Problem 1 — Quality Products vs. Perfection Performed
Setup
Two firms independently choose whether to advertise.
(Advertise, Advertise) \u2192 each earns $500.
(One Advertises, other does not) \u2192 advertiser $1000, other $0.
(Neither) \u2192 each earns $700.
Question 1a — Completed Payoff Matrix
Fill in the matrix given the payoff descriptions.
Perfection Performed
Advertise
Not Advertise
Quality Products
Advertise
QP=500 PP=500
QP=1000 PP=0
Not Advertise
QP=0 PP=1000
QP=700 PP=700
Interpretation: green cell = joint-profit-maximizing (cooperative) outcome. Diagonal "both advertise" isn't shown colored; it's the Nash outcome.
Question 1b — Best joint outcome
Which strategy pair gives the greatest joint profit?
Both Not Advertise — joint profit $1,400
Joint totals: (A,A)=1000; (A,N)=1000; (N,A)=1000; (N,N)=1400.Advertising here cancels out: it's a zero-sum transfer paid to ad networks. Both firms are better off not advertising.
Question 1c — QP's dominant strategy
Advertise
If PP advertises: QP earns 500 (Advertise) vs 0 (Not). Advertise wins.If PP doesn't: QP earns 1000 (Advertise) vs 700 (Not). Advertise wins.Advertise is strictly dominant for QP.
Question 1d — PP's dominant strategy
Advertise
By symmetry, PP faces the same payoffs. If QP advertises, PP gets 500 vs 0. If QP doesn't, PP gets 1000 vs 700.Advertise is strictly dominant for PP too.
Question 1e — Predicted outcome / joint profit
(Advertise, Advertise) — joint profit = $1,000
Both players play their dominant strategy, giving the Nash equilibrium (Advertise, Advertise). Each earns $500; joint profit = $1,000.Prisoner's dilemma: self-interested play ($1,000 total) beats the cooperative ideal ($1,400 total) by $400.
Problem 2 — Ricky Rock Star vs. Harry Hip Hop
Setup
Each musician captures his own genre alone for $5M. Together they can also win a $3M fusion audience (split evenly). If one collaborates while the other goes alone, the solo artist scoops his own market + the fusion audience ($8M); the collaborator gets $0 (too late to release). If both go alone, the fusion audience is disillusioned and dies.
Both Collaborate: each keeps own $5M + half of $3M fusion = $5M + $1.5M = $6.5M.One alone, one collab: solo releases first, grabs own $5M + fusion $3M = $8M; collaborator = $0.Both alone: each keeps own $5M; fusion dies.
Question 2b — Is there a strictly dominant strategy for Ricky?
Yes — Alone strictly dominates Collaborate
If Harry Alone: Ricky earns 5 (Alone) > 0 (Collab).If Harry Collaborates: Ricky earns 8 (Alone) > 6.5 (Collab).Alone wins in every column \u2192 strictly dominant.
Question 2c — Is there a strictly dominant strategy for Harry?
Yes — Alone strictly dominates Collaborate
By symmetry: if Ricky Alone, Harry earns 5 > 0. If Ricky Collaborates, Harry earns 8 > 6.5. Alone always wins.
Both dominant strategies intersect at (Alone, Alone). This is the unique Nash equilibrium: neither wants to unilaterally switch to Collaborate (would drop from $5M to $0).
Question 2e — Is this outcome socially optimal?
No — (Collaborate, Collaborate) at ($6.5M, $6.5M) is socially optimal
Pareto check: moving from (Alone, Alone)=(5,5) to (Collab, Collab)=(6.5, 6.5) makes both musicians strictly better off \u2014 so (Alone, Alone) is Pareto-inefficient.Total surplus: (Alone, Alone) = $10M. (Collab, Collab) = $13M \u2014 the fusion audience's $3M is finally served.Classic prisoner's dilemma: individually rational behavior yields a socially suboptimal outcome. Without an enforceable contract, each musician fears being stranded at $0 and defects to Alone.
Multiple Choice — Figure 17-1 and Table 17-6
Figure 17-1 (for MC 1 & 2)
Duopoly market. Demand P = 10 \u2212 Q (intercepts (0,10) and (10,0)). MR = 10 \u2212 2Q (intercepts (0,10) and (5,0)). Horizontal MC at $6. Zero fixed cost.
MC 1 — Collusion outcome
Two firms able to collude successfully produce:
B Q = 2, P = $8
Collude = monopoly: MR = MC.10 \u2212 2Q = 6 \u2192 2Q = 4 \u2192 Q = 2P from demand: P = 10 \u2212 Q = 10 \u2212 2 = $8Reading P off MR here would give only MR(2) = $6 \u2014 the classic trap.
MC 2 — Per-firm profit under collusion (zero FC)
B $2.00 per firm
Total revenue: P \u00d7 Q = 8 \u00d7 2 = $16Total cost: MC \u00d7 Q (zero FC) = 6 \u00d7 2 = $12Total profit: 16 \u2212 12 = $4 \u2192 split evenly = $2 per firm
Table 17-6 (for MC 3\u20136)
HomeMax vs. Lopes expansion game. Each cell shows (Lopes $M, HomeMax $M).
Lopes
Expand
Do Not
HomeMax
Expand
L=1.0 HM=1.5
L=0.4 HM=3.4
Do Not
L=3.2 HM=0.6
L=2.0 HM=2.5
MC 3 — Lopes's best response
C Expand regardless of HomeMax's decision
If HomeMax Expand: Lopes = 1.0 (Expand) > 0.4 (Not)If HomeMax Not: Lopes = 3.2 (Expand) > 2.0 (Not)Expand dominates Not for Lopes.
MC 4 — HomeMax's best response
C Expand regardless of Lopes's decision
If Lopes Expand: HomeMax = 1.5 (Expand) > 0.6 (Not)If Lopes Not: HomeMax = 3.4 (Expand) > 2.5 (Not)Expand dominates Not for HomeMax.
MC 5 — Lopes's profit at dominant-strategy outcome
B $1.0 million
Both play Expand \u2192 top-left cell \u2192 Lopes = $1.0M.
MC 6 — Nash equilibrium profits
A HomeMax = $1.5M · Lopes = $1.0M
Nash = (Expand, Expand). HomeMax = $1.5M, Lopes = $1.0M.This is a prisoner's dilemma: the (Not Expand, Not Expand) cell at ($2.5M, $2.0M) is better for both, but neither can credibly commit to it.
MC 7 — Which example is an oligopoly?
C A city with two firms licensed to sell school uniforms
Definition: oligopoly = a few firms with strategic interdependence.A: many sellers of homogeneous product = perfect competition. B: one seller = monopoly. D: many differentiated sellers = monopolistic competition. C: two sellers licensed = duopoly = oligopoly.
True or False — Game Theory & Oligopoly
TF 8 — Game theory is just as necessary for competitive/monopoly markets as oligopoly.
B False
Game theory is essential only where firms strategically interact. Competitive firms are price takers; monopolists have no rivals. Game theory matters most for oligopoly.
TF 9 — In competitive markets, strategic interactions are not important.
A True
A competitive firm is too small to affect the market price and doesn't strategize against specific rivals. It just sells at P.
TF 10 — Oligopolies produce more under collusion than without.
B False
Collusion = joint monopoly \u2192 firms restrict output to push the price up. Oligopolies produce less when they collude. In Figure 17-1: collusion Q = 2; Nash competition would push Q closer to 4.
TF 11 — Dominant strategy = best regardless of opponents.
A True
Textbook definition. In our two scenarios, the dominant strategies are Advertise (Q1) and Alone (Q2).