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 high-level 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 out-of-court settlement with SEC in 2000; He was 15 years old.
The SEC Prosecution
Lebed is the first minor ever prosecuted for stock-market 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.
Shortly after his \(11\text{-th}\) birthday Jonathan opened an account with America Online.
He started building a website about pro-wrestling.
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]stock-dogs[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
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 single-seller 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
\[p_{m} = \frac{\text{Marginal Cost}}{\frac{1}{\text{Demand Elasticity}} + 1}\]
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.
In most real-life situations, economic agents do not operate in isolation. Their gains and losses depend not only on their own choices but also on the choices of others.
Markets are typical examples of economic situations where social interactions matter.
How can we study social interactions in economics?
How do economic agents compete and coordinate with each other?
What are the social dilemmas that arise in such situations?
Course Structure Overview
Lecture Structure and Learning Objectives
Structure
Street Fighter Mechanics (Case Study)
Basic Concepts
Examples with pure strategy equilibria
Examples with mixed strategy equilibria
Current Field Developments
Learning Objectives
Explain why social interactions can lead to social dilemmas.
Explain how game theory models social interactions.
Describe the concept of equilibrium in models with interactions.
Illustrate the concept of pure strategy equilibrium in static settings.
Illustrate the concept of mixed strategy equilibrium in static settings.
Street Fighter Mechanics
Street Fighter II: The World Warrior is a fighting game released in 1991.
It was originally released in arcade.
It reestablished the arcade competition from high score chasing to one-vs-one play.
It inspired competitive video game tournaments in the early 2000s.
Today the e-sports market is valued at more than a billion dollars.
Why was Street Fighter II so successful?
Command Grab
Grapplers are (typically large) slow characters that have powerful grappling moves.
The execution of these moves requires the avatars to be close.
Command grabs are special grappling moves that cause a lot of damage.
But they are very slow.
Neutral Jump
Grabs do not work if the defender jumps vertically (neutral jump).
Moreover, because command grabs are so slow, the defender can punish the grappler on his way down.
Normal Grab and Anti-Air
Instead, the grappler can do a normal grab which recovers faster.
In addition, with the fast recovery, the grappler can punish the defender in the air using a follow up, anti-air move.
Throw Technical
An alternative option for the defender is to counter the grab with a technical counter.
This tactic avoids the normal grab and anti-air punishment.
However, it is vulnerable to the grappler's command grab.
How do players resolve this situation?
Social Dilemmas
For some social interactions, individual interests do not always work in favor of society as a whole.
Individual producers' interests suggest using cheap, brown instead of more expensive, green technologies.
However, if all producers act in this way, pollution increases and the lives of everyone become worse off.
A social dilemma is a situation in which actions taken independently by agents pursuing their individual objectives result in inferior outcomes to other outcomes that are feasible if agents coordinate.
Social Interactions
Game theory is the main apparatus used for examining social interactions.
A game is a description of a social interaction specifying
the players (who is participating?),
the feasible actions (when is someone playing? What can she do?)
the information (what is known by players when making their decisions?)
the payoffs (what is the outcome for each possible combination of actions?)
Common knowledge
In the games that we will examine, the utilities and the choices of players are common knowledge.
Common knowledge is information that is known and understood in the same way by all the players of a game.
There is an element of infinite recursion in the idea of common knowledge.
The agents of a game have common knowledge of a property \(P\) when they all know \(P\), they all know that they know \(P\), they all know that they all know that they know \(P\), etc.
Actions and Strategies
Each player in a game has one or more decisions to make.
A single choice made at a particular decision node is called an action.
The collection of all actions of a player in a game is called a pure strategy (or simply strategy when it is understood from context that it is pure).
In games where a player has a single decision to make, her actions and strategies coincide.
Representations of Games
Games can be represented in various ways.
The representations are not always interchangeable.
Some games admit only certain representations. Others can be represented in multiple ways.
Each representation has certain advantages.
Normal Form
Simple games can be represented using a table documenting the primitives of the game.
This representation is called the normal form of a game.
