Context
- Many real markets are neither perfectly competitive nor monopolies. Instead, they are oligopolies comprised of a small number of firms that have large enough market shares and can influence prices.
- Nonetheless, firms' profits do not exclusively depend on their own choices. Their small numbers allow them to utilize a variety of competition strategies.
- How do firms strategically interact?
- What means do they use to compete?
- How do the welfare outcomes of oligopolies compare to those of monopolies and perfect competition?
Course Structure Overview
Lecture Structure and Learning Objectives
Structure
- Microsoft’s Pricing Strategies (Case Study)
- Basic Concepts
- The Cournot and Bertrand Models of Duopolies
- Extensions to Oligopolies with More Firms
- Spatial Competition
- Current Field Developments
Learning Objectives
- Describe oligopolies with competition in quantities and their welfare output.
- Describe oligopolies with competition in prices and their welfare output.
- Contrast the welfare outcomes with the perfectly competitive welfare.
- Illustrate the differences between the results of various modes of competition.
Microsoft's Pricing Strategies
- In the early 1980s, several companies were competing in the operating system market of IBM-compatible PCs.
- In the 1990s and 2010s, Microsoft dominated the operating system market.
- In 2020s Microsoft's dominance stopped, and its operating system is nowadays the second most used.
- How did Microsoft manage to dominate the operating system market?
- How did it lose its primacy?
MS-DOS
- In the early 1980s, the common practice of operating system companies was to charge hardware manufacturers for each operating system copy installed in a computer.
- Microsoft offered an alternative plan.
- Charge computer manufacturers based on (the past number of) built computers.
- The manufacturer was paying a general licensing fee and then could install the operating system in all the computers it produced.
- Microsoft was offering low-priced licensing contracts making their operating system (MS-DOS) very attractive to manufacturers.
The Impact of Microsoft's Early Pricing Strategy
- Effectively, manufacturers could purchase Microsoft's operating system at much lower prices than the operating systems of other software companies.
- A manufacturer had to pay \($50\ -\ $100 \) for installing an alternative operating system on an additional machine.
- It cost nothing to install MS-DOS on an additional machine once a licensing contract with Microsoft has been signed.
- MS-DOS ended up being the default operating system
Android
- Android is a community (open source) operating system for mobile devices based on the Linux kernel.
- The wide use of smartphones and tablets drastically changed the operating system market.
- Although Microsoft offered an operating system suitable for smartphones and tablets, it did not manage to keep its primacy.
StatCounter
The Impact of Android on Microsoft's Pricing Strategy
- Android is free. Anyone can install the operating system on her device after accepting the terms and conditions.
- For mobile device manufacturers, Android is a cheaper operating system alternative for their products.
- This leads to more competitive prices for consumers too.
- Microsoft's operating systems lost their primacy in the overall operating system market in \(2017\).
- Microsoft's operating systems are still dominant in less portable devices, such as desktop PCs and Laptops.
- The rise of Android has also impacted Microsoft's pricing strategies for its desktop operating systems.
- Licensed users were able to upgrade to the last two versions of Microsoft's operating system without paying for a new license.
Competition and Cooperation
- Oligopoly refers to market structures with a small number of interdependent firms.
- Oligopolistic firms typically compete using non cooperative strategies.
- On some occasions, firms collude and use cooperative strategies.
Non cooperative overview
- Oligopolies may compete using pricing strategies or by choosing quantities.
- Different means of competition strategies crucially affect the market outcome.
- The means of competition is a decisive component of the market structure.
Cooperation and collusion
- Oligopolies have used explicitly written collusive strategies in the past (e.g., cartels).
- Nowadays, collusion is usually illegal.
- Instances of tacit collusion have also been documented.
- Tacit collusion strategies do not require explicit contracts or communication.
Competition in Quantities
- The Cournot model of oligopoly describes a market structure with two or more firms such that
- the market does not suffer from any market other failure (imperfect information, externalities, etc.),
- no other firms can enter the market,
- firms sell a homogeneous product,
- firms try to maximize their profits,
- consumers are price takers; firms are simultaneously choosing the quantities that they produce, and
- consumers try to maximize their utility.
Quantity Competition with two Firms
\[\max_{q_{i}} \left\{ p(q_{1} + q_{2}) q_{i} - c(q_{i}) \right\}.\]
- The necessary condition for each firm is
\[p'(q_{1} + q_{2}) q_{i} + p(q_{1} + q_{2}) = c'(q_{i}).\]
- From these conditions, the two best responses are obtained
\[q_{i} = b_{i}(q_{j}) \quad\quad (i\neq j).\]
- Solving the system of these two equations gives the equilibrium point (if it exists).
The Linear Cost Case
- For inverse demand and costs given by
\begin{align*}
p(q) &= p_{0} + p_{1} q \quad &&(p_{0}>0,\ p_{1}<0)\\
c(q) &= c_{1} q \quad &&(c_{1}>0).
\end{align*}
- The best responses become
\[q_{i} = \frac{c_{1} - p_{0} - p_{1} q_{j}}{2 p_{1}}.\]
- The equilibrium quantities are given by
\[q_{i} = \frac{c_{1} - p_{0}}{3 p_{1}}.\]
- The profits are symmetric and can be calculated as
\[\pi_{i} = -\frac{(c_{1} - p_{0})^{2}}{9 p_{1}}.\]
Quantity Competition with More than two Firms
- We extend the problem by allowing \(n>2\) firms that simultaneously choose their supplied quantities.
- Each firm solves
\[\max_{q_{i}} \left\{ p\left( \sum_{j=1}^{n} q_{j} \right) q_{i} - c(q_{i}) \right\}.\]
- Analogously to the two-firm case, we obtain \(n\) best response functions
\[q_{i} = b_{i}\left((q_{j})_{j\neq i}\right) \quad\quad (i = 1,... , n).\]
- Solutions to the system of best responses (if any) are the Nash equilibria of this oligopoly model.
