EC3113: Autumn 2019 Philip Neary Assessed Problem Set
1. Homogeneous Cournot with Multiple Firms
Suppose that in a market there are N 2 firms, all of which have the same constantreturns-to-scale technology with marginal cost c 0, so that
Ci(qi) = cqi for all i.
The market demand is given by
P(Q) = A BQ,
where Q = PN
i qi is the aggregate market output. Assume that A>c and B > 0.
In this problem we will solve for the Cournot equilibrium in this market. You may user
your answers in other problems of this problem set.
(a) 5 marks Denote the joint output of all firms other than i by Qi, so that
Qi = X
j6=i
qj = Q qi.
Derive the best-response function of firm i as a function of Qi.
(b) 5 marks Prove that in equilibrium all firms produce the same output: qi = qj for
all i and j.
[Hint: First, express qiqj as a function of Qi and Qj using the best-response functions.
Then express Qj Qi as a function of qi and qj using the definition of Qi (and Qj ).
Finally, put these two results together to get qi qj = 0.]
(c) 2 marks Use the fact that all firms produce the same output in equilibrium to
express Q and Qi (for an arbitrary firm) as functions of qi and N.
(d) 3 marks Plug your results from (c) into the best-response function to solve for qi.
Use this to get Q.
(e) 5 marks Calculate the market price and the firms’ profits.
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EC3113: Autumn 2019 Philip Neary Assessed Problem Set
2. Netflix with unlimited sharing
Netflix is an American media-services provider and production company headquartered
in Los Gatos, California. The company’s primary business is its subscription-based
streaming service which o↵ers online streaming of a library of films and tv programs.
There is a society of six individuals, {1, 2, 3, 4, 5, 6}, who are connected in a social network
as below. If there is a link between two individuals, then that pair of individuals are
friends. If there is no link between two individuals, then that pair are not friends.
1
2
3 4
5
6
All individuals like Netflix. Specifically, if someone views Netflix they get a benefit of 1.
However, Netflix is costly which is bad. To purchase a Netflix account costs c 2 (0, 1).
Netflix allow multiple devices to stream simultaneously. This means that if some individual purchases a Netflix account, then he/she will share with all of his/her friends.
Each individual has strategy set {0, 1} where 1 means to purchase a Netflix account and
0 means to not purchase. The payo↵ to individual i depends directly on what his/her
friends do. Writing si for the strategy of person i, and si for the vector of strategies of
everyone other than i, the payo↵ to person i, ⇡(si, si) is
⇡i

0, si

=
⇢ 1, if some friend chose to purchase an account
0, if no friend chose to purchase an account
⇡i

1, si

= 1 c, for all si
Answer the following:
(a) 5 marks Does any player have a dominant strategy (strictly or weakly)?
(b) 5 marks Does any player have a dominated strategy (strictly or weakly)?
(c) 10 marks Find all the pure strategy nash equilibria.
(Either write out mathematically or depict graphically.)
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EC3113: Autumn 2019 Philip Neary Assessed Problem Set
3. Netflix with constrained sharing
Now suppose that Netflix change their sharing policy. The purchaser of a Netflix account
is now only allowed to share with a fixed number of others. Specifically, each Netflix
account may only be viewed by the account purchaser and  other people. If an account
holder has (strictly) more than  friends then he/she must choose which  to share with.
If an account holder has less than  friends then he/she may share with all of them.
Suppose that the social network is unchanged. That is, it remains like this:
1
2
3 4
5
6
Answer the following:
(a) 5 marks Write out the strategy set for player 1 for  = 1, 2, and 3.
(b) 5 marks Write out the strategy set for player 3 for  = 1, 2, and 3.
(c) 15 marks Find all the pure strategy nash equilibria for  = 1, 2, and 3.
(Either write out mathematically or depict graphically.)
(d) 5 marks What value for  is optimal for Netflix?
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EC3113: Autumn 2019 Philip Neary Assessed Problem Set
4. Fixed costs
This question is related to what we covered in lecture.
You a smuggler who owns a ship. You have some goods you plan to smuggle. If you
can reach your destination, you can sell the goods on the ship for a net profit of V .
Unfortunately, in order to reach your destination, you must pass two points where there
are corrupt police ocers who will want a bribe. If police ocer i finds you, he will make
a take-it-or-leave-it demand, Pi. If you accept the demand, you pay the police ocer Pi,
and can continue your journey; if not, you return home and have a net return of 0.
The corrupt police ocers try to maximise the amount they earn. (Police ocer i cares
only about what he earns and not what any one else earns.)
You try to maximise profits (money from goods minus payments to police ocers).
We assume that this game is one of perfect information. That is, you know with certainty
that you will meet both police ocers. Everyone knows V , police ocer 2 knows the
demand of police ocer 1 and so on.
(a) 10 marks Draw the game tree.
(You don’t have to draw the entire game tree but you do have to draw a branch for
every part of the game tree.)
(b) 15 marks Compute the subgame-perfect equilibrium and its associated payo↵s.
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EC3113: Autumn 2019 Philip Neary Assessed Problem Set
5. 5 marks Self-evaluation
The total marks available for the previous four questions was 95 marks. What mark out
of 95 do you think you received?
If your prediction is within 8 of the correct total, you will earn 5 marks.
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