Markets, Games, and Competition
 8 minutes read  1646 wordsContext
 The majority of economic transactions take place through markets. Markets have a myriad of different structures. They are central in organizing production and allocating surpluses between participants. On some occasions, market participants cannot affect the outcome.
 However, on other occasions, market participants can follow complicated strategies to affect production allocation in their favor.
 What kind of strategies do market participants employ?
 How do the strategies of different participants interact?
 Do their strategies affect market efficiency besides allocation?
Course Structure Overview
Lecture Structure and Learning Objectives
Structure
 Jonathan Lebed (Case Study)
 Markets, Strategies, and Game Theory
 Basic Foundations
 Current Field Developments
Learning Objectives
 Explain what a market is from an economic perspective.
 Illustrate why participants' interactions are central in determining outcomes and allocations.
 Review the fundamental market structures (monopoly and perfect competition).
 Give a highlevel overview of the alternative market structures and competition strategies.
Jonathan Lebed
 Lebed is a former stock market trader.
 He was raised in New Jersey, US.
 He was prosecuted by the US Securities and Exchange Commission (SEC) for stock manipulation.
 Lebed reached an outofcourt settlement with SEC in 2000; He was 15 years old.
The SEC Prosecution
 Lebed is the first minor ever prosecuted for stockmarket fraud.
 Lebed tools were
 an America Online (AOL) internet connection,
 an E*trade account, and
 four email accounts in Yahoo Finance Message Boards.
 The SEC accused him of making his money through a pump and dump strategy.
Timeline
 Shortly after his \(11\text{th}\) birthday Jonathan opened an account with America Online.
 He started building a website about prowrestling.
 At the age of 12, he invested \($8000\) (via his father) in the stock market, taken from a bond his parents gave him at birth.
 He started building an amateur investor website www[dot]stockdogs[dot]com"
 At 14, the SEC charged him with civil fraud.
 His mother closed his trading account.
 His father opened another account for him!
The Settlement
 Lebed forfeited \($285000\) in profit and interest he had made on \(11\) trades.
 He has never admitted any wrongdoing.
 He kept close to \($500000\) in profit.
Everybody is Manipulating the Market
People who trade stocks, trade based on what they feel will move and they can trade for profit. Nobody makes investment decisions based on reading financial filings. Whether a company is making millions or losing millions, it has no impact on the price of the stock. Whether it is analysts, brokers, advisors, Internet traders, or the companies, everybody is manipulating the market. If it wasn’t for everybody manipulating the market, there wouldn’t be a stock market at all…
Jonathan Lebed, statement to his lawyer, (Lewis 2001)
Perfect Competition
 A market is perfectly competitive if it has a large number of consumers and firms such that
 the market does not suffer from any market failure (imperfect information, externalities, etc.),
 consumers and firms are price takers,
 consumers try to maximize their utility,
 firms try to maximize their profits,
 firms produce a homogeneous commodity or service, and
 there are no entry barriers in the market.
Pareto Efficiency

Profits are zero in perfect competition.

Say that inverse demand and production cost are
\(p(q) = p_{0} + p_{1}q\) \((p_{0}>0, p_{1}<0)\)
\(c(q) = c_{1}q\)

Market price is equal to the firms' marginal costs, i.e., \(p_{c} = c_{1}\), which implies that
\(q_{c} = \frac{p_{0}  c_{1}}{p_{1}}\).

