How Oligopolists Compete Oligopoly – Competition among the Few Oligopoly

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How Oligopolists Compete Oligopoly – Competition among the Few Oligopoly

Ashland University, US has reference to this Academic Journal, Oligopoly Oligopoly – Competition among the Few In an oligopoly there are very few sellers of the good. The product may be differentiated among the sellers (e.g. automobiles) or homogeneous (e.g. gasoline). Entry is often limited either by legal restrictions (e.g. banking in most of the world) or by a very large minimum efficient scale (e.g. overnight mail service) or by strategic behavior. Sill assuming complete in addition to full information. How Oligopolists Compete In an oligopoly firms know that there are only a few large competitors; competitors take account of the effects of their actions on the overall market. To predict the outcome of such a market, economists must model the interaction between firms in addition to so often use game theory or game theoretic principles.

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Three Basic Models Competition in quantities: Cournot-Nash equilibrium Competition in prices: Bertrand-Nash equilibrium Collusive oligopoly: Chamberlin notion of conscious parallelism It is very useful so that know some basic game theory so that understand these models as well as other oligopoly models. Game Theory: Setup List of players: all the players are specified in advance. List of actions: all the actions each player can take. Rules of play: who moves in addition to when. Information structure: who knows what in addition to when. Payoffs: the amount each player gets in consideration of every possible combination of the the players? actions. A Classic Two Player, Two Action Game – The Prisoners? Dilemma Roger?s best response function: If Chris lies, then Roger should confess (check out left column, 1st entries) If Chris confesses, then Roger should confess (right column, 1st entries) Confess is a dominant strategy in consideration of Roger Chris?s best response function: If Roger lies, then Chris should confess (see top row, 2nd entries) If Roger confesses, then Chris should confess (bottom row, 2nd entries) Confess is a dominant strategy in consideration of Chris Chris Lie Confess Roger Lie -1, -1 -6, 0 Confess 0, -6 -5,-5

A Classic Two Player, Two Action Game – The Prisoners? Dilemma There is a single dominant strategy equilibrium: Rogers confesses in addition to Chris confesses They both go so that jail in consideration of 5 years Note: the game is played simultaneously in addition to non-cooperatively! Ways so that sustain the cooperative equilibrium (lie, lie) different payoff structures repeated play in addition to trigger strategies Chris Lie Confess Roger Lie -1,-1 -6, 0 Confess 0, -6 -5,-5 Question: Will There Always Be A Dominant Strategy Equilibrium? Answer?NO! Then what? Look in consideration of Nash Equilibrium. Nash Equilibrium Named after John Nash – a Nobel Prize winner in Economics. The Nash Non-cooperative Equilibrium of a game is a set of actions in consideration of all players that, when played simultaneously, have the property that no player can improve his payoff by playing a different action, given the actions the others are playing. Each player maximizes his or her payoff under the assumption that all other players will do likewise.

Propositional logic 1 . What is (and isn?t) a proposition ? Propositions 3 . Propositional variables Propositional variables 4. Propositional formulas Logical connectives Truth tables: not Truth tables: AND Truth tables: OR Practice: IMPLIES

Another Example – The Price Game Roger?s best response function: If Chris goes low, then Roger should go low (check out left column, 1st entries) If Chris goes high, then Roger should high (right column, 1st entries) There is no dominant strategy in consideration of Roger Chris?s best response function: If Roger goes low, then Chris should go low (see top row, 2nd entries) If Roger goes high, then Chris should go high (bottom row, 2nd entries) There is no dominant strategy in consideration of Chris Chris Low High Roger Low 20, 20 60, 0 High 0, 60 100, 100 Another Example – The Price Game Roger?s best response function: If Chris goes low, then Roger should go low If Chris goes high, then Roger should high Chris?s best response function: If Roger goes low, then Chris should go low If Roger goes high, then Chris should go high Two Nash Equilibria: (low, low) in addition to (high, high) Respective Nash equilibrium payoffs: (20,20) in addition to (100,100) Which equilibrium will prevail? Good question. Chris Low High Roger Low 20, 20 60, 0 High 0, 60 100, 100 Another Example – The Simultaneous Entry Game Get two Nash equilibria: (enter, accommodate) in addition to (not enter, fight) Roger – the entrant enter not enter fight accommodate fight accommodate Chris – the incumbent (Roger = 0,Chris = 0) (Roger = 2, Chris = 2) (Roger =1,Chris = 5) (Roger =1,Chris = 5)

