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Previous lecture
• Demand and supply model
› Complements and substitutes
› Elasticities
› Marginal cost
› Economies and diseconomies of scale
• Perfect competition vs monopoly
› Number of firms
› Barriers to entry
› Homogeneity of product
• Economic welfare and efficiency:
› Consumer and producer surplus
› Deadweight loss
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Market power
• Ability to profitably raise price above perfect
competitive level is called ‘market power’
• The logic of the monopoly model…
› Firms produce and sell less than in a competitive market
› There is deadweight loss / inefficiency
…holds for any firm with market power
• Market power is a form of ‘market failure’
› The privately optimal decision ≠ the socially optimal decision
› In this case: private pricing decision does not maximise
welfare
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What do we do about market power?
• Some market power is good…
› Incentive to innovate/differentiate
› And so it is not illegal to have or use market power
• But ‘substantial’ market power can be bad
› Regulation is sometimes used when there is significant and
enduring market power (eg electricity distribution)
› If used for the purpose of deterring or preventing entry or
substantially damaging a competitor (s46)
› If it is achieved through collusion or mergers (substantial
lessening of competition, s50)
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Outline for today
• In PC/monopoly there is no strategic interaction…
• Game theory:
› Static games
› Dynamic games
• Models of markets based on game theory:
› Bertrand (price) competition
› Cournot (quantity) competition
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Game Theory
• Key features of interactive decision-making:
› Who are the decision-makers?
› In what order do they make decisions?
› What actions are available?
› What are their motives or preferences over outcomes?
• A game is a formal representation of this, with elements:
› Players
› Timing:
Simultaneous or sequential actions
One-shot or repeated game
› Actions (can be discrete or continuous)
› Payoffs
› Strategies (“if she does this, I do that…”)
› Equilibrium or equilibria
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Static games
• A one-shot, simultaneous action game
• Represented by the ‘normal form’ matrix.
• Example: Prisoners’ Dilemma
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Prisoner 1
Betray Co-operate
Prisoner 2
Betray
Co-operate
•
• What will be the outcome (equilibrium)?
2 years
2 years
3 years
No jail
No jail
3 years
1 year
1 year
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Static games – equilibrium concepts
• Dominant strategy equilibrium:
› Is there a “dominant strategy” that yields a higher payoff
regardless of the other player’s action?
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Prisoner 1
Betray Co-operate
Prisoner 2
Betray 2 years 3 years
2 years No jail
Co-operate No jail 1 year
3 years 1 year
• The dominant strategy equilibrium (betray, betray) is inferior
for both players to the alternative (co-operate, co-operate)
Dominant
strategy
Dominant
strategy
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Nash equilibrium: another solution concept
• There is not always a dominant strategy equilibrium
• Define a “best response” function as the optimal
choice given your rival’s action
• Nash equilibrium:
› The intersection of best response functions
› i.e. all players are playing their best responses
› Given their rivals’ actions, in a Nash equilibrium no player has
an incentive to change their own action
› Note a DSE is automatically a Nash equilibrium as well
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Example of Nash equilibrium
• A ‘co-ordination game’ of development of new
technology
› Assume two firms: a TV manufacturer and a broadcaster
› There are costs to both of investing in HDTV technology which
will only be recouped if the other also invests
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TV manufacturer
Invest Don’t invest
Broadcaster
Invest 100 20
100 – 50
Don’t invest – 50 20
20 20
• Nash equilibria: (invest, invest) & (don’t invest, don’t
invest)
• What would happen if the game were sequential?
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Sequential games
• Backward induction
• Represent sequential games and repeated games in
the “extensive form”
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M
B B
Invest Don’t
invest
Invest
Don’t
invest
Don’t
invest
Invest
(100, 100) (–50, 20) (20, –50) (20, 20)(M, B) =
Invest Don’t
invest
Invest
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Ultimatum game
• A one-shot sequential game
• There is a pile of chocolate to be divided amongst 2
players
• Player 1 proposes a split (e.g. 50:50, 80:20, 90:10)
• Player 2 accepts or rejects the offer
› If player 2 accepts, the chocolate is divided as proposed
› If player 2 rejects, neither player receives any chocolate
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Ultimatum game - results
• How many rejected the offer?