Extensive Form
The extensive form of a game is a representation in terms of a tree.
The extensive form depicts more information than the normal form:
It illustrates the order in which the players act.
It illustrates the information available to each player.
Information Set
If a player has the same information at two (or more) nodes, the nodes are connected with a dotted line.
An information set is a collection of decision nodes that the player making decisions cannot distinguish at the time of decision.
The player knows that she is located at one of the nodes of the information set, but she does not know which one of them.
Best Responses
Given a player's strategy, what is the best strategy with which the other player can respond?
A best response strategy is a strategy that maximizes a player's payoff for given strategies of the remaining players of the game.
The best response mapping is an association that gives the strategies that maximize a player's payoff for each combination of strategies of the remaining players of the game.
On some occasions, a player can choose a strategy that makes her better off irrespective of the strategies chosen by other players.
A strategy that, for all strategies other players can choose, gives a higher payoff to a player compared to every other strategy available to her is called a dominant strategy.
\(Left \succ_{B} Right\)
Nash Equilibria
A collection of strategies, one for each player, such that each strategy constitutes a best response to the remaining players' strategies is called a Nash equilibrium.
In short but less accurate, a Nash equilibrium is a collection of mutual best responses.
Intuitively, a Nash equilibrium is a collection of strategies from which no one has an incentive to deviate.
\(NE = \left\{ \left\{ Bottom, Left \right\} \right\}\)
Do Nash equilibria predict the outcome of games?
Nash equilibria do not say how, why, or whether these strategies are reached in a game.
The definition of Nash equilibria suggests that if they are reached, then there is no incentive for anyone to change her behavior.
Are Nash equilibria unique?
Nash equilibria are not unique.
Multiple situations in a game may constitute points from which no one wants to deviate.
The payoffs of the players in different Nash equilibria can be significantly different.
\(NE = \left\{ \left\{ Bottom, Left \right\}, \left\{ Top, Right \right\} \right\}\)
Are Nash equilibria necessarily Pareto efficient?
No. Nash equilibria can be Pareto inefficient.
A classic example is the prisoner's dilemma.
The Grappler Game
Back to the Street Fighter mechanics
Is there no Nash equilibrium in this case?
Mixed strategies
Pure strategies are collections of actions, one for each decision to be made.
Sometimes the players prefer to choose strategies based on some randomization rule.
Players can randomize by assigning the probabilities (weights) with which they use their pure strategies.
A distribution over the player's pure strategies is called a mixed strategy.
A Mixed Strategy Example
The grappler has two pure strategies (\(Command\ Grab\) and \(Normal\ Grab\)).
The mixed strategy \((p, 1-p)\) assigns probability \(p\) to choosing \(Command\ Grab\) and probability \(1-p\) to choosing \(Normal\ Grab\).
Existence of Nash Equilibria
Finite games always have at least one Nash equilibrium in mixed strategies (Nash 1950).
A finite game is a game in which the number of players, actions, and decision nodes are finite.
The Grappler Game's Equilibrium
The grappler performs a \(Command\ Grab\) with probability \(p\) and a \(Normal\ Grab\) with probability \(1-p\).
The grappler chooses these probabilities so that it makes the defender indifferent between \(Neutral\ Jump\) and \(Tech\) (why?).
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
StatCounter
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.
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 failure (imperfect information, externalities, etc.),
no other firms can enter the market,
firms sell a homogeneous product,
firms try to maximize their profits by simultaneously choosing the quantities they produce,
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.
Concise 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.
Strategic interactions and social dilemmas can sometimes be understood in terms of one-shot sandbox cases. In such settings, where time is neglected, promises, threats, and reputation play no role.
However, players have many additional strategies available whenever there is a future, and they can use promises and threats to achieve very different outcomes compared to the atemporal cases.
How does time affect the outcomes of social interactions?
Why is reputation important whenever time is involved?
How can players incorporate time into their strategies?
