08 Game theory and oligopoly Practice Questions PDF

08 Game theory & oligopoly Reading: Waldman & Jensen, Chapter 6 Optional: Chapter 7 (for a more in-depth treatment of oligopoly models) Game theory & oligopoly Oligopoly—a market with a few sellers Each seller has market power, i.e., their output decision affects price E...

08 Game theory & oligopoly Reading: Waldman & Jensen, Chapter 6 Optional: Chapter 7 (for a more in-depth treatment of oligopoly models) Game theory & oligopoly Oligopoly—a market with a few sellers Each seller has market power, i.e., their output decision affects price Each seller knows that the other sellers will react to its output decision, further affecting price Example: Airline industry w/ Southwest, United, & Delta (CMH to Chicago) Southwest knows that if it lowers its own fare, rival firms will likely react by lowering their fares In making its decision, Southwest must anticipate the reactions of its rivals Game theory helps up model strategic decision making Components of games Players The agents choosing Actions The choices that players may make Strategies A plan of action(s) for a player Payoffs Rewards to players For now: players try to maximize their own payoffs (self-interested behavior) Equilibria Components of games One-time games—players interact once Finitely repeated games—players interact for a certain number of “rounds,” the last of which is known to all Infinitely repeated games—player interact for an infinite number of rounds Simultaneous games—players make their decisions at the exact same time Sequential games—one player makes its decision first, and the next player then makes its decision Example game 𝐼𝐼 − 15 corridor Two players Costco 𝑁𝑁 Sam’s Club Decisions of each North 𝑀𝑀 Middle South Assume 𝑆𝑆 Shoppers are evenly distributed along corridor Patronize closest warehouse Example game 𝐼𝐼 − 15 corridor Simultaneous game Both players choose actions at 𝑁𝑁 same time One-time game 𝑀𝑀 Played once 𝑆𝑆 Example game Sam’s 𝐼𝐼 − 15 corridor Club 𝑁𝑁 r, c North Middle South North 50, 50 25, 75 50, 50 𝑀𝑀 Costco Middle 75, 25 50, 50 75, 25 𝑆𝑆 South 50, 50 25, 75 50, 50  Example game Sam’s Dominant strategy Rule of action that outperforms all Club others no matter what opponent chooses r, c North Middle South Not all games Nash equilibrium Each player is doing the best they North 50, 50 25, 75 50, 50 can, given the actions of the other player(s) Can be multiple Costco Middle 75, 25 50, 50 75, 25 Zero-sum game Each player’s gain is offset by another’s loss South 50, 50 25, 75 50, 50 Not all