In the classic Prisoner's Dilemma, the Nash equilibrium (Defect, Defect):

Is stable against unilateral deviation but is not Pareto-efficient

Is both stable and Pareto-efficient

Does not exist because both players have a dominant strategy

Requires the two players to cooperate

A dominant strategy in a non-cooperative game is one that:

Gives a player their best payoff regardless of the opponent's strategy

Requires knowledge of the opponent's payoff function only

Is only defined in cooperative games

Always leads to a Pareto-efficient outcome

The long-run equilibrium under monopolistic competition shows firms producing:

At P = AC but above the minimum point of AC — excess capacity

At P = MC = minimum AC, exactly as under perfect competition

At MR = MC with P far above AC, earning supernormal profit indefinitely

Only perfect competition, among the standard market structures, achieves in long-run equilibrium:

Both allocative efficiency (P = MC) and productive efficiency (output at minimum AC)

A single equilibrium concept applicable to any number of firms

A profit-maximising firm's demand for a factor of production is a derived demand because:

It exists only because of the demand for the final good the factor helps produce

Factor prices are always fixed by the government

Factors have no marginal product

Factor markets are always perfectly competitive

MRP equals VMP for a factor of production when:

The firm sells its output in a perfectly competitive product market (MR = P)

The firm is a monopolist in the product market

The firm is a monopsonist in the factor market

The factor is perfectly inelastic in supply

A monopsonist (single buyer) in the factor market hires up to the point where:

MRP = marginal factor cost (MFC), with MFC above the factor price, hiring less than the competitive quantity

MRP = the average factor price, hiring exactly the competitive quantity

The factor supply curve is perfectly elastic

Which of the following are standard oligopoly models that assume DIFFERENT strategic variables or timing?

Cournot (simultaneous quantity choice)

Bertrand (simultaneous price choice)

Cournot (simultaneous quantity choice)

Bertrand (simultaneous price choice)

Perfect competition (price-taking behaviour)

Non-Cooperative Game Theory, Market Structures and Factor Pricing

Strategic interaction and market structure are two sides of the same question — how do a small number of interdependent decision-makers behave? This chapter covers non-cooperative game theory, the spectrum of market structures from perfect competition to oligopoly and their efficiency properties, and the marginal-productivity theory of factor pricing.

1. Non-Cooperative Game Theory: Dominant Strategy and Nash Equilibrium

A non-cooperative game models players who cannot make binding agreements — each chooses a strategy independently to maximise their own payoff, taking the other's likely choice into account. A dominant strategy gives a player their best payoff regardless of what the opponent does. A Nash equilibrium is a strategy pair (or profile, with more players) where neither player can improve their own payoff by unilaterally changing strategy, given the other's strategy — it need not be Pareto-efficient, which is exactly what the Prisoner's Dilemma is built to show.

The Prisoner's Dilemma payoff matrix (years in prison — lower is better)
Player A \ Player B	B cooperates (stays silent)	B defects (confesses)
A cooperates (stays silent)	A: 1, B: 1	A: 10, B: 0
A defects (confesses)	A: 0, B: 10	A: 5, B: 5

⚠️ Nash equilibrium is not Pareto-efficient here

Confessing (defecting) is each player's dominant strategy — whatever the other does, confessing gives a strictly better payoff — so (Defect, Defect) is the unique Nash equilibrium, at (5, 5) years. Yet (Cooperate, Cooperate), at (1, 1) years, is Pareto-superior for both players. The dilemma is precisely that individually rational strategy choices produce a jointly worse outcome than a coordinated one — NET tests this contrast (dominant-strategy/Nash outcome versus the Pareto-superior cooperative outcome) directly.

2. Market Structures: Competitive and Non-Competitive Equilibria

Perfect competition (many price-taking firms, homogeneous product, free entry/exit) reaches a long-run equilibrium at P = MC = minimum AC, with zero economic (supernormal) profit. Monopoly (a single seller facing the entire market demand curve) equates MR = MC but charges a price above marginal cost, since MR < P for a downward-sloping demand curve; this restricts output below the competitive level and creates a deadweight loss. Monopolistic competition (many firms, differentiated products, free entry) reaches long-run equilibrium at P = AC but above minimum AC — the excess-capacity result — because free entry drives profit to zero while product differentiation still gives each firm some price-setting power. Oligopoly (few interdependent firms) has no single equilibrium concept; the Cournot model (firms choose quantities simultaneously) and Bertrand model (firms choose prices simultaneously) give different Nash equilibria for the same market, and Stackelberg (sequential quantity leadership) gives a first-mover advantage.

