# Market Institutions: Oligopoly

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Market Institutions: Oligopoly
Topic 2 – Part I Market Institutions: Oligopoly

Topic Outline Oligopoly Characterization Stackelberg Model
Cournot Model Cartel Formation and Stability Bertrand Model

Oligopoly Often there are a number of competitors in the market but not so many as to regard each of them as having a negligible effect on price. This is the market structure known as oligopoly Oligopoly industry is characterized by encompassing a small number of firms We will restrict our analysis to the case of two firms (duopoly) that produce identical products

Choosing a Strategy If there are two firms in the market producing a homogeneous product, there are 4 variables of interest: price that each firm charges and quantity that each firm produces When one firm makes its choices of price and quantity, it may already know the choices made by the other firm. The strategic interaction form a sequential game If one firm gets to set its price before the other firm, we call it the price leader and the other firm the price follower Similarly, one firm may get to choose its quantity first, in which case it is a quantity leader and the other firm is a quantity follower

Choosing a Strategy (cont.)
When one firm makes its choices of price and quantity, it may not know the choices made by the other firm. In this case, it has to guess about the other firm’s choices in order to make sensible decisions. The strategic interaction form a simultaneous game Therefore, the competitive strategic interaction between these two firms gives 4 possible scenarios: Quantity leadership  Stackelberg Model Price leadership Simultaneous quantity setting  Cournot Model Simultaneous price setting  Bertrand Model

Choosing a Strategy (cont.)
Another form of interaction is when, instead of the firms competing against each other, they may be able to collude In this case, the two firms can jointly agree to set price and quantity that maximizes the sum of their profits This collusion among oligopolistic firms is called Cartel

Suppose there are two firms in the market (duopoly) One firm (Firm1) choose a level of output before the other firm (Firm 2) After observing the decision of Firm 1, Firm 2 decides a level of output This model is used to describe industries in which there is a dominant firm or natural leader called the Stackelberg leader

This strategic situation can be modeled using an extensive-form game-theoretic representation The SPNE of the game will provide the information about the Stackelberg equilibrium and equilibrium payoffs for both firms (profits)

Model Setup Suppose firm 1 is the leader and that it chooses to produce a quantity y1 Firm 2 responds by choosing quantity y2 Each firm knows that the equilibrium price in the market depends on the total output produced What output should the leader choose to maximize its profits? The answer depends on how the leader thinks that the follower will react to its choice The leader should expect that the follower will attempt to maximize profits as well, given a choice made by the leader Therefore, the leader should consider the follower’s profit-maximization problem in order to make a sensible decision about its own production

Model Solution Start by the end of the game: evaluate the follower’s maximization problem, taking as predetermined the level of output chosen by the leader: The follower chooses y2 such that Π2 (y1, y2) is maximized You will find y2 = f(y1), the reaction function for the follower Solve the leader’s optimization problem, subject to the reaction of the follower The leader chooses y1 such Π1 (y1, y2) is maximized subject to y2 = f(y1), i.e., max Π1 (y1, f(y1))

Simultaneous Quantity Setting: Cournot Model
Two firms are simultaneously trying to decide what quantity to produce. Here each firm has to forecast what the other firm’s output will be in order to make a sensible decision itself Given its forecast, each firm chooses a profit-maximizing output for itself We seek an equilibrium in forecasts: a situation where each firm finds its beliefs about the other firm to be confirmed, and in which each firm’s decision is best response to the strategy they believe the opponent will choose

Model Setup Assume that firm 1 expects that firm 2 will produce y2e units of output. The superscript “e” stands for “expected” output If firm 1 decides to produce y1 units of output, it expects that the total output produced will be Y = y1 + y2e This output will yield a market price p(Y) = p (y1 + y2e)

Model Solution The profit-maximizing problem of firm 1: max profits 1 by choosing y1, taking as given y2e Find reaction function for firm 1 to its beliefs about level of output of firm 2 The profit-maximizing problem of firm 2: max profits 2 by choosing y2, taking as given y1e Find reaction function for firm 2 to its beliefs about level of output of firm 1

Model Solution (cont.) We are searching for an equilibrium (y1, y2) where y1e = y1* and y2e = y2* Combine both reaction functions to obtain optimal (y1*, y2*) such that y1* = f1 (y2*) y2* = f2(y1*)

Model Solution (cont.) In a Cournot equilibrium
Each firm is maximizing its profits, given its beliefs about the other firm’s output choice Those beliefs are confirmed in equilibrium: each firm optimally chooses to produce the amount of output that the other firm expects it to produce Neither firm will find it profitable to change its output once it discovers the choice actually made by the other firm. Therefore, the Cournot equilibrium is an Nash-equilibrium