Micro: Game Theory and Collusion

Subgame Perfect Nash Equilibrium

A NE in which in every subgame you are playing a NE. We can judge if a strategy is subgame perfect by using the single deviation principle.

Information Set

A collection of nodes for which we don't know what has happened before. A subgame cannot break up an information set

Subgame

A complete game within a game (note a subgame is also a subgame of itself)

Nash Equilibrium

A set of strategies (one for each player) such that each player's strategy is the best response to the strategies of the other players (at a NE, no player has an incentive to change her strategies, given what the other players are doing)

What is the effect of inventories and excess capacity on collusion?

Ambiguous. Large excess capacity might increase incentive to deviate. But if rivals have larger excess capacity the punishment is more likely to be strong.

Feasible payoffs

An element of a strategy profile which delivers those payoffs

Which law prohibits anti-competitive agreements?

Competition Act 1998 and EU Article 81

Which law prohibits abuse of market dominance?

Competition Act 1998 and EU Article 82

What laws cover mergers?

Enterprise Act 2002 and European Merger Regulation

Give an example of a measure of industry concentration

Herfindahl index

If firms interact in just one market then which firm has the higher incentive to deviate?

The one with the higher cost/ lower market share

How do multiple market interactions increase the likelihood of collusion? (3)

They may balance out asymmetries (in cost, market share) between firms across markets; increases effective number of interactions (a firm could be punished in one market for deviating in another); more potential profits to gain from collusion

Mixed Strategy Nash Equilibrium

When each player's mixed strategy (a probability distribution over a set of available strategies) is a best response to the other player's mixed strategy. In this situation the expected payoffs of every action in your strategy are equal, making the player willing to randomise

Pure strategy

a complete specification of what the player should do whenever they have to make a choice.

Strategy

a player's complete contingent plan of action for all possible occurrences in the game

Minimax punishment

a strategy which minimises the payoff to the other player, given that the other is responding optimally

explain Spence dixit model

adapted version of stackelberg where firms choose capacities instead of quantities (firms compete in quantities in the SR and capacities in the LR)

Why don't firms collude more often? (4)

antitrust policy (cartels, and even some tacit collusion, are illegal), many industries have a high rate of entry and exit (and thus a small discount factor), threat of a punishment strategy may not be credible (price wars can be a painful punishment strategy to implement, the deviating firm may be able to convince their rival not to start one), not all prices are observed with precision (thus possibility of secret price cuts).

The folk theorem

any feasible payoff pair which gives each player at least her minimax payoff can be supported as a NE of an infinitely repeated game if the discount factor is sufficiently close to 1

What stronger alternative of the Folk theorem has been proposed by later authors such as Friedman?

any feasible payoff pair which gives each player at least her minimax payoff can be supported as a subgame perfect equilibrium of an infinitely repeated game if the discount factor is sufficiently close to 1.

What does the Office of Fair Trading do?

applies the prohibitions and does initial merger reviews

With Cournot competition, the reaction functions slope.... quantities are...

downward, strategic substitutes

If total industry capacity is low in relation to market demand, then

equilibrium prices are greater than MC

iterated deletion

finding the outcome of a game by successively deleting dominated strategies

A collusive agreement will only hold if...

firms gain a greater profit from maintaining the agreement than from deviating

ways to choose between multiple NE

focal points, pareto dominance, elimination of weakly dominated strategies

What does the Competition and Markets Authority do?

full merger review and market references

Collusion more likely if: (6)

many (infinite) periods of competition, firms interact in different markets, fewer firms, symmetrical firms (e.g. product homogeneity), large discount factor (e.g. expected industry growth, low industry turnover), periods of low demand

factors affecting likelihood of collusion

number of firms, real interest rate, frequency of sales, ease of detecting cheating, coordination difficulties

dominated strategy

one whose payoff is inferior to that of another strategy, regardless of what the other player does

When firms interact in multiple markets, they...

pool together their incentive constraints from different markets, using the slackness of the constraint in one market to enforce more collusion in the other

When complete market share info is not available what is often used instead?

sum of the top 4 or 5 firms' shares

What is the SSNIP test?

the size of the relevant market depends on the degree of substitutability between products. Tests for a small but significant non-transitory increase in price

the effect of a merger will depend strongly on what

the type of market competition

what happens when firms interact in multiple markets?

they pool together incentive constraints from different markets, using the slackness of the constraint in one market to enforce collusion in the other. restores symmetry to asymmetric markets

In UK mergers not allowed if

they would lead to a 'substantial lessening of competition' (Enterprise Act 2002)

What trade off do we face when regulating mergers?

trade off between efficiency and market power

What does the folk theorem tell us?

trigger strategies used to sustain a NE will use minimax punishments

With Bertrand competition, the reaction functions slope.... prices are....

upwards, strategic complements

Vertical product differentiation

varying in quality. If the price of two goods are the same all consumers will buy A.

Horizontal product differentiation

varying on dimensions other than quality. If the price of two goods are the same some consumers will buy A and some B

Collusion

when firms set prices above the competitive level (tacit or explicit agreement)

In an infinite game, firms will deviate if the discount factor is equal to or less than

1/no. of firms

Give examples of enforcement and penalties of anti-cartel law

In the last decade the penalties for price-fixing (or other illegal agreements) have been significantly raised. Fines of up to 10% of turnover. Prison sentences in the USA for cartels (e.g. the chairman of Sotheby's went to jail in 2001) and the UK (first in June 2008)

Grim trigger strategy

Initially, a player using grim trigger will cooperate, but as soon as the opponent defects, the player using grim trigger will defect for the remainder of the iterated game

What makes the grim trigger strategy a credible threat?

It is a subgame perfect equilibrium

Who reports that experimental evidence supports use of the pareto criterion to choose between multiple NE?

Motta

Individually rational strategy

One which guarantees the player at least their minimax payoff