Best Responses
- Suppose inverse demand is given by
\begin{align*}
p(q) &= p_{0} + p_{1} q .
\end{align*}
- All firms have (symmetric) costs
\begin{align*}
c(q) &= c_{1} q .
\end{align*}
- The best responses become
\[q_{i} = \frac{c_{1} - p_{0} - p_{1} \sum_{j\neq i} q_{j}}{2 p_{1}}.\]
Market Equilibrium
- The equilibrium quantities are given by
\[q_{i} = \frac{c_{1} - p_{0}}{(n + 1) p_{1}}.\]
\[q = \sum_{i=1}^{n} q_{i} = \sum_{i=1}^{n} \frac{c_{1} - p_{0}}{(n + 1) p_{1}} = \frac{n}{n+1}\frac{c_{1} - p_{0}}{p_{1}},\]
- So, the market price becomes
\[p(q) = p_{0} + p_{1} n \frac{c_{1} - p_{0}}{(n + 1) p_{1}} = \frac{n c_{1} + p_{0}}{n + 1}.\]
\[\pi_{i} = -\frac{(c_{1} - p_{0})^{2}}{(n + 1)^{2} p_{1}}.\]
- The case of two firms can be obtained by replacing \(n=2\) in the above results.
Market Power
- We can also obtain the solution of the monopoly problem if we set \(n=1\).
- With \(n=1\), we get the monopolistic profit
\[\pi_{1} = -\frac{(c_{1} - p_{0})^{2}}{4 p_{1}}.\]
- Profits decrease as the number of firms in the market increases.
- The limiting case is
\[\pi_{i} \xrightarrow[n\to \infty]{} 0.\]
- In addition, \(p(q) \to c_{1}\), \(q_{i}\to 0\), and \(q\to\frac{c_{1}-p_{0}}{p_{1}}\) as \(n\to\infty\).
- The production of each firm becomes negligible, and the total market quantity and price approach those of perfect competition.
A Cournot Competition Exercise
- Suppose that both firms \((i, j \in \{1,2\})\) have the cost function
\[c(q_{i}) = 4 q_{i}.\]
- Let market inverse demand be
\[p(q_{i} + q_{j}) = 28 - 2 \left(q_{i} + q_{j}\right).\]
- Each firm maximizes its profits
\[\max_{q_{i}} \left\{ \left( 28 - 2 \left(q_{i} + q_{j}\right) \right) q_{i} - 4 q_{i} \right\}.\]
Best responses
- The necessary condition for each firm is
\[28 - 2 q_{j} - 4 q_{i} = 4.\]
- Solving for \(q_{i}\) gives the best response of firm \(i\)
\[q_{i} = \frac{24 - 2 q_{j}}{4}.\]
Nash Equilibrium
- Combining the two best responses gives the Nash equilibrium
\[q_{i} = 4 = q_{j}.\]
\[\pi_{i} = 32.\]
What happens if costs are not symmetric?
Competition in Prices
- The Bertrand model of oligopoly describes a market structure with two or more firms such that
- the market does not suffer from any market other failure (imperfect information, externalities, etc.),
- no other firms can enter the market,
- firms sell a homogeneous product,
- firms try to maximize their profits,
- consumers are price takers, and firms are simultaneously choosing prices, and
- consumers try to maximize their utility.
A Bertrand Competition Exercise
- Suppose that both firms \((i, j \in \{1,2\})\) produce at a marginal cost equal to \(4\).
Let the demand for firm \(i\) be
\begin{align*}
d_{i}(p_{i}, p_{j}) = \left\{\begin{aligned}
&10 - \frac{1}{2}p_{i} & p_{i} < p_{j} \\
&5 - \frac{1}{4}p_{i} & p_{i}=p_{j} \\
&0 & p_{i} > p_{j} \end{aligned}\right..
\end{align*}
- The firm with the lowest price gets all the demand.
- If prices are equal, demand is equally split.
Non Equilibrium Prices
- Suppose that firm \(j\) sets a price \(p_{j}\) that is greater than the marginal cost of firm \(i\) (i.e., \(4\)).
- Firm \(i\) can undercut by a small amount and grab all the market. For instance, set price \(p_{i} = \frac{p_{j} + 4}{2}\).
- Thus, firm \(j\) can only set a price equal to firm \(i\)'s marginal cost.
- Analogous arguments hold for firm \(i\)'s pricing strategy.
Equilibrium
- The only possible equilibrium is to set prices equal to the (common) marginal cost.
- Firms do not have any incentive to deviate.
- Setting lower prices leads to losses.
- Setting higher prices leads to zero profits.
- Even with two firms, price competition leads to prices similar to perfect competition.
Spatial Competition
- There are two firms on a street.
- Points on the street are given by \([0, 1]\).
- Each firm chooses a point.
- Firms have the same cost and charge the same price.
- Customers on the street prefer the firm that is the closest.
An illustration of the game
Non equilibrium placements
- If firm \(2\) chooses \(x_{2} > \frac{1}{2}\), firm \(1\) would like to undercut by a small amount and set \(x_{1} = x_{2} - \varepsilon > \frac{1}{2}\).
- Then firm \(2\) has a profitable deviation by changing to \(x_{2} = \frac{1}{2}\).
- Thus any \(x_{2} > \frac{1}{2}\) cannot be an equilibrium.
- Similarly, any \(x_{2} < \frac{1}{2}\) cannot be an equilibrium.
- Analogous arguments hold for firm \(1\) because of symmetry.
Equilibrium placements
- Therefore, the only possible equilibrium is \(x_{1} = \frac{1}{2} = x_{2}\).
- Firms split the market and make equal profits.
- Any deviation leads to fewer profits for the firm that moved.
Current Field Developments
- There are two main types of extensions of the basic models (Cournot and Bertrand).
- Extensions incorporating dynamic decisions (see Dynamic Competition topic) and
- Extensions incorporating decisions under uncertainty (see Competition with Incomplete Information topic)
- Oligopoly models are primarily used in industrial organization to examine
- market power,
- pricing strategies,
- competition policies, and
- R&D and innovation.
