Oligopoly and game theory basics

In short

Oligopoly is a market with a few sellers whose decisions are mutually interdependent, so each firm must guess how rivals will react before choosing price or output. Because there is no single "oligopoly price", economists model the behaviour with game theory - payoff matrices, Nash equilibrium, and the Cournot, Bertrand and Stackelberg solutions. The topic matters in India because most large markets (telecom, cement, paints, aviation, two-wheelers, aerated drinks) are oligopolies and the Competition Commission of India (CCI) prosecutes the collusion the theory predicts. It is examined in BA/MA microeconomics papers, in UGC-NET and Indian Economic Service, and asked in placement rounds for consulting, pricing, FMCG category management and competition-law practice.

Explained

What makes a market oligopoly

• Definition: few sellers, each large enough that its own output or price change visibly affects the market price and hence rivals' profits.
• Mutual interdependence is the defining feature: a firm's best action depends on what rivals do, so the demand curve facing one firm is not determinate without a behavioural assumption.
• Barriers to entry sustain it: scale economies (cement, steel), spectrum or licences (telecom), patents (pharma), brand and distribution (FMCG), network effects (payments, e-commerce).
• Types: *pure/homogeneous* oligopoly (cement, steel, aluminium - products near-identical) versus *differentiated* oligopoly (cars, soaps, smartphones); *collusive* versus *non-collusive*; *open* versus *closed* (entry blocked); duopoly = exactly two sellers.
• Non-price competition dominates differentiated oligopoly - advertising, warranty, dealer network, loyalty points - because a price cut is easily matched while brand strength is not.
• Measurement of concentration: *n-firm concentration ratio* CR₄ = combined market share of the four largest firms; *Herfindahl-Hirschman Index (HHI)* = sum of squared percentage shares. CCI uses market share and HHI-type evidence in merger review, but the Competition Act does not fix statutory HHI thresholds the way some other jurisdictions do.

Non-collusive models

• Cournot (1838) - quantity competition: each firm chooses output assuming the rival's output is fixed; the *reaction function* gives its best output for each rival output, and the intersection is the Cournot-Nash equilibrium. Output exceeds monopoly and falls short of perfect competition; price lies between them.
• With n identical firms and linear demand, each firm's output = (a − c)/((n+1)b) and industry output rises towards the competitive level as n → ∞. This is the standard derivation asked in exams.
• Bertrand - price competition: firms set prices for a homogeneous good; undercutting captures the whole market, so price is driven to marginal cost and profit to zero even with two firms (the Bertrand paradox). Resolved in practice by capacity limits, product differentiation or repeated interaction.
• Stackelberg - sequential quantity choice: a leader moves first, anticipating the follower's reaction function; the leader earns more than in Cournot and the follower less - the first-mover advantage. Leader output = (a − c)/2b, follower = (a − c)/4b in the standard linear case.
• Edgeworth model: duopolists with limited capacity cannot serve the whole market, so prices oscillate between the monopoly price and marginal cost - no stable equilibrium.
• Chamberlin: firms recognise their interdependence and settle at the joint-profit-maximising (monopoly) price without a formal agreement - tacit collusion.
• Sweezy's kinked demand curve: each firm believes rivals will match a price cut (so demand is inelastic below the current price) but ignore a price rise (elastic above). The kink creates a discontinuous MR curve, so marginal cost can shift within the gap without changing price - this explains price rigidity in oligopoly. Criticism: it explains why a price persists but not how it was set in the first place, and empirical support is weak.