Long-run equilibrium and efficiency across market structures
Structure	Long-run price/output rule and efficiency
Perfect competition	P = MC = min AC; both allocative (P = MC) and productive (min AC) efficiency achieved.
Monopoly	MR = MC but P > MC; allocative inefficiency (deadweight loss) and typically output below minimum-AC scale.
Monopolistic competition	P = AC (zero profit) but above minimum AC; excess capacity, allocative inefficiency (P > MC) persists.
Oligopoly	No single price/output rule; outcome depends on the strategic model assumed (Cournot, Bertrand, Stackelberg, collusive).

3. Factor Pricing: The Marginal Productivity Theory

The marginal productivity theory says a profit-maximising firm hires a factor up to the point where its marginal revenue product (MRP = marginal physical product × marginal revenue) equals the factor's price. In a perfectly competitive product market (MR = P), MRP coincides with the value of marginal product (VMP = MPP × P); under imperfect competition in the product market, MRP < VMP because MR < P. The demand for a factor is therefore a derived demand — it exists only because of the demand for the final good it helps produce — and the factor demand curve is the (declining, from diminishing marginal product) MRP curve itself.

ℹ️ MRP versus VMP — where they coincide and where they diverge

Whether MRP equals VMP depends entirely on the product market, not the factor market: with a competitive product market, MR = P at every output level, so MRP = VMP always. With a monopolist or monopolistically competitive seller in the product market, MR < P beyond the first unit, so MRP < VMP — the firm's factor demand curve lies below the value-of-marginal-product curve, a distinction NET has tested as a numerical/graph item.

4. Factor Market Equilibrium and Its Efficiency Implication

Competitive factor and product markets — every factor is paid its VMP, and this pricing rule is exactly what makes the competitive general equilibrium allocatively efficient (see the next chapter's fundamental theorems).
Monopsony (a single buyer of the factor) — the firm faces an upward-sloping factor supply curve, so marginal factor cost (MFC) exceeds the factor price; equilibrium hiring is where MRP = MFC, below the competitive quantity, and the factor is paid less than its MRP.

📖 Why factor pricing sits right before general equilibrium in the syllabus

The MRP = factor price rule is the microeconomic mechanism that a Walrasian general equilibrium system needs to close: households supply factors and are paid marginal products, firms hire factors and sell output, and the whole system's consistency (income paid out exactly equals income earned, exactly equals the value of output) is what the next chapter's general equilibrium analysis formalises.

Key takeaways

A dominant strategy dominates regardless of the opponent's choice; a Nash equilibrium is stable against unilateral deviation but need not be Pareto-efficient — the Prisoner's Dilemma's (Defect, Defect) outcome is the textbook illustration.
Perfect competition alone reaches P = MC = min AC (both allocative and productive efficiency); monopoly restricts output below it, monopolistic competition leaves excess capacity, and oligopoly has no single equilibrium concept (Cournot, Bertrand, Stackelberg give different outcomes).
The marginal productivity theory hires a factor until MRP = factor price; MRP = VMP only under a competitive product market, and factor demand is a derived demand.
A monopsonist (single factor buyer) faces MFC above the factor price and hires where MRP = MFC, below the competitive quantity, paying the factor less than its MRP.
Competitive factor pricing (payment equal to VMP) is the micro-level mechanism that closes the Walrasian general equilibrium system covered in the next chapter.

Practice questions (9)

Attempt each one before opening the answer. Every explanation names the tempting wrong option as well as the right one, because that is where marks are lost.