- Some recent micro-founded, general equilibrium macro models use oligopoly models to describe markets with frictions.
Comprehensive Summary
- Competition is not always perfect.
- In reality, a few large firms have the lion’s share in many markets.
- Such markets are described by oligopoly models.
- Depending on how firms compete (prices or quantities) and the number of firms, oligopoly models give predictions with welfare properties that range from perfect competition to monopoly.
Context
- Competition in real markets is not a static phenomenon. Firms can change their choices from date to date and adapt their strategies based on past events and the reactions of competitive firms.
- In such fluid settings, some firms take the initiative and set the pace of competition in the market. Other firms follow.
- Do firms benefit from assuming a market leader role?
- How does the sequence of moves affect the market power?
- Why does market entry influence the behavior of incumbent firms?
Course Structure Overview
Lecture Structure and Learning Objectives
Structure
- The Model T (Case Study)
- The Stackelberg model
- Sequential Competition in Prices
- The Role of Market Entry in Competition
- Current Field Developments
Learning Objectives
- Describe the impact of move order on market power under quantity competition.
- Describe the impact of move order on market power under price competition.
- Highlight the welfare effects of leadership under various competition means.
- Illustrate the effect of free entry in dynamic competition.
- Illustrate the importance of credibility in entry deterrence.
The Model T
People can have the model T in any color—so long as it's black.
Henry Ford
Ford vs General Motors
- Ford and General Motors are two of the largest automobile companies worldwide.
- They were both founded in the beginning of the \(20^{\text{th}}\) century.
- Since then, they have been competing for the lead in the US automobile market.
Third Time is a Charm
- Henry Ford attempted two times to start an automobile business and failed.
- His third attempt in 1903 was the Ford Motor Company.
- Automobiles were far from affordable back then.
- Until 1908 Ford sold only hundreds or a few thousands of cars per year.
Fordism
- Ford introduced the moving assembly line in 1908.
- The new model T was mass produced instead of hand assembled.
- The new production method drove the cost of model T down, making it affordable to more consumers.
- Model T sold millons over the next 20 years.
- Ford Motor Company transformed from a small startup to the leading automobile company.
Game On
- William Durant incorporated General Motors.
- There were about 45 different car companies in the US, most of them selling a handful of cars.
- General Motors was the opposite of Ford.
- It produced a wide variety of cars for a wide variety of consumer needs.
- In the first 2 years, General Motors cobbled together 30 companies, 11 of which where automakers.
The Market Leader
- Model T's production innovations made Ford the leading car company from about 1910 to 1925.
- The reluctance of Ford to keep introducing innovations and the absence of flexibility changed the situation.
- In 1925, GM surpassed Ford in total revenue and kept ahead until 1986.
- Eventually in 1927, Ford shutdown for 6 months to update its production lines for Model A.
- GM also surpassed Ford in total sales during this period.
Leader-follower Competition in Quantities
- The Stackelberg model of oligopoly describes a market structure with two or more firms such that
- the market does not suffer from any other market failure (imperfect information, externalities, etc),
- no other firms can enter the market,
- firms sell a homogeneous product,
- firms try to maximize their profits,
- consumers are price takers, firms choose the quantities that they produce, the leader chooses first, and the follower(s) choose afterward, and
- consumers try to maximize their utility.
Residual Demand
- The leader chooses the quantity it produces first.
- Thus, the follower does not face the entire market demand but only the demand remaining after the leader's choice.
- The difference between the market demand and the aggregated supplied quantities of all competitive firms is a firm's residual demand.
The Follower's Problem
- We solve the problem with backward induction.
- The follower claims the residual demand.
- For any given quantity \(q_{1}\) produced by the leader, the follower's problem is
\[\max_{q_{2}} \left\{ p(q_{1} + q_{2})q_{2} - c_{2}(q_{2}) \right\}.\]
- Interior optimal solutions require
\[p'(q_{1} + q_{2})q_{2} + p(q_{1} + q_{2}) = c_{2}'(q_{2}).\]
- From this condition, we obtain (solving for \(q_{2}\)) the best response of the follower, say
\[q_{2} = b_{2}(q_{1}).\]
The Leader's Problem
- The leader anticipates the best response of the follower and solves
\[\max_{q_{1}} \left\{ p(q_{1} + b_{2}(q_{1}))q_{1} - c_{1}(q_{1}) \right\}.\]
- Its optimality condition is given by
\[p'(q_{1} + b_{2}(q_{1})) \left(1 + b_{2}'(q_{1})\right) q_{1} + p(q_{1} + b_{2}(q_{1})) = c_{1}'(q_{1}).\]
An Analytic Example
Suppose that the demand and cost functions are given by
\begin{align*}
p(q) &= p_{0} + p_{1} q, \\
c_{1}(q_{1}) &= c q_{1}, \\
c_{2}(q_{2}) &= c q_{2}.