Another Example – The Sequential Entry Game Still get two Nash equilibria: (enter, accommodate) in addition to (not enter, fight) Only one, however, is credible: (enter, accommodate) Roger – the entrant enter not enter fight accommodate fight accommodate Chris – the incumbent (Roger = 0,Chris = 0) (Roger = 2, Chris = 2) (Roger =1,Chris = 5) (Roger = 1,Chris = 5) Another Two Player, Two Action Example The game has two players 1 & 2. Player 1 can move ?up? or ?down? (actions). Player 2 can move ?left? or ?right? (actions). If player 1 moves ?up? in addition to player 2 moves ?left? then player 1 gets $1 in addition to player 2 gets $0 (payoffs). The table shows all possible action pairs in addition to their associated payoffs. Player 1?s Best Strategies If player 2 plays ?right,? the best strategy (action) in consideration of player 1 is so that play ?up.? In this case player 1 will get a payoff of $1, underlined.

Player 2?s Best Strategies If player 1 plays ?up? then player 2?s best strategy (action) is so that play ?right.? In this case, player 2 gets a payoff of $2, underlined. Nash Equilibrium The table shows the best strategy (actions) in consideration of player 1 against both of player 2?s possible actions (underlined first numbers). The table also shows the best strategy (actions) in consideration of player 2 against both of player 1?s possible actions (underlined second numbers). Notice that both numbers are underlined in the cell ?up,right.? This is the Nash Equilibrium. If player 1 plays ?up? the best thing in consideration of player 2 so that do is play ?right? in addition to vice versa. A Non-cooperative Outcome (Cournot-Nash Duopoly – Competition in Quantities) Developed by Antoine Augustin Cournot in 1838. In a two firm oligopoly (called a duopoly), if both firms set their output levels assuming that the other firm?s strategic choice variable (quantities in Cournot competition) is fixed, the equilibrium outcome is a Cournot Nash Non-cooperative Equilibrium. (Note: Cournot solved this oligopoly model many years before Nash invented the equilibrium definition we are using here).

Setup of the Duopoly Problem: Monopoly Outcome The table at the right shows the monopolist?s best choice in consideration of the simple market demand curve shown, assuming only whole quantities can be chosen. The monopolist maximizes profits at X=3, P=$14, alongside economic profits of $21. Assuming only whole quantities can be produced, the competitive equilibrium is X=6, P=$8, the last price at which economic profits are not negative (FC=$0 in addition to MC=$7 in consideration of all X). Duopoly Game: Competition in Quantities Suppose that there are two firms X in addition to Y alongside identical total cost curves that are the same ones shown in consideration of the monopolist in the previous slide: total cost=$7Xi The payoff matrix above shows the economic profits of Firm X (left entry) in addition to Firm Y (right entry) in consideration of each possible quantity supplied of 0 so that 4 units. The payoff in consideration of a firm is determined by finding the price that prevails in consideration of the total quantity supplied (Firm X + Firm Y), then multiplying each quantity by this price in addition to subtracting the firm?s total costs in consideration of that quantity. Note: demand price is PD=20-2X where X=XX + XY Example: Firm X supplies 3 in addition to Firm Y supplies 1 – so X=4 in addition to P=12 Firm X?s payoff = (3 x 12) – 21 = 15 Firm Y?s payoff = (1 x 12) – 7 = 5 Duopoly Game: Nash Equilibrium in Quantities The boxes marked in yellow are the best moves in consideration of Firm X given the indicated quantity supplied by Firm Y. The boxes marked in green are the best moves in consideration of Firm Y given the indicated quantity supplied by Firm X. The payoff in consideration of the cell (X supplies 2, Y supplies 2) is (10, 10). This cell is the Nash Non-cooperative Equilibrium in consideration of this game because it represents the best move in consideration of Firm X given that Firm Y chooses its best move in addition to the best move in consideration of Firm Y given that Firm X chooses its best move. Duopoly outcome: Total quantity supplied = 2 + 2 = 4. Market price = $12. Total economic profits = $10 + $10 = $20. Monopoly outcome: Total quantity supplied = 3. Market price = $14. Total economic profits = $21. Competitive outcome: Total quantity supplied = 6. Market price = $8. Total economic profits = $6.

