# 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.