Collusion, cartels and price leadership

• Cartel: formal agreement to fix price, restrict output, allocate quotas or share markets; it behaves like a multi-plant monopolist, setting industry MR = MC and allocating quota so each member's MC is equal.
• Why cartels break: each member gains by secretly producing above quota (the prisoner's dilemma applied to cartels); detection is hard, demand fluctuates, cost differences make quota sharing contentious, and new entry attracted by high price.
• Market-sharing collusion: non-price agreement on territories or customers - typically easier to police than price fixing.
• Price leadership: (i) *dominant-firm* leadership - the big firm sets price, small firms act as price takers; (ii) *barometric* leadership - the firm best at reading demand leads and others follow; (iii) *collusive/low-cost* leadership.
• Tacit collusion / conscious parallelism: parallel price movements without agreement; lawful in itself, but with "plus factors" (meetings, information exchange through a trade association, implausible uniformity) it becomes evidence of an agreement.
• Indian law: the Competition Act, 2002 (amended substantially by the Competition (Amendment) Act, 2023) bans anti-competitive agreements under Section 3 - horizontal price fixing, output limitation, market sharing and bid rigging are *presumed* to cause appreciable adverse effect on competition (Section 3(3)); abuse of dominance under Section 4; combinations (mergers) regulated under Sections 5-6. Enforcement is by the CCI, with appeals to NCLAT and then the Supreme Court.
• Leniency: the lesser-penalty provision (Section 46) lets a cartel member that discloses first obtain a reduced penalty - a direct application of the prisoner's dilemma to enforcement design. The 2023 amendment added settlement and commitment mechanisms and allowed penalties to be computed on *global turnover*; detailed regulations have been notified in stages, so verify the current penalty regulations before relying on specifics.
• Well-known Indian cartel findings include the cement manufacturers' case and the tyre manufacturers' case; penalties in several cases have been litigated at NCLAT and the Supreme Court, so treat final amounts as case-specific.

Game theory: the basic apparatus

• Game: players, strategies (complete plans of action), payoffs, and information. Normal (strategic) form = payoff matrix; extensive form = game tree, used for sequential games.
• Zero-sum game: one player's gain equals the other's loss; non-zero-sum (variable-sum) games allow mutual gain - most business games are non-zero-sum.
• Dominant strategy: best regardless of what the rival does. Dominated strategy: worse than another whatever the rival does - eliminate it (*iterated elimination of dominated strategies*).
• Nash equilibrium: a strategy pair where no player can gain by unilaterally changing strategy - each is a best response to the other. May be none in pure strategies, one, or many.
• Mixed strategy: randomising over actions with chosen probabilities; every finite game has at least one Nash equilibrium in mixed strategies (Nash's theorem). Needed for games like matching pennies that have no pure-strategy equilibrium.
• Maximin (Wald) criterion: choose the strategy whose worst outcome is best - the conservative rule; minimax is its counterpart for the loss-minimising player. In a strictly determined zero-sum game maximin = minimax = the value of the game (*saddle point*).
• Prisoner's dilemma: confessing (or cheating on a cartel) is the dominant strategy for each, so both end worse off than under cooperation - individual rationality defeats collective rationality. This is the single most asked game in Indian exams and interviews.
• Repeated games: with indefinite repetition, cooperation can be sustained by tit-for-tat or grim trigger punishment, provided the discounted future gain from cooperating exceeds the one-period gain from cheating (the *folk theorem* intuition). A known finite end-date unravels cooperation by backward induction.
• Sequential games and credibility: solve by backward induction (subgame-perfect equilibrium); only threats that are profitable to carry out are credible. A firm can make a threat credible by irreversible commitment - building excess capacity to deter entry.
• Other standard games: *battle of the sexes* (coordination with conflicting preference), *stag hunt* (coordination), *chicken* (brinkmanship, used for price wars), *entry deterrence* game, *Bertrand pricing* game.
• First-mover versus second-mover advantage: first-mover wins in quantity games (Stackelberg); moving second can be better where information is revealed or standards are learned.

Evaluation: efficiency and welfare

• Allocative outcome: price above marginal cost creates deadweight loss, though less than under monopoly; Cournot price falls as the number of firms rises.
• Dynamic argument (Schumpeter, Galbraith): oligopolists have both the profit and the scale to fund R&D, so innovation may be higher than under atomistic competition.
• Costs: wasteful advertising, excess capacity, price rigidity that slows adjustment, and the risk of collusion against consumers.
• Contestable markets theory: even two firms behave competitively if entry and exit are costless - what disciplines firms is the *threat* of entry, not the current count.
• Indian policy stance: behaviour is regulated (Competition Act), not structure - size itself is not an offence; the MRTP Act, 1969 was repealed and replaced by the competition regime. Sector regulators overlay it: TRAI (telecom tariffs and interconnection), RBI/NPCI (payments market-share caps), PNGRB, CERC/SERCs, IRDAI, SEBI, and DGCA/airport economic regulation.

