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Revision pack on oligopoly theory and game theory
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Game Theory: What you need to know...
By Komi!a ChadhaApril 2012
Tuesday, 10 April 12
Outline Cartels and colluding - why do it?
Prisoner’s Dilemma: What is it? What are the strategies and games? Mathematical proof? What is the Nash equilibrium?
Cournot Model
Bertrand Model
Stackelberg Model
Chamberlin Model, is it relevant to oligopolies?
Tuesday, 10 April 12
Cartels and Collusions
Given the concentrated nature of the oligopolistic market, firms may seek to co!ude so that they can benefit #om supernormal profits that monopolies earn.
They may do this by forming a cartel which is essentia!y explicit co!usions but these
are i!egal
Thus they may co!ude i!icitly and this is known as tacit
co!usion and an example of this is price leadership
Tuesday, 10 April 12
What is “prisoner’s dilemma”
It is a model which is explained using a hypothetical & analogous model of two prisoners - please see my video on this: http://a2withkomi!a.blogspot.co.uk/2011/01/competitive-oligopolies-prisoners.html
Tuesday, 10 April 12
Which strategy?
Dominant : Where the strategy of the player is not reliant upon the strategy of
the other player.
Non-dominant: where your strategy is based on the strategy of the other player.
Maximin: When you chose
the highest yielding option from your worst possible
outcomes.
Tit-for-tat: you don’t know how
many times you will encounter, but you cooperate the first time and every
other turn after is a copy of what the other player did.
Sequential games: These are games where you are allowed to make your strategy decision after viewing the activity of the
other player.
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With prisoner’s dilemma it is quite clear that firms are better off to cheat in the short-run, so what is the mathematical
proof for this statement? Look above!
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Nash equilibrium: Where the players may not individually be
at optimal equilibriums but they nevertheless have no incentive to change their
current strategy.
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Cournot ModelThis is a model which suggests that oligopolies compete on
quantity/output.
The main assumption is that each firm takes the other firm’s output as constant and thus derives it’s demand as D-qb
The reactive function is a key part of the model and
suggests that if firm B changes its output then firm A will do
so subsequently.
The model has been criticized for being too naive and
assuming a closed market.
Tuesday, 10 April 12
Mathematics can be used to show that each firms reaction function (which is the derivative of the profit function) is based upon the output of the
other firm.
Graphically the reactive curves, with firm A and B on each axis, show what happens when one firm
changes output.
The intersection is the output they will operate at.
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Bertrand Model
Whereas, the Cournot model explore output competition, the Betrand model suggests price competition exists .
Again each firm assumes the other firms price is constant - the Betrand assumption!
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This model argues that the price competition between the firms results in an oligopoly which achieves the perfectly competitive output of P=MC, as
firms are constantly undercutting one another to gain market share.
Bertrand Model II
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Stackelberg ModelThis model is more similar to Cournot, advocating for quantity competition - so to speak.
However, the key difference is that it sugegsting an oligopoly is an example of a sequential game i.e. that players make their output decisions after seeing what the other players do. Also, output is much more higher in this model.
It is like the output version of price leadership.
The first-mover or quantity setter however always benefits the most.
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Comparison of prices and profits
BERTRAND < STACKELBERG < COURNOT < MONOPOLY
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Chamberlin ModelThe Chamberlin model isn’t very important for oligopoly theory, it is merely the idea of monopolistic competition. That is that firms can have inelastic demand and differentiated goods yet operate in a competitive market.
For more info pleasesee my posts and
booklets/videos onmonopolistic competition.
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End
Thank you for reading!
By Komi!a Chadha
Tuesday, 10 April 12