\end{align*}
The Follower's Problem
- The follower's necessary condition becomes
\[p_{1}q_{2} + p_{0} + p_{1}(q_{1} + q_{2}) = c.\]
- Then, the best response of the follower is
\[b_{2}(q_{1}) = \frac{c - p_{0} - p_{1}q_{1}}{2 p_{1}}.\]
The Leader's Problem
\[\max_{q_{1}} \left\{ p\left(q_{1} + \frac{c - p_{0} - p_{1}q_{1}}{2 p_{1}}\right)q_{1} - c(q_{1}) \right\}.\]
- Its optimality condition is given by
\[\frac{p_{1}}{2}q_{1} + p_{0} + \frac{c - p_{0}}{2} + \frac{p_{1}}{2}q_{1} = c.\]
- Therefore, the leader produces
\[q_{1}^{\ast} = \frac{c - p_{0}}{2 p_{1}}.\]
Market Quantity and Price
- Given the leader's quantity, the follower produces
\[q_{2}^{\ast} = b_{2}(q_{1}^{\ast}) = \frac{c - p_{0}}{2 p_{1}} - \frac{1}{2}\frac{c - p_{0}}{2 p_{1}} = \frac{c - p_{0}}{4 p_{1}}.\]
\[q^{\ast} = q_{1}^{\ast} + q_{2}^{\ast} = 3\frac{c - p_{0}}{4 p_{1}}.\]
\[p(q^{\ast}) = p_{0} + p_{1} q^{\ast} = \frac{p_{0} + 3 c}{4}.\]
Profits
- The follower makes profit
\[\pi_{2} = \left(p(q^{\ast}) - c\right) q_{2}^{\ast} = - \frac{\left(p_{0} - c\right)^{2}}{16p_{1}}.\]
\[\pi_{1} = \left(p(q^{\ast}) - c\right) q_{1}^{\ast} = - \frac{\left(p_{0} - c\right)^{2}}{8p_{1}}.\]
First Move Advantage
- The firms' profits in the Cournot model with symmetric costs are
\[\pi_{c} = - \frac{\left(p_{0} - c\right)^{2}}{9p_{1}}.\]
- Compared to the firms' profits in the Cournot model, we have
\[\pi_{1} > \pi_{c} > \pi_{2}.\]
- The leader makes more profit compared to Cournot competition, while the follower makes less profit.
- However, aggregate profits in the market are less compared to Cournot, i.e.,
\[\pi_{1} + \pi_{2} < 2 \pi_{c}.\]
Leader-Follower Competition in Prices
- Consider a variation of the Stackelberg game in which firms are price setters.
- This is the sequential version of the Bertrand model.
- There are two firms \((i, j \in \{1,2\})\) with marginal cost equal to \(c\).
- Firm \(1\) is the leader (moves first), and firm \(2\) is the follower (moves second).
The demand for firm \(i\) is
\begin{align*}
d_{i}(p_{i}, p_{j}) = \left\{\begin{aligned}
&10 - \frac{1}{2}p_{i} & p_{i} < p_{j} \\
&5 - \frac{1}{4}p_{i} & p_{i}=p_{j} \\
&0 & p_{i} > p_{j} \end{aligned}\right..
\end{align*}
- The firm with the lowest price gets all the demand.
- If prices are equal, demand is equally split.
Non Equilibrium Prices
- Suppose that firm \(1\) sets a price \(p_{1}\) that is greater than the marginal cost of firm \(2\) (i.e., \(c\)).
- Firm \(2\) can undercut by a small amount and grab all the market. For instance, set price \(p_{2} = \frac{c + p_{1}}{2}\).
- Thus, firm \(1\) can only set a price equal to firm \(2\)'s marginal cost.
Equilibrium
- The only possible equilibrium is both firms to set a price equal to the (common) marginal cost.
- Firms do not have any incentive to deviate.
- Setting lower prices leads to losses.
- Setting higher prices leads to zero profits.
- The order with which firms move does not affect the market outcome.
A Game of Market Entry
- Consider a market with one firm already operating and a potential entrant.
- The entrant decides whether to enter the market.
- The incumbent decides whether to follow aggressive or complying competition behavior.
Entry Deterrence with Credible Threat
- \(SPE = \left\{ \left(Stay\ out, Fight \right) \right\}\)
Entry with Non-Credible Threat
- \(SPE = \left\{ \left(Enter, Don't\ fight \right) \right\}\)
Quantity Competition with Costly Entry
- We extend the Cournot duopoly model by allowing firms to choose whether they enter the market.
- Firms enter the market when they can make profits.
- Firms incur a fixed cost \(\bar c\) upon entry.
Market and Dynamics
- There is an infinite number of potential entrants.
- The market's inverse demand is
\[p(q) = p_{0} + p_{1}q \quad(p_{0}>0,\ p_{1}<0).\]
\[c(q) = c_{1}q \quad(c_{1}>0).\]
- The firms that enter the market choose their quantities at the second date simultaneously.
- At the first date, the entrants decide how many of them enter the market.
Unregulated Entry and Exit
- When \(n\) firms enter the market, each firm makes profit
\[\pi_{i}(n) = -\frac{(c_{1} - p_{0})^{2}}{(n + 1)^{2} p_{1}} - \bar c.\]
\[\pi_{i}(n^{e}) = 0 \iff n^{e} = \frac{p_{0} - c_{1}}{\sqrt{- \bar c p_{1}}} - 1.\]
The Social Welfare
- The social welfare is calculated by
\[W(n) = \int_{0}^{n} p(s q(s)) \left(q(s) + sq'(s)\right) \mathrm{d} s - n c(q(n)) - n \bar c.\]
The First Best Solution
- Aggregate profit is maximized when
\[p(n q(n))\left(q(n) + n q'(n)\right) - c(q(n)) - n c'(q(n))q'(n) = \bar c .\]
\[n^{*} = \sqrt[3]{-\frac{(p_{0} - c_{1})^{2}}{p_{1} \bar c}} - 1 .\]
- Comparing with the unregulated entry equilibrium, we have
\[ n^{*} < n^{e} .\]
- With quantity competition, unregulated entry results in excessive entry of firms.
Current Field Developments
- Market dynamics and entry constitute important components of competition policy.
- Mergers and acquisitions are dynamic phenomena modifying the number of firms in the market and their market power.
- Merger cases are central from both an economic and competition law perspective.
- In the US and EU, antitrust laws aim to reduce or avoid excessive market concentration.
- Dynamic market models are commonly used to assess mergers and their impact on market power in court cases.
Comprehensive Summary
- The sequence with which firms act in a market can influence market power.
- If firms compete in quantities, then the leader has a first move advantage.
- If firms compete in prices, then the sequence of moves is irrelevant.
- Competition forces do not concern only firms who already entered in a market.
- Incumbent firms strategically interact with potential competitors looking to enter the market.
- Free entry is a characteristic of market competition that can reduce firms' profits and result to low prices.
- On some occasions (e.g. entry costs), excessive entry can result to economic inefficiencies.