Key points

• Oligopoly - few interdependent sellers; the firm's demand curve is indeterminate without an assumption about rivals' reactions.
• Duopoly - two sellers; the simplest setting for Cournot, Bertrand and Stackelberg.
• Cournot equilibrium - firms compete in quantity; intersection of reaction curves; output between monopoly and competition.
• Bertrand equilibrium - firms compete in price with a homogeneous good; price = MC, zero profit (Bertrand paradox).
• Stackelberg equilibrium - sequential quantities; leader produces twice the follower and earns more (first-mover advantage).
• Kinked demand curve - rivals match cuts but not rises; discontinuous MR explains sticky prices.
• Cartel - formal collusion acting as a joint monopolist; unstable because cheating pays each member.
• Price leadership - dominant, barometric or collusive; a coordination device without a formal agreement.
• Nash equilibrium - mutual best responses; no unilateral gain from deviating.
• Dominant strategy - best whatever the rival does; a dominant-strategy equilibrium is always a Nash equilibrium, not conversely.
• Prisoner's dilemma - the dominant-strategy outcome is jointly worse; explains cartel breakdown and leniency programmes.
• Mixed strategy - randomisation; guarantees existence of equilibrium in finite games.
• Maximin/minimax and saddle point - conservative solution of a zero-sum game; equal values give the game's value.
• Backward induction and credibility - sequential games are solved from the end; non-credible threats are ignored.
• Tit-for-tat - punishment strategy that sustains cooperation in indefinitely repeated games.
• HHI and CR₄ - concentration measures; HHI = Σ(share %)², maximum 10,000 for a monopoly.
• Section 3(3), Competition Act, 2002 - price fixing, output restriction, market sharing and bid rigging presumed anti-competitive; CCI enforces, NCLAT hears appeals.
• Contestability - the threat of entry, not the number of firms, can enforce competitive pricing.

Formulas and examples

Example 1 - Cournot duopoly. Market demand P = 120 − 2Q (₹ per unit, Q in thousand units); both firms have MC = ₹20, no fixed cost.

• Firm 1's profit = (120 − 2q₁ − 2q₂)q₁ − 20q₁. Setting MR = MC: 120 − 4q₁ − 2q₂ = 20 ⇒ q₁ = (100 − 2q₂)/4 = 25 − 0.5q₂.
• By symmetry q₂ = 25 − 0.5q₁. Solving: q = 25/1.5 = 16.67 thousand units each, Q = 33.33.
• Check with the formula: a = 120, b = 2, c = 20, n = 2 ⇒ q = (120 − 20)/(3 × 2) = 16.67. ✔
• P = 120 − 2(33.33) = ₹53.33; profit per firm = (53.33 − 20) × 16.67 = ₹555.6 thousand.
• *Monopoly/cartel benchmark:* Q = (120 − 20)/(2 × 2) = 25, P = (120 + 20)/2 = ₹70, industry profit = 50 × 25 = ₹1,250 thousand (₹625 each) - higher than the Cournot total of ₹1,111 thousand, which is exactly why the cartel is tempting.
• *Perfect competition benchmark:* P = MC = ₹20, Q = 50, profit = 0.

Example 2 - Stackelberg with the same numbers. Leader anticipates q_F = 25 − 0.5q_L.

