Four points…: if it meets all of the above criteria.
Two points…: if it meets criteria (a), (d) and (e) and meets either criterion (b) or (c) but not both.
One point…: if it meets criteria (a), (d) and (e) and meets neither criterion (b) nor (c).
Zero points…: if it misses any of criteria (a), (d) or (e).

Prompt 2G

The answer must consist of a table with columns as required for Prompt 1C. The “Person A’s Action” and “Person B’s Action” columns must be filled in, with one row for each of the profiles of actions in the set of all profiles of actions. Utility levels for Person B must be filled-in in the rows corresponding to the (1) the profile in which Person B participates and Person A does not participate and (2) the profile in which Person B does not participate and Person A does not participate. The utility level at the former profile must be smaller than the utility level at the latter profile.

An answer gets one point if it satisfies all of the above and zero points otherwise.

Prompt 2H

A successful answer meets all the following criteria:

It states that Person B prefers to not participate instead of participate if she expects Person A to not participate.
It states that this preference ordering can be represented by assigning a higher utility level to Person B at the profile in which both Person A and Person B do not participate than at the profile in which Person A does not participates and Person B participates.
It points out that the utility level assigned to Person B at the profile in which Person A and Person B do not participate in the answer to Prompt 2G is higher than the utility level assigned to Person B at the profile in which Person B participates and Person A does not participate.
It must be sufficiently free of errors of spelling, grammar and usage as to be readily and easily comprehensible.
If hand written, it must be immediately and easily legible.

An answer gets…

Four points…: if it meets all of the above criteria.
Two points…: if it meets criteria (a), (d) and (e) and meets either criterion (b) or (c) but not both.
One point…: if it meets criteria (a), (d) and (e) and meets neither criterion (b) nor (c).
Zero points…: if it misses any of criteria (a), (d) or (e).