In the classic Prisoner's Dilemma, the Nash equilibrium (Defect, Defect):
1. Is stable against unilateral deviation but is not Pareto-efficient
2. Is both stable and Pareto-efficient
3. Does not exist because both players have a dominant strategy
4. Requires the two players to cooperate
Show answer
Answer: A — Is stable against unilateral deviation but is not Pareto-efficient
(Defect, Defect) is a Nash equilibrium precisely because confessing is each player's dominant strategy, but (Cooperate, Cooperate) gives both players a strictly better payoff — the dilemma's whole point is that Nash equilibrium need not be Pareto-efficient.
A dominant strategy in a non-cooperative game is one that:
1. Gives a player their best payoff regardless of the opponent's strategy
2. Requires knowledge of the opponent's payoff function only
3. Is only defined in cooperative games
4. Always leads to a Pareto-efficient outcome
Show answer
Answer: A — Gives a player their best payoff regardless of the opponent's strategy
A dominant strategy is best for a player no matter what the opponent does; it is a non-cooperative-game concept and, as the Prisoner's Dilemma shows, need not lead to a Pareto-efficient outcome.
The long-run equilibrium under monopolistic competition shows firms producing:
1. At P = AC but above the minimum point of AC — excess capacity
2. At P = MC = minimum AC, exactly as under perfect competition
3. At MR = MC with P far above AC, earning supernormal profit indefinitely
4. Below their shutdown point
Show answer
Answer: A — At P = AC but above the minimum point of AC — excess capacity
Free entry drives long-run profit to zero (P = AC), but product differentiation still lets each firm face a downward-sloping demand curve, so the tangency occurs above minimum AC — the excess-capacity theorem.
Only perfect competition, among the standard market structures, achieves in long-run equilibrium:
1. Both allocative efficiency (P = MC) and productive efficiency (output at minimum AC)
2. Zero economic profit only
3. Product differentiation
4. A single equilibrium concept applicable to any number of firms
Show answer
Answer: A — Both allocative efficiency (P = MC) and productive efficiency (output at minimum AC)
Monopoly and monopolistic competition both leave P > MC (allocative inefficiency); monopolistic competition also leaves output below the minimum-AC scale (excess capacity) even though profit is zero — only perfect competition delivers both efficiency properties together.
A profit-maximising firm's demand for a factor of production is a derived demand because:
1. It exists only because of the demand for the final good the factor helps produce
2. Factor prices are always fixed by the government
3. Factors have no marginal product
4. Factor markets are always perfectly competitive
Show answer
Answer: A — It exists only because of the demand for the final good the factor helps produce
A factor is demanded only instrumentally, for the output it can produce and sell — hence the label 'derived' demand — and its demand curve is the (declining) marginal revenue product curve.
MRP equals VMP for a factor of production when:
1. The firm sells its output in a perfectly competitive product market (MR = P)
2. The firm is a monopolist in the product market
3. The firm is a monopsonist in the factor market
4. The factor is perfectly inelastic in supply
Show answer
Answer: A — The firm sells its output in a perfectly competitive product market (MR = P)
MRP = MPP × MR and VMP = MPP × P; the two coincide only when MR = P, which holds precisely in a perfectly competitive product market — under any imperfectly competitive product market MR < P, so MRP < VMP.
A monopsonist (single buyer) in the factor market hires up to the point where:
1. MRP = marginal factor cost (MFC), with MFC above the factor price, hiring less than the competitive quantity
2. MRP = the average factor price, hiring exactly the competitive quantity
3. MFC = 0
4. The factor supply curve is perfectly elastic
Show answer
Answer: A — MRP = marginal factor cost (MFC), with MFC above the factor price, hiring less than the competitive quantity
Facing an upward-sloping factor supply curve, a monopsonist's marginal factor cost exceeds the average factor price; equating MRP to MFC (not to the factor price itself) yields hiring below the competitive level and payment below MRP.
Which of the following are standard oligopoly models that assume DIFFERENT strategic variables or timing?
1. Cournot (simultaneous quantity choice)
2. Bertrand (simultaneous price choice)
3. Stackelberg (sequential quantity leadership)
4. Perfect competition (price-taking behaviour)
Show answer
Answer: A — Cournot (simultaneous quantity choice); B — Bertrand (simultaneous price choice); C — Stackelberg (sequential quantity leadership)
Cournot, Bertrand and Stackelberg are all oligopoly models differing in strategic variable (quantity vs price) or timing (simultaneous vs sequential); perfect competition is a separate market structure altogether, with no strategic interaction between price-taking firms.
Name the theorem describing monopolistic competition's long-run outcome of firms producing at P = AC but above the minimum point of the AC curve.
Numerical answer — type the value.
Show answer
Answer: excess capacity theorem
The excess-capacity theorem is the standard name for this result — free entry eliminates profit but product differentiation keeps each firm's demand curve downward-sloping, so the tangency solution sits above minimum efficient scale.