• Leader profit = (120 − 2q_L − 2(25 − 0.5q_L))q_L − 20q_L = (70 − q_L)q_L − 20q_L = 50q_L − q_L².
• d/dq_L = 50 − 2q_L = 0 ⇒ q_L = 25; q_F = 25 − 12.5 = 12.5; Q = 37.5; P = 120 − 75 = ₹45.
• Leader profit = (45 − 20) × 25 = ₹625 thousand; follower profit = 25 × 12.5 = ₹312.5 thousand.
• Moving first raises the leader's profit from ₹555.6 to ₹625 thousand and cuts the follower's to ₹312.5 thousand.

Example 3 - prisoner's dilemma in a price war. Two cement firms choose High or Low price; payoffs are profits in ₹ crore (Firm A, Firm B):

• If B plays High, A gets 60 by Low versus 50 by High → Low is better. If B plays Low, A gets 30 by Low versus 20 by High → Low is better.
• So Low is A's dominant strategy, and by symmetry B's. The unique Nash equilibrium is (Low, Low) = (30, 30), though (High, High) = (50, 50) is better for both. This is the cartel's instability in one table.
• *Sustaining cooperation:* one-period gain from cheating = 60 − 50 = 10; permanent loss if punished = 50 − 30 = 20 per period thereafter. Grim-trigger cooperation pays if 10 ≤ δ(20)/(1 − δ) ⇒ 10 − 10δ ≤ 20δ ⇒ δ ≥ 1/3, i.e. a discount rate r ≤ 200%. With patient firms and frequent interaction, tacit collusion is easy - which is why CCI treats concentrated, repeated-bidding markets as high risk.

Example 4 - mixed strategy in an anti-coordination (chicken-type) game. Firm A chooses Advertise/Not; Firm B chooses Advertise/Not; payoffs (A, B) in ₹ lakh:

• Here the two off-diagonal cells (Ad, No Ad) and (No Ad, Ad) are pure-strategy Nash equilibria, but neither is reachable when the firms move simultaneously without coordination, so the symmetric solution is a mixed-strategy equilibrium. Let A advertise with probability p. B's payoff from Ad = p(0) + (1 − p)(3) = 3 − 3p; from No Ad = p(1) + (1 − p)(0) = p.
• Indifference: 3 − 3p = p ⇒ p = 0.75. By symmetry B advertises with probability 0.75 (solving A's indifference the same way, with B's probability q: 3(1 − q) = q ⇒ q = 0.75... note the roles reverse, so each firm advertises with probability 0.75 in this symmetric game).
• A's expected payoff = 0.75(0.75 × 0 + 0.25 × 3) + 0.25(0.75 × 1 + 0.25 × 0) = 0.75(0.75) + 0.25(0.75) = ₹0.75 lakh.

Example 5 - concentration measurement. Market shares in a four-firm industry: 40%, 30%, 20%, 10%.

• CR₄ = 40 + 30 + 20 + 10 = 100%; CR₂ = 70%.
• HHI = 40² + 30² + 20² + 10² = 1,600 + 900 + 400 + 100 = 3,000 - highly concentrated.
• If the two smallest merge (shares become 40, 30, 30): HHI = 1,600 + 900 + 900 = 3,400, a rise of 400 - the kind of delta that invites close scrutiny in merger review.
• Lerner index check: in Example 1 at Cournot, L = (53.33 − 20)/53.33 = 0.625, so the implied firm-level demand elasticity is 1/0.625 = 1.6.

Where it is used

• Competition law and economics: CCI, law firms and economic consultancies build cartel screens, bid-rigging analysis and merger HHI simulations; game theory underpins the leniency programme's design.
• Telecom and spectrum auctions: DoT/TRAI auction design, reserve prices and bidding strategy in a three-private-player market (Reliance Jio, Bharti Airtel, Vodafone Idea plus BSNL) are pure game theory.
• Pricing and category management: FMCG, paints, cement, tyres, airlines and quick-commerce firms run competitor-reaction models; Stackelberg logic drives new-product launch timing and airline fare matching.
• Public procurement and tendering: NHAI, Indian Railways, CPWD and PSU tenders use bid-rigging detection and reverse-auction design on GeM; identical bids and rotation patterns are standard red flags.
• Strategy consulting and MBA-track roles: cases at McKinsey, BCG, Bain and Big-Four consulting routinely ask Nash equilibrium, entry deterrence and price-war reasoning.
• Regulated-sector analysis: power exchanges and CERC market-power monitoring, port and airport tariff setting, and RBI/NPCI's market-share cap on UPI apps are all oligopoly interventions.