Properties of the Cournot-Nash Equilibrium in consideration of Duopoly When the duopolists compete in quantities, we can compare the outcome so that both the monopoly in addition to competitive outcomes. Each duopolist produces less than a monopolist in the same market but together they produce more than the monopolist in addition to less than the amount two competitive firms would have produced alongside the same cost structure in addition to demand curves. The sum of the economic profits of each duopolist is less than the economic profits of a monopoly in the same market. The market price is less than the one a monopolist would charge but more than the competitive price. Deadweight loss is less than in consideration of a monopoly in the same market but still positive, thus greater than the deadweight loss from a competitive market. Duopoly Game: Competition in Prices (J. Bertrand 1883) Firm X in addition to Y have the same cost structure in addition to face the same market as in the previous example. Now, instead of playing a game in quantities, they play a game in prices allowing only the choices indicated. The payoff matrix above shows the economic profits of Firm X (left entry) in addition to Firm Y (right entry) in consideration of each possible price chosen $8, $10, $12, $14, $16. If the two firms choose the same price they split the market in half; otherwise, the firm that chooses the lower price sells the market quantity in addition to the other firm sells nothing. Example: Firm X charges $12 in addition to Firm Y charges $12 Market X = 4, both firms sell 2 units at $12 in addition to have total costs of $14. Firm X payoff = Firm Y payoff = 2 x $12 – $14 = $10. Example: Firm X charges $10 in addition to Firm Y charges $8. Market X = 6, Firm Y sells all 6 units, Firm X sells nothing. Firm X payoff = $0; Firm Y payoff = 6 x $8 – $42 = $6. Duopoly Game: Bertrand-Nash Equilibrium in Prices The boxes marked in yellow are the best moves in consideration of Firm X given the indicated quantity supplied by Firm Y. The boxes marked in green are the best moves in consideration of Firm Y given the indicated quantity supplied by Firm X. The payoff in consideration of the cell (X charges $8, Y charges $8) is (3, 3) in addition to the payoff in consideration of the cell (X charges $10, Y charges $10) is (7.5, 7.5). Both cells are the Nash Non-cooperative Equilibria in consideration of this game. Duopoly competition in prices in this market does not have a unique equilibrium (a common occurrence in game theory). This game predicts that the market price fluctuates between $8 in addition to $10. This game predicts that the market quantity fluctuates between 4 in addition to 6. It is not uncommon in consideration of the competition in quantities game so that give different results from the competition in prices game.

