Chapters 13 & 14: Imperfect Competition & Game Theory

Reality: Imperfect Competition Perfect competition and monopoly represent idealized market structures that rarely exist These are useful in showing tendency and direction, but in the real world the payoff to an action often depends not only on the action itself, but also on how it relates to actions taken by others Read the 3 economist, 3 lawyer parable on page 455, it’s funny (particularly if you are an economist) Game theory is a useful tool to use to analyze likely outcomes when individual payoffs depend on the actions of others Three elements of game theory: 1) the players, 2) the list of possible strategies, and 3) the payoffs associated with each combination of strategies

Algebraic Example of Game Theory in the Marketplace MEXICO OIL VENEZUELA PETROLEUM Cooperate (P=5) Cheat (P=4)

Oligopoly Assumptions: Restricted entry Few firms producing Implications: The actions of one oligopoly firm will affect the prices and profits of the other firm(s) in the market There are several possible hypotheses about how oligopoly firms behave May collude and act as a monopoly May compete against each other and drive prices to the perfectly competitive level May compete, but arrive at equilibrium somewhere between the monopoly and perfectly competitive prices The exact structure of the oligopoly likely depends on the products they are producing and the degree of product differentiation

Cournot Duopoly Model Two firms in the market that sell identical products Each firm assumes that the other will keep production levels fixed regardless of their own production Each firm has a “reaction function” that determines of the optimal level of output given the other firm’s output Q1 Firm 2’s reaction function Q1*=(a-bQ2)/2b Q2*=(a-bQ1)/2b a/3b Firm 1’s reaction function Q2 a/3b

Bertrand Model Two firms in the market that sell identical products Each firm assumes that the other will keep prices fixed at the current level regardless of the price they set Each firm’s best strategy is to sell just below the price of the other firm so that they can capture the entire market demand The firms will continue to reduce the price until it reaches the competitive market price

Stackelberg Model Two firms in the market that sell identical products The market consists of a “leader” and a “follower” The follower is a naïve Cournot duopolist The leader will choose its quantity level by taking into account how that will affect the follower’s response Q1 Firm 2’s reaction function Firm 1’s [leader’s] demand curve: P = a - b[Q1 + (a-bQ1)/2] = (a-bQ1)/2 Firm 2’s [follower’s] reaction function : (a-bQ1)/2b a/2b Firm 1’s reaction function Q2 a/4b

Comparison of Oligopoly Models · Monopoly a/2 · Cournot Assume MC=0 · Stackelberg Bertrand/ Perfect Competition · a/2b a/b

Monopolistic Competition Differentiated products Many sellers Free entry Each seller faces a downward-sloping demand curve UnderCuts Cheap Snips Dean Suarez Salon

Classic Prisoner’s Dilemma CLYDE Squeal Remain Silent BONNIE 12 years for B 12 years for C 0 years for B 20 years for C 20 years for B 0 years for C 1 year for B 1 year for C They both will end up squealing which is the socially WORST (for those two) possible outcome because the total years in prison is the greatest with this strategy. Payoff to an action often depends not only on the action itself, but also on how it relates to actions taken by others

Game Theory Nash equilibrium - the combination of strategies in are such that neither player has any incentive to change given the strategy of others Players in games may have dominant or non-dominant strategies Dominant strategy - when a player has a strategy in a game that produces better results regardless of the strategy chosen by other players (opponents) Each player may have a dominant strategy, but the result of each player exercising their dominant strategy may be less beneficial for the players (e.g. price wars) and/or society as a whole Non-dominant strategy - when at least one player does not have a dominant strategy, rather the best strategy for that player is dependent on what others choose Nash equilibrium may occur even if a player does not have a dominant strategy b/c one (or more players) bases decision on what others will do

Nash Equilibrium: Dominant Strategy PEPSI Advertise Don’t Advertise COKE C: $100 m P: $100 m C: $250 m P: $25 m C: $25 m P: $250 m C: $200 m P: $200 m

Nash Equilibrium: Non-Dominant Strategy ADIDAS Advertise Don’t Advertise NIKE N: $100 A: $100 N: $135 A: $200 N: $50 A: $125 N: $140 A: $115