Course Structure Overview
Lecture Structure and Learning Objectives
Structure
Buying an Empire (Case Study)
Repeated Games
Sequential Games
Backward Induction and Subgame Perfect Equilibria
Current Field Developments
Learning Objectives
Illustrate the relevance of time in social interactions.
Explain how incorporating time can affect the results of interactions.
Describe the role of backward induction when analyzing dynamic interactions.
Illustrate the concept of subgame perfect equilibrium in dynamic settings.
Explain how move order and patience affect the bargaining power of interacting agents.
Buying an Empire
Auctions are typical examples of economic interactions studied by game theory.
One of the most significant historical auctions took place in 193 AD.
A trigger strategy is a strategy, where at each iteration of a repeated game an action is selected based on the coordination state of the game. If all players coordinated in the past then a coordinating action is chosen for the current iteration. Instead, past defections trigger players to choose punishing actions for the current iteration.
Trigger strategies can be further specified as
Grim trigger strategies, where the punishment continues indefinitely after a player defects.
Tit for tat strategies, where the punishment is only applied for a limited number of dates after a defection.
Coordination in Prisoner's Dilemma
Players can coordinate by using trigger strategies.
If at all previous dates the other player has denied, then deny. Otherwise, confess.
If players coordinate, then each gets a payoff of \(-1\) at each date, thus
\[u_{c,i} = -\frac{1}{1 - \delta}\]
Can Coordination be Supported?
If player \(i\) deviates at the current date, then her payoff at the current date is \(0\).
At every subsequent date, her payoff is \(-3\), because her past deviation triggers the other player's punishment.
Therefore,
\[u_{d,i} = -3\frac{\delta}{1 - \delta}\]
Coordination can be supported if such a deviation is not profitable, i.e.
As long as players are patient enough, the underlying threats of trigger strategies make coordination feasible.
Sequential Games
A game is called sequential if its players play sequentially instead of simultaneously.
Nash equilibria also exist in such games.
We can find some of them using backward induction.
The best action of the player that acts at the last date is calculated.
Given this best response, the best action of the player that acts at the previous to last date is calculated.
We continue in this fashion until we have calculated the best action of the player who acts at the initial date.
Backward Induction
\(SPE = \left\{ \left\{Bottom, \left(Left', Right \right)\right\} \right\}\)
Subgame Perfect Equilibria
A subgame of a dynamic game is the restriction of the game starting from a particular decision node and including all subsequent decision nodes and branches (actions) of the original game.
A collection of strategies, one for each player, such that its restriction to each subgame of the original game constitutes a Nash equilibrium of this subgame is called subgame perfect equilibrium.
This implies that the past does not matter in optimal decisions once a decision node is reached.
Equilibria of this type are typically abbreviated as SPE.
Backward induction can be used to calculate subgame perfect equilibria.
Bargaining
A process through which two or more people decide how to share a surplus is called cooperative bargaining (or simply bargaining).
Players negotiate how to divide the surplus (a value) in one or more rounds.
Take it or Leave it Game
There are two players negotiating how to share a surplus of unit value.
Player \(A\) moves first and makes an offer \(x\in[0,1]\).
Player \(B\) moves second and decides whether to accept or reject the offer.
If the offer is accepted, player \(A\) gets \(x\), and player \(B\) gets \(1-x\).
If the offer is rejected, both players get zero.
First Move Advantage
Player \(B\) accepts if \(1-x \ge 0\) or, equivalently, if \(x\le 1\).
Player \(A\) offers \(x = 1\).
Counter-Proposal
Suppose that player \(B\) can make a counteroffer.
She can offer \(y\in[0,1]\) if she rejects the offer of player \(A\).
If the counteroffer is accepted, player \(A\) gets \(1-y\), and player \(B\) gets \(y\).
If the counteroffer is rejected, both players get zero.
Last Offer Advantage
Player \(A\) accepts the counteroffer if \(1-y \ge 0\) or, equivalently, if \(y\le 1\).
Player \(B\) offers \(y = 1\).
Player \(B\) accepts the first offer if \(1-x \ge y = 1\) or , equivalently, if \(x \le 0\).
