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Game Playing in Class
GAME 1—Check Marks
Prepare a handout or cards and ask students to place either a blank line or a check mark
on the paper. Tell them that if fewer than half of the students in the class answer with a check
mark, 5 points (if you count experiment points toward the grade or if this is included on a quiz)
will be added to the score of each person who makes the check mark. But if more than half of the
class answers with a check mark, then 5 points will be taken away from the score of each person
who makes the check mark. (You can achieve the same incentive structure in a variety of ways.)
Collect the cards or quizzes and collate the answers to the question.
Consideration of the results from this game can lead to an interesting discussion. The
game has asymmetric Nash equilibria in pure strategies and a symmetric Nash equilibrium in
mixed strategies. Which one (if any) would you or the students expect to emerge? What kind of
coordination would be needed to achieve a particular asymmetric pure-strategy outcome? What
ethical or redistributive issues would arise if the students did act in coordination? Should students
who did badly on previous quizzes be allowed to get the extra points here, or should the
allocation be made by a lottery that gives an equal chance to everyone? If a plan of joint action is
devised, would anyone try to cheat? And so on. Exercise U2 at the end of the chapter addresses
these same issues.
GAME 2—Investment Game
This game starts with each person receiving an imaginary $5 from the instructor. We have
also been successful using small candies as a substitute for currency in this game; students can be
given the rights to 10 jellybeans instead, for example. Students are each asked to divide their
“funds” between two different investment opportunities: Asset A and Asset B. Asset A is a riskless
investment with a zero rate of return; any money invested in this asset is returned intact at the end
Games of Strategy, Fourth Edition Copyright © 2015 W. W. Norton & Company
of the game. Asset B works in the following way: each student chooses to invest some amount
between $0 and $5 (or 0 and 10 jellybeans, inclusive) in Asset B. These amounts will be added
together, and the sum will become the Asset B investment pool. The size of this investment pool
will be increased by 50%. The funds in the investment pool will then be divided equally among
all the participants in the game. (In other words, an individual’s share of the Asset B investment
pool depends only on the total amount invested in the pool and not on how much the individual
personally invested in Asset B.)
You might want to give your students an example of how the game could proceed.
Suppose that there are 25 people who participate in the game, that Sarah Student invests $2.00 in
Asset A and $3.00 in Asset B, and that the total amount invested in Asset B (from all 25 people) is
$60.00. In this case, the Asset B pool is increased to $90.00 after the investment decisions are
made, and $90.00 is then divided equally among the 25 participants. Each player collects $3.60
from the Asset B investment pool. Sarah Student ends the game with her $2.00 from Asset A and
$3.60 from the Asset B pool for a total of $5.60.
Ask students to divide the $5 between the two assets in any way they choose. After
thinking about this game for a few moments, ask them to indicate how much of the $5 they wish
to invest in each asset and have them indicate this on a card or handout.
This game is a multiperson prisoners’ dilemma game or a collective-action game with a
payoff structure resembling a prisoners’ dilemma. Those who invest in Asset A defect while those
who invest in Asset B cooperate. You can calculate the amount of free riding that takes place in
the game by taking the proportion of the dollars invested in Asset A to the total number of dollars
available to be invested and discuss the implications of the outcomes observed.
You can also use a slightly simpler version of this game in which students can put their
entire $5 either into Asset A or into Asset B. This case is easier to analyze, and you can draw a
simple diagram showing payoffs from cooperation (this payoff is [7.5 number investing in
B]/number in class) and defection (this payoff is 5 + [7.5 number investing in B]/number in
Games of Strategy, Fourth Edition Copyright © 2015 W. W. Norton & Company
class). Defection is a dominant strategy for each player, but the class as a whole would be better
off if all cooperated.
There are many versions of this public goods game that appear in the literature. For some
ideas about ways to vary this game see www.marietta.edu/~delemeeg/expernom/s93.html.
