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Thinking Strategically. The kinked demand curve model of Oligopoly. Assume no cooperation or collusion among firms

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The kinked demand curve model of oligopoly l.jpg
The kinked demand curve model of Oligopoly

  • Assume no cooperation or collusion among firms

  • This model helps explain why the prices in some oligopolistic markets change very slowly over time – individual firms are basically afraid to change price because of what other firms might do.


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Kinked Demand Curve

  • Assume that we have 3 firms: A, B, & C

  • Products are similar

  • The shape of the demand curve for A’s product tells us how much QD changes when there is a price change (elasticity) – this depends on the pricing behavior and similarity of the substitutes B and C.


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Kinked Demand Curve

Consider what happens when A changes its price:

1. If firm A lowers price then B and C can follow the price change or ignore it.

  • If B and C follow then they also lower price because they are afraid of losing their market share to firm A.

  • If B and C ignore the price change by A, then they maintain the higher price because they don’t believe that people will switch.

    2. If firm A raises price then B and C can follow the price change or ignore it.

  • If B and C follow then they also raise price because they don’t believe that people will switch, so they can increase profits by also charging more.

  • If B and C ignore the price change by A, then they maintain the lower price because they believe that people will switch, and they can capture some of firm A’s market share by having a lower price.


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Kinked Demand Curve

Notice that if the competitors B and C ignore the price change – then we have more price difference than before, so consumers are more likely to switch between products.

If A lowers price and B and C do not follow:

  • consumers are more likely to substitute toward A

  • decrease in the Price of A => big increase in QD for A

    So if A raises price and B and C do not follow:

  • consumers are more likely to substitute toward B and C

  • increase in the Price of A => big decrease in QD for A

    If the other firms do not follow then the demand for A’s product will be relatively ELASTIC (flat slope).


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Kinked Demand Curve

  • On the other hand, if the other firms do follow A’s price changes, then there is going to be less substitution taking place and the demand for A’s product is going to be relatively INELASTIC (steep slope).


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Kinked Demand Curve

Now…Pretend that you are firms B and C and I am firm A.

And you think that your product is a close substitute for my product.

  • What will you do if I raise price?

    • Nothing. Keep your price low to try and capture my market share.

    • You do not follow => this makes my demand ELASTIC (flat) above the current price.

  • What will you do if I lower price?

    • Follow and also lower price so that I do not capture your market share.

    • This makes my demand INELASTIC (steep) below the current price


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Kinked Demand Curve

  • When firms believe that their product is a close substitute for their competitor’s product, they do not have much incentive to change price:

  • A price decrease will be matched, so they have nothing to gain by lowering price.

  • A price increase will not be matched, so they have a lot to lose by raising price.


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Theory of Games

  • The payoff of many actions depends upon the actions of others

    • For example, an imperfectly competitive firm must weigh the responses of rivals when deciding whether to cut their prices

    • The decisions of competing firms are often interdependent


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Game theory

  • A mathematical technique for analyzing the decisions of interdependent oligopolistic firms in uncertain situations.

  • A “game” is simply a competitive situation where two or more firms or individuals pursue their interests and no person can dictate the final outcome or “payoff”.

  • Players choose their strategy without certain knowledge of the other players strategies, but may eventually learn which way the opposition is leaning.


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Elements of a Game

  • Basic elements

    • The players

    • The strategies

    • The payoffs

  • Payoff matrix

    • The fundamental tool of game theory.

    • This is simply a way of organizing the potential outcomes of a given game in a table that describes the payoffs in a game for each possible combination of strategies


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Strategies

  • Dominant strategy

    • A strategy that yields a higher payoff no matter what the other players in a game choose

  • Dominated strategy

    • Any other strategy available to a player who has a dominant strategy

  • Nash Equilibrium

    • Any combination of strategies in which each player’s strategy is his best choice, given the other players’ strategies

    • IOW: Nash equilibrium is achieved when all players are playing their best strategy given what the other players are doing.


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A simple game and payoff matrix

  • Duopoly situation – each of the two firms A and B must decide whether to mount an expensive advertising campaign.

  • If each firm decides not to advertise, each will earn a profit of $50,000.

  • If one firm advertises and the other does not, the firm that does will increase its profits by 50% to $75,000, and drive the competition into a loss.

  • If both firms advertise, they will earn $10,000 each because the advertising expense forced by competition wipes out large profits


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Example continued…

  • If firms could agree to collude, the optimal strategy would obviously be to not advertise – maximize joint profits = $100,000

    • Let’s assume they cannot collude, and therefore do not know what the competition is doing.

  • A “Dominant Strategy” is the one that is best no matter what the opposition does.


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The Payoff Matrix

Firm B

Don’t AdvertiseAdvertise

Don’t

Advertise

Firm A

Advertise

A profit = $50

B profit = $50

A loss = $25

B profit = $75

A profit = $75

B loss = $25

A profit = $10

B profit = $10


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New Game: “The Prisoner’s Dilemma”

  • You and your friend Bugsy are the prime suspects for knocking over a liquor store. The cops pick you up, and immediately after your arrest you and Bugsy are separated and questioned individually by the DA. Without a confession, the DA has insufficient evidence for a conviction. During your interrogation, you are told the following:

  • The police do have sufficient evidence to convict you and Bugsy of a lesser crime.

