Monopolistic Competition and Oligopoly

This is Unit Nine of Principles of Microeconomics, part two of two: Nash equilibrium, the cartel as a game, and the four market structures side by side. Part one closed on the dominant strategy, and on the fact that many games have none. This part supplies the more general idea, a set of choices where nobody gains by changing alone, and uses it on a cartel, on a coordination game, and on the question of why tacit collusion survives where formal cartels cannot. It ends by placing all four structures on one table, where the decision rule never changes and only the demand curve does. By the end you will be able to define Nash equilibrium and read a payoff matrix in four steps. To model a duopoly cartel as a game. To find the equilibria of a game with no dominant strategy. To say what repetition and a kinked demand curve do to pricing. And to classify a market structure, hold all four on one table, and explain why the cartel breaks.

Three entries on Nash equilibrium and the matrix: the general idea, the four-step reading, and the cartel as a game.

The more general idea.

MIC 0826 Nash Equilibrium

A Nash equilibrium is a set of strategies, one per player, where each choice is the best reply to the others', so nobody gains by changing alone; every dominant strategy equilibrium is one, and both confessing is one, since given the other's confession neither would switch. The term is the exam's, from Nash's nineteen fifty paper; neither source uses it.

Reading a matrix with both ideas.

MIC 0827 Reading a Payoff Matrix

Four steps. For the row player, compare its payoffs down each column and mark its better choice in each; if the same row wins both, that is its dominant strategy. Do the same for the column player across each row. A cell where both players' marks meet is a Nash equilibrium. Then compare it with the cell both would prefer, if one exists, and name the gap. Two bottlers each choose to hold output or expand: both hold, ten million each; one expands while the other holds, fourteen against four; both expand, six each. For the first firm expanding beats holding whether the rival holds or expands, so it is dominant, and the same holds for the second. Both expand, six each, is the Nash equilibrium, and both would prefer the ten each from holding. Compare a player's own payoffs only, never the two players' against each other, and find the equilibrium where the marks meet, not in the cell with the largest total.

The game as a cartel.

MIC 0828 The Duopoly Game

Take that matrix with hold output as cooperating and expand as cheating. Cheating is each firm's dominant strategy, both cheating is the Nash equilibrium, and the cooperative cell pays both more. The price mechanism behind the numbers: the cheater sells more at nearly the cartel price, the holder loses share, and when both cheat the extra output pushes the price down for both. The two bottlers agree to hold output and share a monopoly profit of twenty million, ten each. If one quietly expands it earns fourteen while the other's sales fall to four; if both expand the price falls and each earns six. Each firm's best reply to any choice by the other is to expand, so both do, and the twenty million shrinks to twelve. The cheater's fourteen depends on the other holding, which is why the cartel cannot rest on one firm's honesty, and the numbers are illustrative: what makes the game a dilemma is only the ordering of the four payoffs.

Three entries beyond the dominant strategy: a game with none, what repetition changes, and the kinked demand curve.

A game with no dominant strategy.

MIC 0829 A Game Without a Dominant Strategy

Some games have no dominant strategy, and then only the Nash idea works. Mark each player's best reply to each choice by the other, as before; if a player's best reply changes with the other's choice, it has no dominant strategy. A Nash equilibrium is still any cell where both best replies meet, and there may be more than one, or none in pure choices; report every equilibrium found. Two firms choose between two incompatible technical standards: both on the first, eight million each; both on the second, six each; split, two each. For the first firm the first standard is best when the rival picks it and the second is best when the rival picks that, so there is no dominant strategy, and both best replies meet in two cells. Two Nash equilibria, one better than the other, and nothing in the game says which they reach. Two equilibria is not a mistake; coordination games have them, and history or a first mover often decides. The worse one is still an equilibrium, since once there neither firm gains by switching alone, which is why inferior standards can persist.

What changes when the game repeats.

MIC 0830 Repeated Games: Tit-for-Tat and Triggers

Real oligopolies play repeatedly. A firm can answer cheating with cheating and cooperation with cooperation, tit-for-tat, or threaten a permanent price war, a trigger strategy, and either can hold a tacit cartel; a rival who knows every cut will be matched has less reason to cut. Repetition makes cooperation possible, not certain, and the one-shot logic returns when the game is expected to end.

A curve built from the same idea.

MIC 0831 The Kinked Demand Curve

If rivals match a firm's cuts but not its rises, its demand curve is kinked at the current price: elastic above, inelastic below. A cut sells little more, since all cut; a rise loses many, since none follow; so neither pays, and price sticks. The kink explains stickiness, not how the price got there, and the idea is anchor-only.

Three entries to close: naming a structure from its features, the four on one table, and the unit's second capstone, why the cartel breaks.

Naming a structure from its features.