The total welfare is equal to the consumer’s surplus
\(W_{c} = \Pi_{d,c} = \frac{\left(p_{0}  p_{c}\right) q_{c}}{2} = \frac{\left(p_{0}  c_{1}\right)^2}{2 p_{1}}\)
Price Setting
 Is price taking behavior an appropriate assumption for monopolies?
 The justification for price taking is based on competition.
 Attempts to change prices do not work because other firms do not follow them.
 However, this is not a valid argument in a singleseller market.
 A firm (or a consumer) is a price setter if it can influence the market price of the products it produces (consumes). Price setters consider market prices as (at least partially) endogenous.
Monopoly
 Perfect competition requires that a large number (formally an infinite number) of firms (sellers) exist in the market.
 What about the other extreme case of a single firm in a market?
 A market structure with exclusive possession of supply by a single seller is called a monopoly. The single firm (or seller) in a market is called a monopolist.
 Market demand and firm demand are identical in monopolistic markets.
Markup Pricing
 The monopolist sets the price of the commodity it produces using a markup.
 The monopolist pricing rule can be calculated by \[p_{m} = \frac{\text{Marginal Cost}}{\frac{1}{\text{Demand Elasticity}} + 1}\]
How do Marginal Cost Changes Affect Profit?
How do Elasticity Changes Affect Profit?
Deadweight Loss

The monopolist makes a profit
\(\pi_{m} = \frac{\left(p_{0}  c_{1}\right)^2}{4 p_{1}}\).

The consumer’s surplus is
\(\Pi_{d,m} = \frac{\left(p_{0}  p_{m}\right) q_{m}}{2} = \frac{\left(p_{0}  c_{1}\right)^2}{8 p_{1}}\).

Therefore, the total welfare is
\(W_{m} =  \frac{3\left(p_{0}  c_{1}\right)^2}{8 p_{1}}\).
Current Field Developments
 The transaction cost theory of the firm focusing on the firm relation to the market started developing in the 1930’s.
 Managerial and behavioral theories of the firm focusing on internal organization started developing in the 1960’s.
 Industrial organization is an economic field that builds on the theory of the firm and examines the interactions of market participants and the welfare properties of market structures.
Concise Summary
 For economics, markets are the primary coordination mechanism of production and allocation.
 When studying competition and market structure, it is convenient to abstract from organizational aspects and consider the firm a black box.
 Based on this, various firm models can be used to analyze competition in the market (monopoly, oligopoly, perfect competition, etc.)
 Monopoly and perfect competition are simple models that ignore the interactions of market participants.
 In reality, however, firms use various strategies based on prices and quantities to compete in a market.
Further Reading
 Belleflamme and Peitz (2010, secs. 1.11.4, 2.1.12.1.4)
 Varian (2010, chap. 1)
 Chandler (1992)
Exercises
Group A

Consider a market with inverse demand given by \(p(q) = p_{0} + p_{1}q\) with \(p_{0}>0\) and \(p_{1}<0\).
 Calculate the demand function (i.e., invert \(p\)). For which values of price is demand nonnegative?
 Calculate the demand elasticity as a function of price using the demand function. What is the sign of elasticity?
 Calculate the demand elasticity as a function of quantity using the inverse demand function.
 Substitute the quantity variable in the result of part (c) with the demand calculated in part (a) and verify that you get the result of part (b).
 Calculate the quantity for which demand exhibits unitary elasticity.

Fix a value for \(p\) and solve for \(q\) to get \[q(p)=\frac{p_{0}}{p_{1}} + \frac{1}{p_{1}} p.\] Since \(p_{1}<0\), demand is nonnegative if and only if \(p \le p_{0}\).

We calculate
\begin{align*} E(p) &= \frac{\mathrm{d} q}{\mathrm{d} p} \frac{p}{q(p)} \\ &= q'(p) \frac{p}{q(p)} \\ &= \frac{1}{p_{1}} \frac{p}{\frac{p_{0}}{p_{1}} + \frac{1}{p_{1}} p} \\ &= \frac{p}{p_{0} + p} \end{align*}
For every \(0 \le p\le p_{0}\) is nonpositive.