  • If you and Bugsy both confess to the liquor store heist, you will each get a 5 year sentence.

  • If neither of you confesses, you will each be charged with the lesser crime, and sent up the river for 1 year.

  • If Bugsy confesses (turns state’s evidence) and you do not, Bugsy will go free while you will be convicted of the liquor store robbery and get sent to the big house for 7 years.

  • Bugsy is told the exact same information.

  • What will you do?


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The Payoff Matrix

You

Don’t ConfessConfess

Don’t

Confess

Bugsy

Confess

Bugsy = 1 year

You = 1 year

Bugsy =7 years

You = Free

Bugsy = Free

You = 7 years

Bugsy =5 years

You = 5 years


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Prisoner’s Dilemma

  • Prisoner’s Dilemma

    • Each player has a dominant strategy

    • It results in payoffs that are smaller than if each had played a dominated strategy

  • Produces conflict between narrow self-interest of individuals and the broader interest of larger communities


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Naturalist applications of prisoner’s dilemma

  • Why do people shout at parties?

  • Why does everyone stand up at concerts?


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There are some games where one player does not have a dominant strategy but the outcome is predictable …

A

Left Right

Top

B

Bottom

A’s behavior is predictable in this case.

B profit = 100

A profit = 0

B profit = 100

A profit = 100

B loss = 100

A profit = 0

B profit = 200

A profit = 100


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One more … dominant strategy but the outcome is predictable …

A

Left Right

Top

B

Bottom

Here, A’s behavior is again predictable – choose Right is the dominant strategy – but now B stands to lose a great deal if by chance A chooses left instead

B profit = 100

A profit = 0

B profit = 100

A profit = 100

B loss = 10,000

A profit = 0

B profit = 200

A profit = 100


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Cartels dominant strategy but the outcome is predictable …

  • Cartel

    • A group of firms who sell a similar product who have joined together in an agreement to act as a monopoly – restrict output and raise price

    • Normally cartels involve several firms

      • Make retaliation against a dissenter difficult

    • Agreements are not legally enforceable and are hence inherently unstable


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Reasons for collusion among firms dominant strategy but the outcome is predictable …

  • to reduce the uncertainty of a noncooperative situation – competition over market share makes firms unsure of what to do with regard to pricing decisions – they’re afraid to change prices – so to avoid the possibility of a price war, firms might try to cooperate.

  • to increase profits – this need for profit can turn out to be the downfall of most cartels – GREED


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Collusion dominant strategy but the outcome is predictable …

  • Overt collusion is illegal in the US.

  • Most cartels fail. This is because 3 things are needed for a cartel to be successful, and they’re tough to accomplish –

  • 1st, the firms must come to an agreement as to what the price and quantity should be –tough to do because different firms will have different cost structures and different assessments of market demand, so what is the profit-maximizing price and quantity for one firm is not likely to be the profit-maximizing combination for another firm.

  • 2nd, the cartel members must adhere to the agreed upon price and production levels – no cheating. But each firm knows that if it cheats and the others do not, that they can have higher profits.

  • 3rd, there must be the potential for monopoly power – the market demand curve must be relatively inelastic so that there are potential gains from increasing price – it has to be a good with few substitutes.


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Is the NCAA a cartel? dominant strategy but the outcome is predictable …

  • Where do the big profits come from at large state schools?

    • sports

  • Is it a competitive market?

    • many schools… but the large profits suggest that there is some monopoly power.

  • The NCAA creates this market power and profit by restricting output – limit the number of games per season, limit the number of teams per division, strict eligibility guidelines for schools…

  • Up until 1984 the NCAA restricted the number of games on TV and charged very high prices compared to today – but the supreme court called it illegal collusion and as a result we have much more games on TV today than 20 years ago.

  • Can we say the same things can be said for professional sports?


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Example: collusion dominant strategy but the outcome is predictable …

  • 2 firms sell bottled water with MC = 0

  • The firms agree to act as a monopolist and set price in order to maximize joint profits (P*).

  • Each will produce ½ of the output.

  • No enforcement mechanism.

  • Cheating by 1 firm = selling the water at < P* => that firm gains entire market.


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The Market Demand for Mineral Water dominant strategy but the outcome is predictable …Q* = 1000, P* = 1.00 = > profits = $500 each


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Temptation to Violate the Cartel Agreement dominant strategy but the outcome is predictable …if 1 firm cheats => profits = $990 & 0


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Create the payoff matrix for this game dominant strategy but the outcome is predictable …

  • Firms 1 & 2

  • Options: collude (price = $1.00) or cheat (price = 0.90)

  • Is there a dominant strategy for each firm?

  • Is there an incentive to cut prices even more?


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Games with Timing dominant strategy but the outcome is predictable …

  • Previously we assumed that players moved at the same time

    • However, timing is of the essence

  • Decision tree or game tree

    • A diagram that

      • Describes the possible moves in a game in sequence

      • Lists the payoffs that correspond to each possible combination of moves


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Irrational (?) behavior and the role of preferences dominant strategy but the outcome is predictable …

  • Assuming people are narrowly self-interested does not always capture the full range of motives

    • Restaurants frequented mainly by out-of-towners have the same tipping rates as those with mainly repeat customers

    • People care about being treated justly

    • Sympathy for a trading partner can make a business person trustworthy