Performance: Bertrand vs. Cournot When the duopolists compete in prices, we can compare the outcome so that both the monopoly in addition to competitive outcomes, but it can be more difficult so that find an equilibrium. Classic results (when an equilibrium exists in addition to is unique). N=1 then XBN = XSM in addition to PBN= PSM N>1 then XBN = X* in addition to PBN = P* Bertrand compared so that Cournot. N=1 then XCN = XSM in addition to PCN= PSM N>1 then X* > XCN > XSM in addition to P*< PCN < PSM N gets large enough, XCN = X* in addition to PCN=P* Results have different implications in consideration of anti-trust action. Should MCI be able so that merge alongside Sprint? N goes from 3 so that 2. Should Coke be allowed so that merge alongside Dr. Pepper? Should Pepsi be allowed so that merge alongside 7-Up? Good questions. A Cooperative Outcome (Collusion) The duopolists can do better than the Nash Non-cooperative Equilibrium. Because the equilibrium is non-cooperative, we have ruled out the possibility of collusion between the two firms. Collusion means that the firms explicitly cooperate in choosing a market price in addition to the division of output between them. If the duopolists collude in addition to divide up the market privately, they can produce the monopoly quantity in addition to divide the monopoly economic profits. Since the monopoly economic profits are more than the sum of the duopoly profits, the duopolists are better off if they collude. When we allow the possibility of collusion the game can turn out differently. Duopoly Game: Collusion In our previous example Firm X in addition to Firm Y can cooperate in addition to agree so that charge $14 in addition to so that produce 3 units between them. They will earn the monopoly profits of $21 in this case. There is $1 of additional profit compared so that the quantity game in addition to at least $6 of additional profit compared so that the price game. Any division of this extra profit between the two firms makes both firms willing so that collude rather than play the non-cooperative game. The possibility of collusion is excluded from the non-cooperative games by the assumption that the firms? strategies consist of either choosing a quantity or choosing a price. Collusion involves choosing a market quantity (or price), production quotas in consideration of each member in addition to a division of the monopoly profit between the two firms. Collusion Problems Frequently, side payments are essential so that the cooperative solution. Especially when the cartel members have different cost structures. OPEC example: Iran in addition to Saudi Arabia. Iran?s marginal costs increase more quickly than do Saudi Arabia?s. Suppose they do not cooperate in addition to end up at the Cournot-Nash solution: Get profits such that: ?SA + ?I = ?joint Suppose they cooperate in addition to implement the monopoly solution: Get profits such that: ?SA + ?I = ?joint Since Iran has the crummy marginal cost curve, it will be told not so that produce very much in the collusive arrangement. Could be that: ?SA > ?SA in addition to ?joint > ?joint but ?I > ?I ! If joint cartel profit is larger than the joint non-cooperative profit, then there is enough so that make side payments so that Iran so that get Iran?s cooperation. Will the side payments be made? Are they legal? Good questions. Collusion Problems Side payments aside, there is also a compelling incentive so that cheat on the cartel arrangement. Cheating often means that someone is violating the cartel?s production limits – producing more than they agreed to. More ends up on the market than was supposed to. The price ends up lower than it was supposed to. The cartel starts so that experience dissention. Steps are taken so that shore up the cartel agreement. This strong internal tendency so that cheat led Milton Friedman so that once opine that cartels were nothing more than ?a flash in the pan.? How successful are cartels? How often do they form? Are they able so that substantially raise the market? For how long? Good questions.

Parsons, Thomas General Manager

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Journal Ratings by Ashland University

This Particular Journal got reviewed and rated by Performance: Bertrand vs. Cournot When the duopolists compete in prices, we can compare the outcome so that both the monopoly in addition to competitive outcomes, but it can be more difficult so that find an equilibrium. Classic results (when an equilibrium exists in addition to is unique). N=1 then XBN = XSM in addition to PBN= PSM N>1 then XBN = X* in addition to PBN = P* Bertrand compared so that Cournot. N=1 then XCN = XSM in addition to PCN= PSM N>1 then X* > XCN > XSM in addition to P*< PCN < PSM N gets large enough, XCN = X* in addition to PCN=P* Results have different implications in consideration of anti-trust action. Should MCI be able so that merge alongside Sprint? N goes from 3 so that 2. Should Coke be allowed so that merge alongside Dr. Pepper? Should Pepsi be allowed so that merge alongside 7-Up? Good questions. A Cooperative Outcome (Collusion) The duopolists can do better than the Nash Non-cooperative Equilibrium. Because the equilibrium is non-cooperative, we have ruled out the possibility of collusion between the two firms. Collusion means that the firms explicitly cooperate in choosing a market price in addition to the division of output between them. If the duopolists collude in addition to divide up the market privately, they can produce the monopoly quantity in addition to divide the monopoly economic profits. Since the monopoly economic profits are more than the sum of the duopoly profits, the duopolists are better off if they collude. When we allow the possibility of collusion the game can turn out differently. Duopoly Game: Collusion In our previous example Firm X in addition to Firm Y can cooperate in addition to agree so that charge $14 in addition to so that produce 3 units between them. They will earn the monopoly profits of $21 in this case. There is $1 of additional profit compared so that the quantity game in addition to at least $6 of additional profit compared so that the price game. Any division of this extra profit between the two firms makes both firms willing so that collude rather than play the non-cooperative game. The possibility of collusion is excluded from the non-cooperative games by the assumption that the firms? strategies consist of either choosing a quantity or choosing a price. Collusion involves choosing a market quantity (or price), production quotas in consideration of each member in addition to a division of the monopoly profit between the two firms. and short form of this particular Institution is US and gave this Journal an Excellent Rating.