Collusion and Market Power
Context
- Markets with intense competition tend to reduce the competing firms' market power. Firms could form cartels to control the market and extract a greater share of the economic surplus if left unregulated. For this reason, collusion and cartel formation are illegal practices in most market economies today.
- However, legally binding contracts are not necessary for firms to coordinate. Firms can use dynamic strategies to collude tacitly.
- What kind of strategies can lead to tacit collusion?
- What is the role of the means of competition in tacit collusion?
- How can competition authorities measure market power?
Course Structure Overview
Lecture Structure and Learning Objectives
Structure
- Our Customers are Our Enemies (Case Study)
- Tacit Collusion
- Trigger Strategies with Quantity Competition
- Trigger Strategies with Price Competition
- Market Power
- Current Field Developments
Learning Objectives
- Illustrate that in dynamic settings, credible promises and threats can be used to induce tacit collusion.
- Illustrate that tacit collusion is achievable both when firms compete in quantities and prices
- Describe tacit collusion under price competition.
- Describe tacit collusion under quantity competition.
- Explain how market power can be statistically measured and estimated.
Our Customers are Our Enemies
- Lysine is an amino acid that speeds the development of lean muscle tissue in humans and animals.
- It is essential for humans, but we cannot synthesize it.
- It has to be obtained from the diet.
The Lysine Industry
- At the end of the 1980s, the world lysine industry consisted of three significant sellers:
- Ajinomoto,
- Kyowa, and
- Sewon.
- The three largest consumption regions were Japan, Europe, and North America.
- Most production took place in Japan, but it was based on imports of US dextrose.
- Ajinomoto had the largest share of the world market.
The ADM Entry
- In February 1991, Archer Daniel Midland Co. (ADM) entered the market and built by far the world's largest lysine plant in the US.
- ADM hired biochemist Mark Whitacre, Ph.D., as head of the new division.
- ADM's plant was three times the size of Ajinomoto's largest plant.
- ADM gave Ajinomoto and Kyowa executives an unrestricted tour to show its production capacity.
- Companies engaged in a price war.
- Three months before ADM's entry, the average US lysine price was \($1.22\) per pound.
- After an 18-month price war, the US price averaged \($0.68\) per pound.
- ADM's share of the US market reached \(80\%\).
The Lysine Association
- After the price war, ADM was willing to soften competition.
- In 1992, Mark Whitacre and his boss Terrance Wilson met with top Ajinomoto and Kyowa managers.
- Wilson proposed forming a world lysine association that would regularly meet.
- The new association would collect and distribute market information.
- Wilson also suggested that the new association could provide a convenient cover for illegal price-fixing discussions! (Connor, 2001)
- After a year, the lysine association was founded, met quarterly, and performed the two functions that Wilson proposed.
Price Fixing
- There were \(25\) price fixing meetings in total.
- The first one took place in the Nikko Hotel in Mexico on June 23, 1992.
- The average Lysine price immediately jumped by more than \(12\%\).
- Consensus was not always easy to reach. The companies distrusted each other!
- There was a breakdown of the cartel during the spring and summer of 1993, and the lysine price plummeted.
- The crisis was resolved at a meeting in Irvine, California in October 1993 between ADM's and Ajinomoto Executives. But…
- This meeting and many others were caught on video by the FBI.
Frenemies
WILSON: The only thing we need to talk here because we are gonna get manipulated by these God damn buyers, they're sh, they can be smarter than us if we let them be smarter.
MIMOTO: (Laughs).
WILSON: Okay?
MIMOTO: (ui).
WILSON: They are not your friend. They are not my friend. And we gotta have 'em. Thank God we gotta have 'em, but they are not my friends. You're my friend. I wanna be closer to you than I am to any customer. 'Cause you can make us, I can make money, I can't make money. At least in this kind of a market. And all I wanna is ta tell you again is let's-let's put the prices on the board.
Co-conspirator explains how end-of-year compensation scheme eliminates incentives to cheat on cartel
The Whistle-blower
- In 1992, Mark Whitacre became an FBI whistle-blower. He is the highest-level corporate executive to ever have done so.
- Whitacre's wife pressured him into becoming a whistle-blower. She threatened to inform the FBI herself, if Whitacre wouldn't do it.
- Whitacre informed the FBI that he and other ADM executives performed illegal price-fixing operations.
- Over the next three years, Whitacre collected information and recorded conversations with ADM executives and competitors.
- ADM settlement involved the greatest US federal charges at the time.
- Whitacre was convicted for embezzling and money laundering, which he performed while cooperating with the FBI in the price fixing case.
What can we Learn?
- Why did ADM initially engage in a price war?
- Why did it initiate the price fixing discussions afterward?
- Why was there so much distrust among companies?
Tacit Collusion
- When there is a future, firms can use reputation and/or threats to coordinate.
- Coordination increases their profits.
- Explicit contracts are not needed.
- Trigger strategies can induce coordination.
- Trigger strategies work both when firms compete in quantities and prices.
Tacit Collusion in Quantity Competition
- When coordinating, firms produce at the monopolistic level and split the market.
- Alternatively, firms play their static Cournot strategies.
- On every date, there are two potential game states.
- Either both firms have always cooperated in the past.
- Or, at least one of them deviated.
- The trigger strategy is to produce the monopolistic quantity at state 1 and the Cournot quantity at state 2.
The Problem
- Suppose that both firms discount future profits by \(\delta \in (0,1)\).
- Firms aim to maximize the series of discounted flow profits, i.e.
\[V_{i} = \max_{(q_{i,t})_{t}} \left\{ \sum_{t=0}^{\infty} \delta^{t} \pi_{i,t}(q_{1,t}, q_{2,t}) \right\}.\]
Non Coordinating Equilibrium
- There are many equilibria in the game.
- The non coordinating equilibrium is one in which the stage game Nash equilibrium is played at every date.