MIC 0832 Classifying a Market Structure

From a description, read four features: how many firms, whether products are identical or differentiated, how easy entry is, and how much control each firm has over price. Many firms, identical products, free entry, no price control is perfect competition; many firms, differentiated products, easy entry, some control is monopolistic competition; a few firms, high barriers, interdependent pricing is oligopoly; one firm, blocked entry, no close substitutes is monopoly. Then say which demand curve the firm faces and what happens to profit in the long run. Hundreds of wheat farms with easy entry: perfect competition, flat demand, zero long-run profit. Dozens of coffee shops with different menus: monopolistic competition, demand sloping down, zero long-run profit. Three wireless carriers behind spectrum licenses: oligopoly, each watching the others, profit that can persist. One licensed water utility: monopoly, the market's demand, profit behind the barrier. The number of firms alone misleads, since a few firms with easy entry behave competitively and many differentiated firms are not perfect competitors; ask about the long run, because persistent profit is the mark of a barrier.

All four side by side.

MIC 0833 The Four Structures on One Table

Hold the four structures as one table with seven rows. Number of firms: many, many, few, one. Product: identical, differentiated, either, unique. Entry: free, easy, hard, blocked. The firm's demand curve: flat; downward sloping and elastic; downward sloping and dependent on rivals; the whole market's. Marginal revenue: equal to price in perfect competition, below it in the other three. The rule for quantity: marginal revenue equals marginal cost in every structure without exception, which for a price taker reads price equals marginal cost. Long-run profit: zero under free or easy entry, durable behind barriers. Efficiency: perfect competition passes both tests, monopolistic competition fails both by a little, oligopoly and monopoly by more. The table has a diagonal: from many firms to one, the demand curve steepens, price rises above marginal cost, entry weakens as a discipline, and profit becomes durable. What never changes is the decision rule; what changes is the demand curve it is applied to and whether anyone can arrive to compete the result away. One product across four structures: wheat, a thousand farms taking twenty-five dollars and growing to marginal cost; pizza, forty shops, entry pulling the price from sixteen to the tangency at fourteen; cement, three plants behind a large efficient scale, profit persisting unless a price war breaks out; water, one utility behind a network, pricing at the monopoly point unless unit ten's rules forbid it. Three cautions. Zero long-run profit does not make monopolistic competition efficient, since entry removes the profit and leaves the excess capacity. Marginal revenue equals marginal cost is not a special monopoly rule. And the table classifies the model, not the world; most real markets are a blend, and the question is which row a market most resembles on entry and on the demand curve the firm faces.

Why the cartel breaks.

MIC 0834 Why the Cartel Breaks

A cartel is an attempt to turn an oligopoly into a monopoly by agreement, and game theory explains why the attempt usually fails and sometimes succeeds. The prize: if the few firms restrict output together they share the monopoly profit, and every member is better off than under competition. One member's incentive: at the cartel price its marginal revenue on a little extra output is nearly the full price, far above its marginal cost, because the price cut its extra units cause is spread over the whole industry while the extra sales are its own. Expanding is profitable whatever the others do, so it is a dominant strategy, all expanding is the Nash equilibrium, and the industry lands at the cell every member likes least. Entrants, outsiders and the law push the same way, since the law makes the agreement unenforceable. What holds a cartel together is repetition: played every quarter for years, a member can punish cheating with tit-for-tat or a trigger, and the expected loss from punishment can outweigh the one-time gain. That is why tacit collusion survives where formal cartels cannot, and why it frays when demand falls, costs change, or the end comes into view. The two bottlers over twenty quarters under tit-for-tat: a firm that cheats once gains four million this quarter and then earns six a quarter instead of ten for as long as the punishment lasts. One quarter of punishment costs four million, exactly cancelling the gain; two quarters cost eight, and the cheat no longer pays. As long as each firm expects to be in the market next year, holding output is its best reply, and the tacit cartel holds without a word being written down. Three cautions. The dominant strategy result is about a single play and repeated play adds the future to the payoffs, so the two conclusions do not conflict. Tacit collusion is not proved by parallel prices and is not stable, since every member is still tempted every quarter. And the analysis is positive: it explains what cartels do, and unit ten takes up what the law does about them.

Look at what you can now do. You can define a Nash equilibrium as a set of choices where nobody gains by changing alone, and read a two-by-two matrix in four steps, one player at a time, to the cell where the marks meet. You can model a duopoly cartel as that game, show that cheating is dominant, and explain the price mechanism that shrinks the cartel's profit when both cheat. You can find the equilibria of a game with no dominant strategy, and say why a coordination game can hold two and why the worse one can persist. You can say that repetition makes cooperation possible but not certain, and that a kinked demand curve explains why a price sticks but not where it came from. And you can classify a market structure from four features, hold all four on one table under a single decision rule, and explain why a cartel breaks in a single play and can hold when the game repeats. Unit ten asks what governments do about market power.