• How many offered 50% to the other player?
• How many offered less than 50% to the other player?
• How many offered more than 50% to the other
player?
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• Assume one shot game with perfectly rationale players
• Backward induction
• Player 2 should accept any amount greater than 0
• Player 1 should offer smallest amount possible
• Outcomes often different to theory because repeated
game, fairness etc
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Price competition
• When firms compete on price, what is the optimal
strategy and how competitive will the market be?
• Assume imperfect substitutes
• ‘Best responses’: the higher your rival’s price, the
higher your own:
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PA
PQ
Firm Q b.r.
Firm A b.r.
200
200 300
300
Nash equilibrium: the
intersection of best responses
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Price competition (continued)
• Perfect substitutes: “Bertrand competition”
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PT
PJ
J b.r.T b.r.
MCJ
MCT
45° line
• Best response: price just below your competitor (but not < MC)
• Nash equilibrium: P=MC, zero profit
• Are just two firms sufficient to generate a perfectly competitive market?
Nash equilibrium: the
intersection of best responses
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Quantity competition: the Cournot model
• Firms set quantities and let the market determine a
price
• Can represent setting of capacities followed by
capacity-constrained price-setting
• Cournot quantity ‘best responses’:
› Firms choose quantity such that Marginal Revenue = MC
› MR can be broken down into
Additional revenue from one additional sale, which depends on
the price (and therefore quantity sold)
Loss of revenue from lower price on existing sales, which depends
upon how much the increase in the firm’s output alters the price
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Quantity competition: the Cournot model
• The best response to 0 is the monopoly quantity (e.g. 500)
• The best response to the PC quantity (e.g. 1000) is 0
• The Nash equilibrium sees P > MC, with the price-cost margin
decreasing as the number of firms increases
• For n=1 and n=∞ Cournot produces the monopoly and PC models
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QT
QJ
Firm J b.r.
Firm T b.r.
Nash equilibrium: the
intersection of best responses
1000
500
500 1000
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Example: Monopoly with entry deterrence
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• An example of ‘strategic commitment’
• The threat of entry can discipline a monopolist into
more competitive pricing; a ‘contestable market’
Monopolist
Entrant Entrant
Small
capacity
Large
capacity
Enter
Don’t
enter
Don’t
enter
Enter
(20, 20) (60, 0) (0, –20) (40, 0)Profits for (M, E) =
Enter
Don’t
enter
Large
capacity
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Predatory pricing
• A firm ‘predator’ sets a low price for sufficient period
such that rival (or rivals) exit
• Typically involves
› Loss of profit by predator when set low prices initially; and
› Phase where predator is able to set higher prices when faces
less competition – need market power
• What is the difference between predation prices
and competitive prices?
› Risk of stifling competition
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Predatory pricing theories
• Reputation models
› Incumbent make a loss fighting entrants in order to
discourage others
• Deep pocket theory
› Small firm’s borrowing is restricted
• Signalling
› Incumbent signals that it has very low costs
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Repeated prisoners dilemma (RPD) and collusion
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Firm 1
Compete Collude
Firm 2
Compete 5 1
5 14
Collude 14 10
1 10
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10
5
1 2 3
Nash eqm in one
shot game
Firm 1 payoff from
always collude
Firm 1 payoff from
compete today
Number of
periods from now
Payoffperperiod(firm1)
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According to this RPD model, firms are more likely
to collude when..
• They are patient
• Frequent interactions between firms
› Benefit of cheating is small
• Cheating is easy to detect
• Fewer firms
• Necessary conditions for collusion:
› Agree on collusive outcome
› Monitor collusion and punish cheaters
› Prevent entry (or accommodate)
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How can we stop collusion?
• Market outcomes of collusion and competition look
the same
• No competition authority has detected collusion by
examining market outcomes alone
• Leniency programs in combination with large fines
and are very effective:
› Create a strong incentive to apply for leniency
› “unquestionably, the single greatest investigative tool
available to anti-cartel enforcers” Scott D. Hammond
U.S. Department of Justice
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