- All firms use the oligopolistic quantity competition production levels at every date, which leads to flow profits
\[\pi_{i,t} = - \frac{(c_{1}-p_{0})^{2}}{9 p_{1}} \quad\quad (i=1,2\quad t\ge 0).\]
- Each firm's expected future series of profits is
\[V_{i} = - \frac{1}{1-\delta}\frac{(c_{1}-p_{0})^{2}}{9 p_{1}} \quad\quad (i=1,2\quad t\ge 0).\]
Coordinating Equilibrium with Trigger Strategies
- Another equilibrium can be obtained when firms play the trigger strategies.
- Firms produce half the monopolistic quantity and split the monopolistic profits, i.e.,
\[\pi_{i,t} = - \frac{1}{2}\frac{(c_{1}-p_{0})^{2}}{4 p_{1}} \quad\quad (i=1,2\quad t\ge 0).\]
- If firms coordinate with these profits as flow utilities, they get
\[V_{m, i} = - \frac{1}{1-\delta}\frac{(c_{1}-p_{0})^{2}}{8 p_{1}} \quad\quad (i=1,2\quad t\ge 0).\]
Deviating from Coordination
- Is there any incentive to deviate?
- Suppose that firm 1 deviates at the current date.
- The best response to firm 2's choice of monopolistic profits is
\[q_{1,0} = \frac{3}{8}\frac{c_{1}-p_{0}}{p_{1}}.\]
- Then, firm 1's profit at the current date is
\[\pi_{1,t} = - \frac{9}{64}\frac{(c_{1}-p_{0})^{2}}{p_{1}}.\]
- On future dates, the firms revert to the non coordinating quantities because they use trigger strategies.
- The total discounted profit of the deviating firm is
\[V_{d,1} = - \frac{9}{64}\frac{(c_{1}-p_{0})^{2}}{p_{1}} - \frac{\delta}{1 - \delta} \frac{(c_{1}-p_{0})^{2}}{9 p_{1}}.\]
Can Coordination be Supported?
- The coordination outcome is sustainable if the deviation profit is less than the coordination profit, namely if
\begin{align*}
V_{d,1} &= - \frac{9}{64}\frac{(c_{1}-p_{0})^{2}}{p_{1}} - \frac{\delta}{1 - \delta} \frac{(c_{1}-p_{0})^{2}}{9 p_{1}} \\
&< - \frac{1}{1 - \delta} \frac{(c_{1}-p_{0})^{2}}{8 p_{1}} = V_{m,1}.
\end{align*}
- This is equivalent to \(\delta > \frac{9}{17}\).
- As long as firms value future profits enough, there is room for cooperation.
Tacit Collusion in Price Competition
- When coordinating, firms produce at the monopolistic level and split the market.
- Alternatively, firms play their static Bertrand strategies.
- On every date, there are two potential states.
- Either both firms have always cooperated in the past.
- Or, at least one of them deviated.
- The trigger strategy is to use the monopoly price at state 1 and the Bertrand price at state 2.
The Problem
- Suppose again that both discount future profits by \(\delta \in (0,1)\).
- Firms aim to maximize the series of discounted flow profits, i.e.
\[V_{i} = \max_{(p_{i,t})_{t}} \left\{ \sum_{t=0}^{\infty} \delta^{t} \pi_{i,t}(p_{1,t}, p_{2,t}) \right\}.\]
Non Coordinating Equilibrium
- Firms price at marginal cost when non coordinating.
- They make zero profits at each date.
- Therefore, \(V_{i}=0\).
Coordinating Equilibrium with Trigger Strategies
- As in the case of quantity competition, if firms produce half the monopolistic quantity and split the monopolistic profits, they get
\[\pi_{i,t} = - \frac{1}{2}\frac{(c_{1}-p_{0})^{2}}{4 p_{1}} \quad\quad (i=1,2\quad t\ge 0).\]
- If firms coordinate, then
\[V_{m, i} = - \frac{1}{1-\delta}\frac{(c_{1}-p_{0})^{2}}{8 p_{1}} \quad\quad (i=1,2\quad t\ge 0).\]
Deviating from Coordination
- Suppose that firm 1 deviates at the current date.
- The best response to firm 2's choice of monopolistic pricing is to slightly undercut the market price by \(\varepsilon\)
- Then, firm 1 takes all the market and makes almost the monopolistic profit
- For simplicity, drop \(\varepsilon\), so that
\[\pi_{1,t} = - \frac{(c_{1}-p_{0})^{2}}{4 p_{1}}.\]
- On future dates, the firms have zero profits because they use trigger strategies.
- The total discounted profit of the deviating firm is
\[V_{d,1} = - \frac{(c_{1}-p_{0})^{2}}{4 p_{1}}.\]
Can Coordination be Supported?
The coordination outcome is sustainable if the deviation profit is less than the coordination profit, namely if
\begin{align*}
V_{1,d} &= - \frac{(c_{1}-p_{0})^{2}}{4 p_{1}} \\
&< - \frac{1}{1 - \delta} \frac{(c_{1}-p_{0})^{2}}{8 p_{1}} = V_{1,m}.
\end{align*}
- This is equivalent to \(\delta > \frac{1}{2}\).
- As long as firms value future profits enough, there is room for cooperation.
- Why is the lower bound \(\delta\) in quantity competition greater than in price competition?
Market Power
- In legal cases of competition law, market power is a central element based on which decisions are drawn.
- Market power refers to the ability of the firm to raise prices above marginal cost (the perfectly competitive price level).
- Marginal cost is not always observable, so it is not always easy to assess market power.
The Lerner Index
- The Lerner index (usually denoted \(L\)) is defined as the markup, i.e., the difference between price and marginal cost, as a percentage of the price.
\[L = \frac{p-c'}{p}\]
- Prices are observed, but marginal costs are typically not, and firms are not always eager to reveal this information.
Concentration Index
- A concentration index is a statistic that measures the degree of concentration of the market. A market is concentrated when only a few firms have a large share of the market.