GAME 3—Fishing Game
Here are directions for students to be written on a handout. Imagine that you own a fleet
of boats that are used to catch fish in a particular lake. There is one other fleet of fishing boats
that also operates in this lake. On any given single day, the amount of fish caught by your fleet
depends both on the number of boats you sent out and on the number the other fleet sent out. The
following table shows the number of pounds of fish caught by each fleet in a day, depending on
how many boats each fleet sent out. (Your catch is shown first.) Suppose that a pound of fish can
be sold for $1 and that it costs $10 to send out a fishing boat for a day.
1
Other fleet
0 boats 1 boat 2 boats 3 boats 4 boats 5 boats
Your
fleet
0 boats 0, 0 0, 32 0, 60 0, 84 0, 104 0, 120
1 boat 32, 0 30, 30 28, 56 26, 78 24, 96 22, 110
2 boats 60, 0 56, 28 52, 52 48, 72 44, 88 40, 100
3 boats 84, 0 78, 26 72, 48 66, 66 60, 80 54, 90
4 boats 104, 0 96, 24 88, 44 80, 60 72, 72 64, 80
5 boats 120, 0 110, 22 100, 40 90, 54 80, 64 72, 72
If you want to send out the number of boats that will maximize your own profit (bearing
in mind that the owner of the other fleet will also be picking a number of boats to maximize his
profit), how many of your boats would you send out?
Games of Strategy, Fourth Edition Copyright © 2015 W. W. Norton & Company
Now, suppose that you can pick the number of boats that both your fleet and the other
fleet send out (but, to be fair, you have to allow the other fleet to send out exactly the same
number of boats that you send out). Again assuming that you are interested in maximizing your
profit, how many of your boats would you send out in this case?
You may also want to show students the following table indicating how many fish are
caught for a given number of boats on the lake and the profits gained for the different
combinations of boats sent out by each fleet:
Games of Strategy, Fourth Edition Copyright © 2015 W. W. Norton & Company
2 Total boats Fish caught
1 32
2 60
3 84
4 104
5 120
6 132
7 140
8 144
9 144
10 144
The original matrix was produced by allocating the number of fish caught proportionally among
all the boats sent out.
The following matrix shows the profit earned by each firm as a function of the number of
boats sent out by each fleet. It was constructed from the original matrix by subtracting the $10
cost of sending out each fishing boat; students often do this calculation for themselves as they
play the game if they are not provided with the following matrix:
3
Other fleet
0 boats 1 boat 2 boats 3 boats 4 boats 5 boats
Your
fleet
0 boats 0, 0 0, 22 0, 40 0, 54 0, 64 0, 70
1 boat 22, 0 20, 20 18, 36 16, 48 14, 56 12, 60
2 boats 40, 0 36, 18 32, 32 28, 42 24, 48 20, 50
3 boats 54, 0 48, 16 42, 28 36, 36 30, 40 24, 40
4 boats 64, 0 56, 14 48, 24 40, 30 32, 32 24, 30
5 boats 70, 0 60, 12 50, 20 40, 24 30, 24 22, 22
Games of Strategy, Fourth Edition Copyright © 2015 W. W. Norton & Company
This game shows that a good individual outcome may be inversely related to a good
outcome for the other player so that some type of coordination is necessary to get a jointly
optimal outcome. When each player pursues a course of action designed only to better his payoff,
the final outcome may be bad for him. This game has an externality; putting more of your boats
on the lake hurts the other fleet’s potential catch (and potential profit). From a societal perspective
(total profit), an outcome with two fleets and three boats each is better (132 fish and a total of 72
profit) than a single fleet sending out all five of its boats (120 fish and $70 profit).
To analyze the game from an individual’s perspective, you could derive best-response
curves showing each fleet’s best number of boats (the number of boats that gives each fleet the
most profit) given the number of boats sent out by the other fleet. To analyze the game from a
social perspective, you can graph total profits (to both fleets) as a function of the number of boats
sent out (from 1 to 10). You will want to ask the class about solutions to the externality problem
here and get them to think about how the externality might be internalized in this case.
Games of Strategy, Fourth Edition Copyright © 2015 W. W. Norton & Company