Interview questions

• Q: Why is an oligopolist's demand curve indeterminate? A: Because the quantity it sells at any price depends on rivals' reactions, which are not given by the market data alone - a behavioural assumption must be added.
• Q: What is a Nash equilibrium in plain words? A: A combination of strategies in which no player can improve its payoff by changing its own strategy while the others keep theirs.
• Q: Is every dominant-strategy equilibrium a Nash equilibrium, and conversely? A: Every dominant-strategy equilibrium is Nash, but many Nash equilibria involve no dominant strategy - Nash is the weaker, more general concept.
• Q: Why does the Bertrand model give price = marginal cost with just two firms? A: With identical products, any firm pricing a rupee below the rival takes the whole market, so undercutting continues until no margin is left.
• Q: How does Cournot output compare with monopoly and competition? A: It lies between them: total output is higher and price lower than monopoly, but output is lower and price higher than perfect competition, and it approaches the competitive outcome as the number of firms rises.
• Q: Why does the leader earn more in Stackelberg than in Cournot? A: By committing to a large output first, it forces the follower onto its reaction curve and shifts the residual demand in its favour - credible commitment is the source of the advantage.
• Q: What does the kinked demand curve explain and what does it fail to explain? A: It explains price rigidity through a discontinuous MR curve, but not how the prevailing price was reached, and empirical support for the asymmetric reaction is weak.
• Q: Why do cartels collapse? A: Each member's dominant strategy is to exceed quota secretly, cost and demand differences make quotas contentious, and high prices attract entry - the classic prisoner's dilemma.
• Q: How can collusion survive if cheating is dominant in one period? A: With indefinite repetition and patient firms, punishment strategies such as tit-for-tat or grim trigger make the discounted loss from retaliation exceed the one-shot gain.
• Q: What makes a threat credible, and give a business example? A: It must be in the threatener's own interest to carry out; building irreversible excess capacity or a low-cost plant makes a "we will flood the market" threat credible to an entrant.
• Q: Which Indian law deals with cartels and what is presumed under it? A: The Competition Act, 2002, as amended in 2023 - under Section 3(3), horizontal price fixing, output limitation, market sharing and bid rigging are presumed to have an appreciable adverse effect on competition, enforced by the CCI with appeals to NCLAT.
• Q: Is parallel pricing by itself illegal in India? A: No - identical prices can result from similar costs; CCI needs an agreement or understanding, usually shown through plus factors such as meetings, information exchange or implausibly uniform conduct.

Common mistakes

• Treating Cournot and Bertrand as interchangeable - one is quantity competition with positive profit, the other price competition with zero profit; the exam question's wording decides which.
• Forgetting to double the quantity coefficient when deriving MR from P = a − bQ, so the reaction function comes out wrong (MR = a − 2bq₁ − bq₂ for firm 1, not a − bq₁ − bq₂).
• Writing total output instead of per-firm output when using qᵢ = (a − c)/((n+1)b), or using it when the firms have unequal marginal costs.
• Claiming the prisoner's dilemma has no Nash equilibrium - it has exactly one; what it lacks is Pareto efficiency.
• Looking for a pure-strategy equilibrium only, and concluding "no equilibrium exists" instead of solving for mixed strategies.
• Using the kinked demand curve to explain the *level* of price, and drawing a continuous MR through the kink.
• Confusing an HHI based on fractions (maximum 1) with one based on percentages (maximum 10,000), or citing a statutory Indian HHI threshold - the Act works through market share, dominance and effects, not a fixed HHI number.

Related topics

Perfect competition and monopoly · Production and costs · Elasticity of demand · Welfare economics and market failure · Behavioural and information economics · Managerial economics