Oligopoly Problem

8/3/2019 Oligopoly Problem

1/17


2/17

Oligopoly pricing resembles a repeated prisoners'dilemma game. Each firm has an incentive tomoderately lower its price and thus increase itssales at its competitors' expense.

However, each firm knows that its rivals wouldpromptly discover such deviation and follow suitshortly

The problem of interdependence has thwartedeconomists' attempts to develop a good theory of

oligopoly. When there are only a few sellers, eachrecognizes that his decisions affect others whomay react to what he does.


3/17

The Oligopolist is big enough to affect themarket in some way, dealing with a multitudeof individual consumers.

His decision can hugely impact sales


4/17

The"prisoners' dilemma" was first described in the field of "gametheory", which is a branch of applied mathematics andeconomics dealing with choices made under conflict anduncertainty.

Suppose that the police believe Dave and Henry have committeda crime but the evidence is weak. The police have placed Daveand Henry in jail, in separate cells. The police need theconfession of at least one of the prisoners in order to get aconviction.

If neither prisoner confesses, then the police can only convictthem on a minor charge with a three-month prison term. Eachprisoner is offered the following deal: if one testifies against theother while the other remains the silent, the one who testifies

will not be convicted of anything, while the one who remainssilent will go to jail for 20 years. If both confess, then each willreceive a five-year jail term.


5/17


6/17

The optimum result for the two together is to stay silent,in which Dave and Henry will each get only three monthsprison time. However, each prisoner does not haveknowledge of what the other prisoner will do.

The most rational response from the individual is toconfess. If the other prisoner stays silent, then that person

gets off free; if the other prisoner confesses, then theprison term will be less (five years vs. 20 years. The prisoners' dilemma illustrates a situation in which

individuals arrive at a non-optimal solution, due to a lackof cooperation and trust. A similar situation occurs witholigopolies. If firms within an oligopolistic industry have

cooperation and trust with each other, then they cantheoretically maximize industry profits by setting amonopolistic price. Firms would then have to figure outhow to fairly divide up the Profits.


7/17


8/17

The Prisoners Dilemma is a good example ofa static game of complete information. This isprobably the simplest form of a game thatinvolves the interaction of multiple

individuals in a decision making process.


9/17

One obvious response to the analysis of theprisoner's dilemma is that its result is correct, butonly because the game is being played only once.

Many real-world situations involve repeated plays.Both Convicts will eventually get out of jail, resume

their profession, and be caught again. Each knowsthat if he betrays his partner this time around, he canexpect his partner to treat him similarly next time, sothey both refuse to confess.

The argument is persuasive, but it is not clear if it isrighte. The victim will respond by betraying on the

next turn, and perhaps several more. On net, itseems that both players are better off cooperatingevery turn.


10/17

A Game is defined as :1. A set of players

2. A set of possible strategies for each player

3. A payoff or outcome function that assignspayoffs to each player for each combinationof strategies (one strategy for each player).


11/17

Nash equilibrium concept we have to rememberwhat an equilibrium here means.

equilibrium means that no one wishes to changetheir behavior as long as nothing else changes.Remember that a simple demand and supply

equilibrium means that consumers arepurchasing their desired quantity demanded andsuppliers are selling their desired quantitysupplied and neither wants to change as long asthe other doesn't.

But, we also learned that a change on one side ofthe market (such as a change in income or achange in production costs) will lead to newdesired quantities on both sides


12/17

A Nash equilibrium exists when each player isdoing the best she can given what the otherplayer is doing. In other words, neither wishes tochange strategies so long as the other playerdoesn't.

This approach assumes that the oligopoly firmsmake no attempt to work together. Perhaps theybelieve that agreements are not worth makingbecause they are too hard to enforce, or thatthere are too many firms for any agreement to be

reached. In such a situation, each firm tries to maximize

its profit independently. If each firm actsindependently, the result is a Nash equilibrium.


13/17

Consider the driving game to the right. In many coutriesdrivers drive on the right hand side of the road, in othercountries they drive on the left. But, no matter whereyou drive, it's best to do what the other drivers aredoing.

This simple payoff matrix illustrates this. In the US for


14/17

Part of the definition of Nash equilibrium is that eachplayer takes what the other players are doing as givenwhen deciding what he should do; he holds theirbehavior constant and adjusts his to maximize hisgains.

This means that, in describing the game, we must becareful what we define a strategy to be; as you willsee, different definitions lead to differentconclusions.

The two obvious alternatives are to define a strategyby quantity or by price. In the former case, each firm

decides how much to sell and lets the marketdetermine what price it can sell it at; in the latter, thefirm chooses its price and lets the market determinequantity.


15/17

On this interpretation of Nash equilibrium, eachfirm observes the quantities being produced bythe other firms and calculates how much itshould produce to maximize its profit, assuming

that their output stays the same. One firm in an oligopoly calculates its profit-maximizing quantity of output where marginalrevenue equals marginal cost. Marginal revenue

is calculated from the residual demand curve (itsshare in the industry demand curve). Other firms are assumed to hold the quantitythey produce constant.


16/17

Each firm observes the prices that other firmsare charging and picks the price thatmaximizes its profit on the assumption thattheir prices will not change.

One firm in an oligopoly chooses its profit-maximizing price. All other firms areassumed to hold their prices constant; thelowest such price is P1. The firm maximizesits profit producing Q* and selling it for justunder P1.


17/17

Oligopoly Problem

Documents

Transcript of Oligopoly Problem