Between perfect competition's many price-takers and monopoly's single seller sits the messiest and most economically consequential structure of all: oligopoly, a market with a few firms, each large enough that its own output or pricing decision visibly affects the others, the defining feature economists call strategic interdependence. Once a rival's best move depends on what you do, and your best move depends on what it does, the demand-and-supply machinery of the competitive-market model is no longer enough; you need game theory, the formal study of decisions where the outcome depends on more than one decision-maker.
Nash equilibrium and the prisoner's dilemma
A game is specified by its players, each player's available strategies, and a payoff for every combination of strategies chosen, usually displayed as a payoff matrix for two players with two strategies each. A strategy is a dominant strategy if it is a player's best choice no matter what the other player does, check every row (or column) against every possible response and see if one strategy always wins. A Nash equilibrium is a pair (or set) of strategies, one per player, such that no single player can improve their own payoff by unilaterally switching, given what everyone else is doing, a mutual best response, not necessarily the best joint outcome. The canonical illustration, the Prisoner's Dilemma, is a payoff structure in which each player has a dominant strategy that, played by both, leaves both players worse off than if they had cooperated, the single most important cautionary result in the whole of game theory, because it proves that individually rational behavior does not add up to a collectively rational outcome, and it is the exact logical skeleton behind every failed price war and every collapsed cartel you will ever analyze. Worked Example 8 does not merely assert an abstract Prisoner's Dilemma matrix, it derives one directly from a real (synthetic) oligopoly's own cost and demand curves, so you see the dilemma emerge from the economics rather than being handed as a parable.
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Cournot competition formula
Cournot competition models oligopolists who simultaneously choose quantities, each taking the other's output as given and anticipating how the market-clearing price will respond to the combined total. For n symmetric firms facing linear inverse demand P = a − bQ and constant marginal cost c, each firm's profit-maximizing quantity (found from its own first-order condition, holding rivals' output fixed) solves to a single, general, closed-form Cournot-Nash equilibrium: qi* = (a − c) / ((n+1)b), total quantity Q* = n·qi*, and price P* = (a + nc)/(n+1). The formula is worth sitting with, because it nests both benchmarks you already know: set n = 1 and it collapses to exactly the standalone monopoly solution from monopoly (a single Cournot "competitor" behaves like a monopolist, because there is no rival to react to); let n → ∞ and price falls monotonically toward c, the perfectly competitive outcome from perfect competition. Cournot oligopoly is the entire missing middle of the spectrum, indexed continuously by the number of firms. Worked Example 8 tabulates this convergence for a specific market and shows the price falling steadily as n rises from 1 through 2, 3, 6, and beyond, toward marginal cost, a table you should be able to reproduce for any linear demand-and-cost system, by hand or in Python, on demand.
Bertrand competition and the Bertrand paradox
Bertrand competition models the same few oligopolists choosing prices instead of quantities, each simultaneously trying to undercut the other for a homogeneous, perfectly substitutable good. The result is famously discontinuous with Cournot's smooth convergence and is known as the Bertrand paradox: with even just two identical firms selling an undifferentiated good, each firm's best response to any rival price above marginal cost is to undercut it by the smallest possible amount and capture the entire market, a race that has only one stopping point, P = MC, the fully competitive outcome, reached with as few as two rivals rather than requiring n → ∞. The lesson this contrast teaches, and it is one of the most important, and most counter-intuitive, results in this entire module, is that the number of competitors matters far less than what they compete on. Three Cournot firms can sustain a price comfortably above marginal cost forever (Worked Example 8's own table shows exactly this); two Bertrand firms selling an identical good cannot sustain any markup at all. Whether a real industry behaves more like Cournot or more like Bertrand turns on things this module can now name precisely: how homogeneous the product actually is (differentiation breaks the Bertrand knife-edge, restoring a markup, precisely perfect competition's monopolistic-competition result), whether firms compete on committed capacity rather than infinitely flexible price (a capacity constraint reintroduces Cournot-like behavior even in a price-setting game), and whether the interaction is a one-shot game or a repeated one.
When can firms in an oligopoly collude?
That last distinction is the game-theoretic key to why oligopolies sometimes hold prices up despite Bertrand's pessimistic prediction: if the same rivals interact every period, indefinitely, cooperation (an implicit or explicit agreement to hold the high, collusive price) can become individually rational after all, provided cheating today is punished tomorrow, and provided each firm values future profit enough relative to the present, captured by a discount factor, δ (between 0 and 1, where a δ near 1 means a firm cares almost as much about next period's profit as this period's). Under the simplest enforcement rule, a grim trigger: cooperate as long as the rival has always cooperated, and punish forever (revert to the non-cooperative Nash outcome) the instant a rival deviates, collusion is sustainable if and only if the discounted value of cooperating forever is at least as large as the one-time gain from cheating followed by permanent punishment: δ ≥ (πd − πc) / (πd − πn), where πd is the one-shot payoff from deviating while the rival still cooperates, πc is each firm's payoff from mutual cooperation, and πn is the payoff both earn once punishment sets in (the ordinary, non-cooperative Nash outcome. Bertrand's zero markup, in the harshest case). This single inequality is the formal reason cartels and tacit price coordination can hold, and it is also the reason they frequently don't: raise the temptation to cheat (πd), lower the value of continued cooperation (πc), lower the future weight a firm places on tomorrow's profit (δ), or introduce a detection lag, letting a cheater enjoy the deviation payoff for more than one period before punishment lands, and the threshold discount factor required to sustain collusion rises sharply, exactly as Worked Example 9 computes. The pricing-power section returns to this inequality by name when it reads the Bharti Airtel/Jio telecom shock and the industry's later tariff-hike coordination as two sides of precisely this condition flipping.
Two standard completions of the oligopoly picture sit in EC1.05 rather than here, and the oligopoly story is incomplete without them. The kinked-demand model explains why oligopoly prices are often sticky in both directions, and the Stackelberg solve replaces Cournot's simultaneous move with a leader who commits first and a follower who best-responds, which changes the equilibrium quantities and the profit split. EC1.05 works both on a demand system of the same shape as the one used above.