We have
\begin{align*} E(q) &= \frac{\mathrm{d} q}{\mathrm{d} p} \frac{p(q)}{q} \\ &= \frac{1}{\frac{\mathrm{d} p}{\mathrm{d} q}} \frac{p(q)}{q} \\ &= \frac{1}{p'(q)} \frac{p(q)}{q} \\ &= \frac{1}{p_{1}} \frac{p_{0} + p_{1}q}{q} \end{align*}

Substituting gives
\begin{align*} E(q(p)) &= \frac{p_{0} + p_{1}q(p)}{p_{1} q(p)} \\ &= \frac{p_{0}  p_{0} + p}{ p_{0} + p} \\ &= \frac{p}{p_{0} + p} \end{align*}

Using part (c), we have \(E(q)=1\) if and only if \[p_{0} + p_{1}q = p_{1}q,\] or equivalently \[q = \frac{p_{0}}{2p_{1}}.\]

Consider a monopolist in a market with inverse demand \(p(q) = p_{0} + p_{1}q\), where \(p_{0}>0\) and \(p_{1} < 0\). The monopolist’s cost function is given by \(c(q) = c_{1}q\), where \(0 < c_{1}\).
 Set up the maximization problem of the monopolist for which the monopolist chooses the produced quantity.
 Calculate the monopoly quantity, price, and profit.
 Instead, suppose that the monopolist is choosing prices. Calculate the demand function and set up the maximization problem.
 Calculate the quantity, price, and profit. Compare them to the maximization problem over quantities. Are the results the same? Why, or why not?
 Calculate the consumer welfare and the total welfare.
 Compare with the welfare of the perfect competition case and calculate the deadweight loss.

The monopolist solves \[\max_{q} \left\{ p(q)q  c(q) \right\}\]

The first order condition is \[p'(q)q + p(q) = c'(q) \iff p_{0} + 2p_{1}q = c_{1},\] which gives
\begin{align*} q_{m} &= \frac{p_{0}  c_{1}}{2p_{1}}, \\ p_{m} &= \frac{c_{1} + p_{0}}{2}, \end{align*}
and \[\pi_{m} = \frac{(p_{0}  c_{1})^{2}}{4p_{1}}.\]

The demand function is \[q(p) = \frac{1}{p_{1}} (p_{0}  p)\] and the monopolist problem is \[\max_{p} \left\{ q(p)p  c(q(p)) \right\}.\]

The first order condition is \[q'(p)p + q(p) = c'(q)q'(p) \iff \frac{1}{p_{1}}(2p  p_{0}) = \frac{c_{1}}{p_{1}},\] which leads to the same price, quantity, and profit as in part (b). The result is the same because inverse demand is affine (more generally because inverse demand is onetoone).

The consumer welfare is
\begin{align*} C_{m} &= \int_{0}^{q_{m}} (p(q)  p_{m}) \mathrm{d} q \\ &= p_{0}q_{m} + \frac{p_{1}}{2} q_{m}^2  p_{m} q_{m} \\ &= \frac{1}{2} q_{m} (p_{0}  p_{m})\\ &= \frac{(p_{0}  c_{1})^{2}}{8p_{1}}, \end{align*}
so the total welfare is \[W_{m} = C_{m} + \pi_{m} =  3 \frac{(p_{0}  c_{1})^{2}}{8p_{1}}.\]

In perfect competition, \(p_{c} = c_{1}\). Then, \[q_{c}=\frac{c_{1}  p_{0}}{p_{1}}\] and profits are zero. The competition’s total welfare is
\begin{align*} W_{c} &= C_{c} \\ &= \int_{0}^{q_{c}} (p(q)  c_{1}) \mathrm{d} q \\ &= p_{0}q_{c} + \frac{p_{1}}{2} q_{c}^2  c_{1} q_{c} \\ &= \frac{1}{2} q_{c} (p_{0}  p_{c})\\ &= \frac{(p_{0}  c_{1})^{2}}{2p_{1}}. \end{align*}
Finally, the deadweight loss is \[D = W_{c}  W_{m} = \frac{(p_{0}  c_{1})^{2}}{8p_{1}}.\]