Player \(A\) offers \(x = 0\).
Alternating Offers
Suppose that the counter-proposal game is infinitely repeated until a deal is reached.
Every time a player rejects an offer, she makes a counteroffer.
Players discount every offer-round with factors \(\delta_{A},\delta_{B}\in[0,1)\).
A Recursive Equilibrium
Suppose the game is at date \(t\) and player \(B\) makes an offer.
Player \(A\) accepts if \(y\le 1\), so player \(B\) offers \(y=1\).
At date \(t-1\), player \(B\) accepts if \(x\le 1-\delta_{B}\), so player \(A\) offers \(x=1-\delta_{B}\).
At date \(t-2\), player \(A\) accepts if \(y\le 1 - \delta_{A} + \delta_{A}\delta_{B}\), so player \(B\) offers \(y=1 - \delta_{A} + \delta_{A}\delta_{B}\).
Recursively, one can show that player \(A\) offers
If player \(A\) becomes more patient (\(\delta_{A}\ \uparrow\))
she is more willing to postpone acceptance for the next date
player \(B\) loses bargaining power
player \(A\) gets a greater part of the surplus (\(x\ \uparrow\))
If player \(B\) becomes more patient (\(\delta_{B}\ \uparrow\))
she is more willing to postpone acceptance for the next date
player \(A\) loses bargaining power
player \(A\) gets a smaller part of the surplus (\(x\ \downarrow\))
Current Field Developments
Much of modern work in game theory is dynamic.
The folk theorem is a fundamental theoretical result stating that in infinitely repeated games, any feasible payoff vector can be achieved by a subgame perfect equilibrium if players are sufficiently patient.
Since its development by Friedman (1971), much subsequent work has focused on equilibrium refinements that give stricter predictions.
Another active area of work in game theory focuses on extensions of preferences of players that include behavioral traits (e.g., regret, cognitive costs, etc.).
Concise Summary
Time is of the essence in strategic interactions.
Many outcomes of simultaneous interactions can be overturned when time is taken into account.
If there is a future, coordination can be supported even in cases when the corresponding simultaneous interaction results in non coordination (i.e. the prisoners' dilemma).
Patience is central in determining what types of coordination can be achieved and how the coordination gains can be split.
Players can use strategies involving threats and promises to induce coordination.
Nevertheless, these promises and threats have to be credible.
The subgame perfect equilibrium is a refinement of the Nash equilibrium accounting for credibility issues.
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.
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.
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.
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 by 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 example, with \(n\) firms in the market, \(\alpha_{i} = q_{i} / Q\) denoting the share of firm \(i\), and a \(M\) denoting a subset firms, the M-concentration ratio is given by
\[I_{M} = \sum_{i\in M} \alpha_{i}.\]
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 affecting demand.
One approach to estimating market power is to start from the equation
\[MR(\lambda) = p + \lambda p'(q;x) q\]
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.,
\[MR(\lambda) = p + p'(q;x) q.\]
If \(\lambda=1/n\), then the market is represented by a symmetric \(n\text{-firm}\) Cournot model, i.e.,
\[MR(\lambda) = p + \frac{1}{n}p'(q;x) q.\]
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
\[p = c'(q;w) - \lambda p'(q;x) q.\]
From this expression, we can obtain estimates of \(\lambda\).
Current Field Developments
Recent work further investigates methods for estimating market power.
Connor, John M. 2000. “Archer Daniels Midland:Price Fixer To The World.” Working Papers 00-11. Purdue University, College of Agriculture, Department of Agricultural Economics. https://ideas.repec.org/p/pae/wpaper/00-11.html.
———. 2001. “Our Customers Are Our Enemies: The Lysine Cartel of 1992-1995.” Review of Industrial Organization 18 (1): 5–21. https://doi.org/10.1023/A:1026513927396.
Friedman, James W. 1971. “A Non-cooperative Equilibrium for Supergames.” The Review of Economic Studies 38 (1): 1–12. https://doi.org/10.2307/2296617.