ECOS2001 · Intermediate Microeconomics
Static Games & Oligopoly
Game theory analyses interaction where each player's payoff depends on what others do. A normal-form game lists players, strategies and payoffs; solution concepts run from dominance (and iterated elimination of dominated strategies) up to Nash equilibrium, a profile where everyone best-responds to everyone else. A pure-strategy Nash equilibrium is a mutual-best-response cell; a mixed-strategy equilibrium makes rivals indifferent. The leading application is Cournot oligopoly: firms choose quantities, each maximising profit given the rival's output, producing reaction functions that intersect at the equilibrium. Compared with the monopoly benchmark (MR = MC) and perfect competition (P = MC), Cournot output lies in between, leaving a deadweight loss.
What this chapter covers
- 01Normal-form games: players, strategies, payoffs
- 02Dominance and iterated elimination of dominated strategies (IESDS)
- 03Best responses and Nash equilibrium (pure strategies)
- 04Mixed-strategy equilibrium: make the rival indifferent
- 05Cournot duopoly: reaction functions, q*, P*, profit
- 06Monopoly benchmark MR = MC and the deadweight loss vs competition
Cournot duopoly: quantities, price, profit and deadweight loss
- 3 marksFirm 1's profit: π₁ = (120 − q₁ − q₂)q₁ − 30q₁. First-order condition: 120 − 2q₁ − q₂ − 30 = 0, giving the reaction function q₁ = (90 − q₂)/2.
- 2 marksBy symmetry q₁ = q₂ = q: substitute to get q = (90 − q)/2 → 2q = 90 − q → 3q = 90 → q = 30. So q₁* = q₂* = 30 and Q = 60.
- 2 marksMarket price: P = 120 − 60 = 60. Each firm's profit: π = (P − MC)·q = (60 − 30)·30 = 30·30 = 900.
- 2 marksPerfect-competition benchmark P = MC = 30 gives Q_c = 120 − 30 = 90. Consumer surplus there CS_c = (1/2)·90·(120 − 30) = (1/2)·90·90 = 4050 (the whole-surplus triangle, since price = MC).
- 1 markCournot total surplus = CS + total profit = (1/2)·60·(120 − 60) + 2·900 = (1/2)·60·60 + 1800 = 1800 + 1800 = 3600. Deadweight loss = 4050 − 3600 = 450.
Key terms
- Dominant strategy
- A strategy that yields a higher payoff than any alternative no matter what rivals do; iterated elimination of dominated strategies (IESDS) simplifies a game by deleting such never-best options.
- Best response
- The strategy that maximises a player's payoff given the others' strategies; a Nash equilibrium is a profile where every player is simultaneously best-responding.
- Cournot equilibrium
- The Nash equilibrium of quantity competition: reaction functions q₁(q₂) and q₂(q₁) intersect at q₁*, q₂*, with price between monopoly and competition.
- Reaction function
- A firm's profit-maximising output as a function of the rival's output, derived from its first-order condition; the intersection of both gives the Cournot outcome.
Static Games & Oligopoly FAQ
How is a Nash equilibrium found in a payoff matrix?
Find each player's best response to every strategy of the other (underline the best payoffs), then look for a cell where both players' best responses coincide — that mutual-best-response cell is a pure-strategy Nash equilibrium. If none exists in pure strategies, solve for a mixed-strategy equilibrium that makes each player indifferent.
Where does monopoly fit, given there is no separate monopoly week?
Monopoly appears as the market-power benchmark inside the competition and games material: a monopolist sets MR = MC, and the Cournot outcome is compared against both monopoly (least output) and perfect competition (most output) to measure the deadweight loss. Collusion in repeated games is also analysed as the firms behaving like one monopoly.
Exam move
Master the Cournot drill — one reaction function, symmetry, then price, profit and deadweight loss — because it is a staple short-answer pattern. Separately practise spotting pure-strategy Nash equilibria by underlining best responses, and the indifference trick for mixed strategies.