- The concentration ratio is the sum of the market shares of a subset of firms in the market. For \(n\) firms in the market, with \(\alpha_{i} = q_{i} / Q\) denoting the share of firm \(i\), the \(m\text{-firms}\) concentration ratio is given by
\[I_{m} = \sum_{i=1}^{m} \alpha_{i}.\]
- If \(I_{m}\) is close to one, it means that most of the market is controlled by the \(m\) firms included in the calculation.
- If \(m\) is small, this suggests that the market is concentrated.
Herfindahl Index
- The Herfindahl Index is a statistic that measures the degree of concentration of the market by considering the full distribution of market shares. It is defined as the sum of squares (\(\mathcal{L}^2\) norm) of market shares of all active firms in the market.
- For \(n\) firms in the market, with \(\alpha_{i} = q_{i} / Q\) denoting the share of firm \(i\), the Herfindahl index is
\[I_{H} = \sum_{i=1}^{n} \alpha_{i}^{2}.\]
- The closer is the value of \(I_{H}\) to one, the more concentrated the market is.
Estimating Market Power
- Suppose that we know the inverse market demand \(p(q,x)\), where \(q\) is the market quantity and \(x\) is a vector of other exogenous characteristics.
- One approach to estimate market power is to start from the equation
\[MR(\lambda) = p + \lambda \frac{\partial p(q,x)}{\partial q} q\]
- If \(\lambda=0\), then \(MR(\lambda) = p\), i.e., the market is perfectly competitive.
- If \(\lambda=1\), then the market is a monopoly, i.e.,
\[MR(\lambda) = p + \frac{\partial p(q,x)}{\partial q} q.\]
- If \(\lambda=1/n\), then the market is represented by a symmetric \(n\text{-firm}\) Cournot model, i.e.,
\[MR(\lambda) = p + \frac{1}{n}\frac{\partial p(q,x)}{\partial q} q.\]
Equilibrium
- Suppose that \(c'(q,w)\) is the marginal cost function, where \(w\) is a vector of exogenous characteristics affecting cost.
- In equilibrium, for all firms in the market, it holds
\[p + \lambda \frac{\partial p(q,x)}{\partial q} q = c'(q,w).\]
- From this expression, we can obtain estimates of \(\lambda\).
Current Field Developments
- Recent work further investigates methods for estimating market power.
- There is a plethora of methods for estimating market power (Perloff, Karp, & Golan, 2007).
- Recent antitrust cases in the EU are those against Google for Goggle Shipping and Google AdSense.
- Google has been fined with over \(8\) billion Euro for these cases.
- In 2020, a case has been filed against Facebook in the US for suppressing competition from social media rivals.
Comprehensive Summary
- Firms can employ trigger strategies to induce collusion in the market.
- Explicit use of contracts is not required.
- Collusion can be sustained both under quantity and price competition.
- Quantity competition requires firms to value future profits more than price competition.
- Market power can be measured by statistics such as the Herfindahl index.
- Market power can be estimated using a variation of the first order condition of the Cournot model.
Competition with Incomplete Information
Context
- Including uncertainty in market models complicates the analysis. However, some results obtained when ignoring it can be less conducive. For instance, the nature of online marketplaces has many characteristics resembling price competition.
- Yet, many firms make profits in such marketplaces, contrary to the model predictions of deterministic competition in prices.
- How can uncertainty affect competition in markets?
- Do the insights and results of competition change when uncertainty is taken into account?
- Does uncertainty have a uniform impact in all markets?
Course Structure Overview
Lecture Structure and Learning Objectives
Structure
- Web Search (Case Study)
- Competition in Quantities with Cost Uncertainty
- Competition in Prices with Cost Uncertainty
- Comparison with the Deterministic cases and Conclusions
- Current Field Developments
Learning Objectives
- Introduce cost uncertainty in quantity competition and describe the basic mechanisms.
- Illustrate the impact of uncertainty on the market outcomes of quantity competition.
- Introduce cost uncertainty in price competition and describe the basic mechanisms.
- Illustrate the impact of uncertainty on the market outcomes of price competition.
Web Search
- At the beginning of the 1990s, search engines were not invented yet.
- People had to actually type the exact URL to visit a website.
- So, how did people find websites?
In a Web without Google
- Yahoo, founded in 1994, was the first startup company attempting to resolve this issue.
- Its solution was based on manually creating URL directories.
- Similar to yellow pages telephone directories, Yahoo was collecting and categorizing URLs.
- Web users had to visit one website and search for the information they were seeking in a hierarchical catalog.
- By 1997, the startup was the second most visited website (behind AOL).
Web Crawlers
- In 1998, Larry Page and Sergey Brin (the founders of Google) approached Yahoo.
- They pitched PageRank, their search engine algorithm (Arthur, 2011).
- PageRank was offering an alternative way of searching the web.
- Instead of browsing a hierarchical catalog, users can find information by entering relevant keywords.
- The new approach was less familiar than catalog searching (like searching the yellow pages).
- It was highly uncertain whether there was user demand for such a tool.
The Birth of a Tech Giant
- The business model for the PageRank tool was also uncertain.
- With catalog search, Yahoo could place relevant ads in the corresponding catalogs.
- The PageRank tool would take users away from searching the catalog and reduce Yahoo's advertising revenue.
- Yahoo was not interested in PageRank.
- Soon after, PageRank was patented and became the core algorithm of Google's search engine.
- Google introduced algorithms associating search keywords with relevant ads.
- Instead of reducing advertising revenue, the alternative approach led to much greater revenues than Yahoo ever achieved.
Competition in Quantities with Cost Uncertainty
- There are two firms in the market.
- The inverse demand function is
\[p(q) = p_{0} + p_{1}q \quad\quad (p_{0}>0,\ p_{1}<0).\]
- Firm \(i=1,2\) has cost function
\[c(q_{i}, s) = c_{s,i} q_{i}.\]
- The random variable \(c_{s,i}\) takes the values \(0 < c_{l} < c_{h} < p_{0}\) with equal probability.
- The value of \(c_{s,i}\) is observed by firm \(i\) but not by firm \(j\) (private information).
- The random variables \(c_{s,i}\) and \(c_{s,j}\) are independent.
The Expected Profit
- The profit of firm \(i\) is stochastic, even after \(c_{s,i}\) is observed, because the cost of firm \(j\) is not observed.
- Given the observed value of \(c_{s,i}\), firm \(i\) maximizes its expected profit.
\[\max_{q_{s,i}} \sum_{r=l,h} \frac{1}{2} \left[ p(q_{s,i} + q_{r,j})q_{s,i} - c(q_{s,i}, s)\right] \quad\quad (s=l,h).\]
Best responses
- The necessary condition for firm \(i\) is
\[p_{0} + 2 p_{1} q_{s,i} + p_{1} \sum_{r=l,h} \frac{1}{2} q_{r,j} = c_{s,i}.\]
- Solving for \(q_{s,i}\) gives the best response of firm \(i\) at state \(c_{s,i}\)
\[q_{s,i} = \frac{c_{s,i} - p_{0} - p_{1} \sum_{r=l,h} \frac{1}{2} q_{r,j}}{2 p_{1}}.\]
Bayesian Nash Equilibrium
- Calculating the expected value of the best responses of \(i\) gives
\[\sum_{s=l,h} \frac{1}{2} q_{s,i} = \frac{\sum_{s=l,h} \frac{1}{2} c_{s,i} - p_{1} \sum_{r=l,h} \frac{1}{2} q_{r,j} - p_{0}}{2 p_{1}}.\]
- Since the game is symmetric, we expect \(q_{s,j}=q_{s,i}\) for both states \(s=l,h\), so
\[\sum_{s=l,h} \frac{1}{2} q_{s,i} = \frac{\sum_{s=l,h} \frac{1}{2} c_{s,i} - p_{0}}{3 p_{1}}.\]
- Substituting into the best response, we obtain
\[q_{s,i} = \frac{3c_{s,i} - 2 p_{0} - \sum_{r=l,h} \frac{1}{2} c_{r,i}}{6 p_{1}} = \frac{3c_{s,i} - 2 p_{0} - \mathbb{E} c_{i}}{6 p_{1}}.\]
What is the Impact of Stochasticity?
- Firm \(i\) may produce less or more compared to the deterministic case (say \(q\)) depending on the realization of \(c_{s,i}\).
- If \(c_{s,i}>\mathbb{E} c_{i}\), then production is too costly and \(q_{s,i} < q\).
- If \(c_{s,i}<\mathbb{E} c_{i}\), then production is cheap and \(q_{s,i}>q\).
- On average, uncertainty cancels out \(\mathbb{E} q_{i} = q\).
- The market price and quantity can be either greater or less than in the deterministic case, with uncertainty also canceling out on average.
- However, uncertainty reduces the profits of the firms (why?).
- The more uncertain production gets (i.e., the more volatile is \(c_{s,i}\)), the fewer profits firms make on average.
Competition in Prices with Cost Uncertainty
- There are two firms in the market.
- Firm \(i=1,2\) has cost function
\[c(q_{i}, \theta_{i}) = \theta_{i} q_{i}.\]
- The random variables \(\theta_{i}\) are identically, independently, and uniformly distributed on \([0, 1]\).
- The value of \(\theta_{i}\) is observed by firm \(i\) but not by other firms (private information).
Let the demand for firm \(i\) be
\begin{align*}
d_{i}(p_{i}, p_{j}) = \left\{\begin{aligned}
&1 - p_{i} & p_{i} < p_{j} \\
&\frac{1 - p_{i}}{2} & p_{i} = p_{j} \\
&0 & p_{i} > p_{j} \end{aligned}\right..
\end{align*}
Profit Maximization
Given the choice \(p_{j}\) of the other firm, firm \(i\) maximizes its expected profit
\begin{align*}
\pi_{i} &= \max_{p_{i}} \mathbb{E} \left[ \left( p_{i}(\theta_{i}) - \theta_{i} \right) d_{i}(p_{i}(\theta_{i}), p_{j}(\theta_{j}))\right] \\
&= \max_{p_{i}} \left\{ \left( p_{i}(\theta_{i}) - \theta_{i} \right) (1 - p_{i}(\theta_{i})) \mathbb{P}(p_{i}(\theta_{i}) < p_{j}(\theta_{j}) ) \right\} .
\end{align*}
Symmetric Bayesian Nash Equilibrium
- With a bit more mathematics and some calculations…
- Firms choose
\[p^{\ast}(\theta_{i}) = \frac{1 + 2 \theta_{i}}{3} \quad (i =1, 2).\]
- In contrast with the deterministic case, all firms price above their marginal cost, i.e.,
\[p^{\ast}(\theta_{i}) > \theta_{i}.\]
- For \(n\) firms the equilibrium prices are
\[p^{\ast}(\theta_{i}) = \frac{1 + n \theta_{i}}{n+1} \quad (i =1, \dots, n).\]
- The markup decreases in the number of firms in the market (the market becomes more competitive)
\[\frac{\mathrm{d} p^{\ast}(\theta_{i})}{\mathrm{d} n} < 0.\]
- The limiting case gives the perfect competition pricing
\[\lim_{n\to\infty} p^{\ast}(\theta_{i}) = \theta_{i}.\]
Current Field Developments
- Models with dynamic, stochastic competition are state of the art in finance and industrial organization.
- Many of them are not analytically solvable, and numerical methods are used to approximate their solutions.
- Such models are also used in estimations and calibrations to
- examine how well their predictions match observed data, and
- obtain estimates that help organizations and governments to make educated strategic decisions.
Comprehensive Summary
- The calculations can get complicated even for simple stochastic models.
- However, stochastic components can make some market models more conducive.
- Quantity competition with stochastic marginal costs results to fewer expected profits compared to when uncertainty is absent.
- Price competition with stochastic marginal costs leads to positive markups.
- Firms have positive profits, contrasting the deterministic case.