games Here, a fixed-sum game… Archetypal game: prisoner’s dilemma One-time & simultaneous game Clyde Does any player have a dominant strategy? If so, what is it? r, c Confess Deny What is the Nash equilibrium here? Confess -10, -10 -1, -15 Bonnie Is the Nash equilibrium efficient? Deny -15, -1 -5, -5 Archetypal game: prisoner’s dilemma Cooperation difficult Must change the payoff matrix Clyde by detecting & punishing defection r, c Confess Deny Gang retaliation for “snitching” adds punishment −10 (in disutility) No longer a prisoner’s dilemma  Confess -20, -10 -10, -20 -11, -15 -1, -15 the Nash equilibrium is now Bonnie efficient e.g., “omertá,” “code of silence,” Deny -15, -15,-11 -1 -5, -5 “snitches get stitches” Archetypal game: prisoner’s dilemma Prisoner’s dilemma game One-time, simultaneous game Clyde Each would be better off if they cooperated But each has a dominant strategy r, c Confess Deny of non-cooperation Confess -10, -10 -1, -15 We can think of many situations that seem like this… Bonnie Deny -15, -1 -5, -5 Example: voting Everybody Any individual’s vote does NOT else matter for the outcome of any election Make an Suppose it takes effort to research r, c informed vote good policy & make an informed vote… Make an Enjoy good Enjoy good Dominant strategy for the informed vote policy less effort , policy less effort individual? You (an individual) What happens when every Vote with Enjoy good , Enjoy good policy less individual adopts this strategy? your gut policy effort No benefits for anyone… (not shown) This is a prisoner’s dilemma Example: government Everybody Suppose voluntary, free, else communal association Individuals can voluntarily choose to pay taxes to a public treasury, r, c Pay taxes from which public goods are provided: national defense, law & Enjoy Enjoy order, mosquito abatement, etc. Pay taxes benefits , benefits An individual’s tax payments don’t You less taxes less taxes really matter much for the (an individual) provision to the whole Enjoy , Enjoy Free ride benefits benefits less taxes Example: government Everybody Dominant strategy for the else individual? What happens when every r, c Pay taxes individual adopts this strategy? No benefits for anyone… (not shown) Enjoy Enjoy Pay taxes benefits , benefits This is a prisoner’s dilemma You less taxes less taxes The government can be viewed (an individual) Enjoy , Enjoy as a cartel of citizens, coercing Free ride benefits benefits less taxes all to pay taxes for mutual An alternative view: benefit… Government as a cartel of robbers…  Example: oligopoly Oligopolistic beer industry Price $14 Suppose a beer industry duopoly $13 $12 Duff Beer $11 Fudd Beer $10 $9 Some barrier to entry $8 $7 $6 Both have same, constant costs Competitive $5 equilibrium 𝑀𝑀𝐶𝐶𝐷𝐷 = 𝐴𝐴𝐶𝐶𝐷𝐷 = 𝑀𝑀𝐶𝐶𝐹𝐹 = 𝐴𝐴𝐶𝐶𝐹𝐹 = $2 $4 $3 𝑝𝑝𝑐𝑐 = $2 𝑀𝑀𝑀𝑀 = 𝐴𝐴𝐴𝐴 $1 Market demand Suppose a linear, inverse demand $0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 curve Quantity (1,000s)  Example: oligopoly Oligopolistic beer industry Price $14 Perfect oligopoly $13 $12 Tacit collusion (“meeting of the $11 Perfect minds”) $10 oligopoly Overt collusion (a cartel) $9 𝑝𝑝𝑚𝑚 = $8 Perfect oligopoly behaves like a $7 $6 collective monopoly $5 Competitive equilibrium Both produce 𝑞𝑞𝐷𝐷 = 𝑞𝑞𝐹𝐹 = 3,000 $4 $3 Total output 𝑄𝑄 = 6,000 𝑝𝑝𝑐𝑐 = $2 𝑀𝑀𝑀𝑀 = 𝐴𝐴𝐴𝐴 Market price 𝑝𝑝𝑚𝑚 = $8 $1 𝑀𝑀𝑅𝑅𝑚𝑚 = 𝑀𝑀𝐶𝐶𝑚𝑚 𝑀𝑀𝑅𝑅 Market demand $0 𝑚𝑚 Profit for each 𝜋𝜋𝐷𝐷 = 𝜋𝜋𝐹𝐹 = $18,000 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Quantity (1,000s)  Example: oligopoly Oligopolistic beer industry Price $14 Suppose ONE of them (Duff) $13 $12 produces 1,000 more it should $11 Perfect under perfect oligopoly $10 $9 oligopoly Duff produces 𝑞𝑞𝐷𝐷 = 4,000 One of them 𝑝𝑝𝑚𝑚 = $8 produces more Fudd produces 𝑞𝑞𝐹𝐹 = 3,000 $7 $6 Total output 𝑄𝑄 = 7,000 $5 Competitive Market price 𝑝𝑝𝑚𝑚 = $7 $4 equilibrium $3 Profit for Duff 𝜋𝜋𝐷𝐷 = $20,000 𝑝𝑝𝑐𝑐 = $2 𝑀𝑀𝑀𝑀 = 𝐴𝐴𝐴𝐴 Profit for Fudd 𝜋𝜋𝐹𝐹 = $15,000 $1 𝑀𝑀𝑅𝑅𝑚𝑚 = 𝑀𝑀𝐶𝐶𝑚𝑚 𝑀𝑀𝑅𝑅 Market demand 𝑚𝑚 $0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Quantity (1,000s)  Example: oligopoly Oligopolistic beer industry Price $14 Suppose ONE of them (Fudd) $13 $12 produces 1,000 more it should $11 Perfect under perfect oligopoly $10 $9 oligopoly Duff produces 𝑞𝑞𝐷𝐷 = 3,000 One of them 𝑝𝑝𝑚𝑚 = $8 produces more Fudd produces 𝑞𝑞𝐹𝐹 = 4,000 $7 $6 Total output 𝑄𝑄 = 7,000 $5 Competitive Market price 𝑝𝑝𝑚𝑚 = $7 $4 equilibrium $3 Profit for Duff 𝜋𝜋𝐷𝐷 = $15,000 𝑝𝑝𝑐𝑐 = $2 𝑀𝑀𝑀𝑀 = 𝐴𝐴𝐴𝐴 Profit for Fudd 𝜋𝜋𝐹𝐹 = $20,000 $1 𝑀𝑀𝑅𝑅𝑚𝑚 = 𝑀𝑀𝐶𝐶𝑚𝑚 𝑀𝑀𝑅𝑅 Market demand 𝑚𝑚 $0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Quantity (1,000s)  Example: oligopoly Oligopolistic beer industry Price $14 Suppose BOTH of them produce $13 $12 1,000 more each should under $11 Perfect perfect oligopoly $10 $9 oligopoly Duff produces 𝑞𝑞𝐷𝐷 = 4,000 One of them 𝑝𝑝𝑚𝑚 = $8 produces more Fudd produces 𝑞𝑞𝐹𝐹 = 4,000 $7 $6 Both of them Total output 𝑄𝑄 = 8,000 produce more $5 Market price 𝑝𝑝𝑚𝑚 = $6 $4 $3 Profit for Duff 𝜋𝜋𝐷𝐷 = $16,000 𝑝𝑝𝑐𝑐 = $2 𝑀𝑀𝑀𝑀 = 𝐴𝐴𝐴𝐴 Profit for Fudd 𝜋𝜋𝐹𝐹 = $16,000 $1 𝑀𝑀𝑅𝑅𝑚𝑚 = 𝑀𝑀𝐶𝐶𝑚𝑚 𝑀𝑀𝑅𝑅 Market demand 𝑚𝑚 $0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Quantity (1,000s) Example: oligopoly Fudd Beer Using the previous numbers to Produce Produce think of this as a one-time, r, c 3,000 units 4,000 units simultaneous game The “perfect oligopoly” or the cartel is unstable—both have a Produce $18K, $18K $15K, $20K dominant strategy to defect 3,000 units (prisoner’s dilemma) Duff Cooperation (tacit or overt) is Beer difficult to sustain… Produce $20K, $15K $16K, $16K 4,000 units Example: oligopoly Fudd Beer But, there are many, many more Produce Produce choices for Duff and Fudd than r, c 3,000 units 4,000 units 3,000 & 4,000… Is there an equilibrium if we Produce $18K, $18K $15K, $20K expand these choices? 3,000 units Duff Beer The Cournot-Nash model of Produce oligopoly… $20K, $15K $16K, $16K 4,000 units  Cournot-Nash oligopoly Oligopolistic beer industry Price $14 There is an equilibrium under $13 $12 these conditions (Cournot-Nash) $11 $10 Perfect Key Cournot-Nash assumption: oligopoly $9 each believes the other is holding 𝑝𝑝𝑚𝑚 = $8 $7 its output constant $6 i.e., when I act, you don’t change $5 your behavior $4 $3 i.e., when you act, I don’t change 𝑝𝑝𝑐𝑐 = $2 𝑀𝑀𝑀𝑀 = 𝐴𝐴𝐴𝐴 my behavior $1 $0 𝑀𝑀𝑅𝑅𝑚𝑚 = 𝑀𝑀𝐶𝐶𝑚𝑚 𝑀𝑀𝑅𝑅 𝑚𝑚 Market demand (simultaneous game) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Quantity (1,000s)  Cournot-Nash oligopoly Oligopolistic beer industry Price $14 First, you’ve noticed that if we $13 $12 have constant costs and a linear $11 inverse demand curve, then a $10 $9 Monopoly monopoly always produces 𝑝𝑝𝑚𝑚 = $8 exactly one-half the competitive $7 $6 equilibrium level of output $5 𝑄𝑄𝑐𝑐 = 12,000 $4 $3 𝑄𝑄𝑚𝑚 = 6,000 𝑝𝑝𝑐𝑐 = $2 𝑀𝑀𝑀𝑀 = 𝐴𝐴𝐴𝐴 $1 𝑀𝑀𝑅𝑅𝑚𝑚 = 𝑀𝑀𝐶𝐶𝑚𝑚 𝑀𝑀𝑅𝑅 Market demand 𝑚𝑚 $0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Quantity (1,000s)  Cournot-Nash oligopoly Oligopolistic beer industry Price $14 𝑞𝑞𝐹𝐹 Let’s consider Duff’s best action $13 $12 $14 $13 Suppose Fudd produces 𝑞𝑞𝐹𝐹 = $11 $10 $12 4,000 units $11 $9 𝑝𝑝𝑚𝑚 = $8 $10 Duff faces the residual demand $9 $7 $8 (𝑅𝑅𝐷𝐷𝐷𝐷 ) entirely to itself $6 $7 $5 $6 $4 $5 𝑅𝑅𝐷𝐷𝐷𝐷 $3 $4 𝑝𝑝𝑐𝑐 = $2 $3 𝑀𝑀𝑀𝑀 = 𝐴𝐴𝐴𝐴 $1 $2 𝑀𝑀𝑅𝑅𝑚𝑚 Market demand $0 $1 0 1 2 $0 3 4 5 6 7 8 9 10 11 12 13 14 Quantity (1,000s) 0 1 2 3 4 5 6 𝑞𝑞𝐷𝐷 12 7 8 9 10 11 (1,000s) 13 14  Cournot-Nash oligopoly Oligopolistic beer industry Price $14 𝑞𝑞𝐹𝐹 Let’s consider Duff’s best action $13 $12 $14 $13 Suppose Fudd produces 𝑞𝑞𝐹𝐹 = $11 $10 $12 4,000 units $11 $9 𝑝𝑝𝑚𝑚 = $8 $10 Duff faces the residual demand $9 $7 $8 (𝑅𝑅𝐷𝐷 ) entirely to itself 𝐷𝐷 $6 𝑀𝑀𝑅𝑅𝐷𝐷 = 𝑀𝑀𝑀𝑀 $5 $7 $6 Duff behaves like a monopolist $4 $5 𝑅𝑅𝐷𝐷𝐷𝐷 for its residual demand, having $3 $4 𝑝𝑝𝑐𝑐 = $2 $3 𝑀𝑀𝑀𝑀 = 𝐴𝐴𝐴𝐴some 𝑀𝑀𝑅𝑅𝐷𝐷 $1 $2 𝑀𝑀𝑅𝑅𝑚𝑚 𝑀𝑀𝑅𝑅𝐷𝐷 Market demand $0 $1 3 4 5 6 7 8 9 10 11 12 13 14 Quantity (1,000s) 0 1 2 $0 0 1 2 3 4 5 6 7 8 9 10 11 𝑞𝑞𝐷𝐷 12 (1,000s) 13 14  Cournot-Nash oligopoly Oligopolistic beer industry Price $14 𝑞𝑞𝐹𝐹 Since Duff is a monopolist on its $13 $12 $14 residual demand, it produces $13 $11 $12 exactly one-half the difference $10 $9 $11 between: 𝑝𝑝𝑚𝑚 = $8 $10 1 $7 $9 𝑞𝑞𝐷𝐷 = 𝑄𝑄𝑐𝑐 − 𝑞𝑞𝐹𝐹 $6 $8 $7 𝑀𝑀𝑅𝑅𝐷𝐷 = 𝑀𝑀𝑀𝑀 2 $5 $6 Fudd does the exact same thing $4 𝑅𝑅𝐷𝐷𝐷𝐷 $3 $5 $4 in equilibrium for the exact same 𝑝𝑝𝑐𝑐 = $2 $3 reason: 𝑀𝑀𝑀𝑀 = 𝐴𝐴𝐴𝐴 $1 $2 𝑀𝑀𝑅𝑅𝑚𝑚 𝑀𝑀𝑅𝑅𝐷𝐷 Market demand 1 $0 $1 𝑞𝑞𝐹𝐹 = 𝑄𝑄𝑐𝑐 − 𝑞𝑞𝐷𝐷 3 4 5 6 7 8 9 10 11 12 13 14 Quantity (1,000s) 0 1 2 $0 2 0 1 2 3 4 5 6 7 8 9 10 11 𝑞𝑞𝐷𝐷 12 (1,000s) 13 14 The simple algebra of Cournot-Nash duopoly Thus, in equilibrium, 1 1 1 1 𝑞𝑞𝐷𝐷 = 𝑄𝑄𝑐𝑐 − 𝑄𝑄𝑐𝑐 + 𝑞𝑞𝐷𝐷 𝑞𝑞𝐷𝐷 = 𝑄𝑄𝑐𝑐 − 𝑞𝑞𝑓𝑓 2 2 2 2 1 1 1 1 𝑞𝑞𝐷𝐷 = 𝑄𝑄𝑐𝑐 − 𝑄𝑄𝐶𝐶 + 𝑞𝑞𝐷𝐷 𝑞𝑞𝐹𝐹 = 𝑄𝑄𝑐𝑐 − 𝑞𝑞𝐷𝐷 2 4 4 2 By substitution, 3 1 𝑞𝑞𝐷𝐷 = 𝑄𝑄𝐶𝐶 Because both 4 4 1 1 firms are equal: 𝑞𝑞𝐷𝐷 = 𝑄𝑄𝑐𝑐 − 𝑄𝑄𝑐𝑐 − 𝑞𝑞𝐷𝐷 1 1 2 2 𝑞𝑞𝐷𝐷 = 𝑄𝑄𝐶𝐶 𝑞𝑞𝐹𝐹 = 𝑄𝑄𝑐𝑐 3 3  Cournot-Nash oligopoly Oligopolistic beer industry Price $14 𝑞𝑞𝐹𝐹 Both firms each produce ⅓ of the $13 $12 $14 competitive output level, for a $13 $11 $12 total of ⅔ of the competitive $10 $9 $11 output level $10 Cournot-Nash 𝑝𝑝𝑚𝑚 = $8 $7 $9 duopoly Here, $8 𝑝𝑝𝐶𝐶𝐶𝐶 = $6 $7 𝑄𝑄𝑐𝑐 = 12,000 $5 $4 $6 𝑅𝑅𝐷𝐷𝐷𝐷 𝑞𝑞𝐷𝐷 = 𝑞𝑞𝐹𝐹 = 4,000 $5 2 $3 $4 𝑄𝑄 𝐶𝐶𝐶𝐶 = 8,000 3 12,000 = 8,000 𝑝𝑝𝑐𝑐 = $2 𝑀𝑀𝑀𝑀 = 𝐴𝐴𝐴𝐴 $1 $3 𝑝𝑝𝐶𝐶𝐶𝐶 = $6 $2 𝑀𝑀𝑅𝑅𝑚𝑚 𝑀𝑀𝑅𝑅𝐷𝐷 Market demand $0 $1 𝜋𝜋𝐷𝐷 = 𝜋𝜋𝐹𝐹 = $16,000 3 4 5 6 7 8 9 10 11 12 13 14 Quantity (1,000s) 0 1 2 $0 0 1 2 3 4 5 6 7 8 9 10 11 𝑞𝑞𝐷𝐷 12 (1,000s) 13 14  Cournot-Nash oligopoly Oligopolistic beer industry Price $14 Cournot-Nash duopoly $13 $12 equilibrium lies between $11 Perfect monopoly & competition $10 = Monopoly oligopoly $9 Cournot-Nash 𝑝𝑝𝑚𝑚 = $8 duopoly $7 Efficiency? 𝑝𝑝𝐶𝐶𝐶𝐶 = $6 $5 Competitive $4 equilibrium $3 𝑝𝑝𝑐𝑐 = $2 𝑀𝑀𝑀𝑀 = 𝐴𝐴𝐴𝐴 $1 𝑀𝑀𝑅𝑅𝑚𝑚 Market demand $0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Quantity (1,000s) Finitely repeated prisoner’s dilemma Fudd Beer Often, oligopolists don’t just play Produce Produce games once: r, c 3,000 units 4,000 units Infinitely repeated games Finitely repeated games Produce $18K, $18K $15K, $20K We’ll come back to infinitely 3,000 units repeated games in the future Duff (Chapter 13) Beer Produce $20K, $15K $16K, $16K 4,000 units Finitely repeated prisoner’s dilemma Fudd Beer Often, oligopolists don’t just play games once: r, c Cooperate Defect Infinitely repeated games Finitely repeated games Cooperate $18K, $18K $15K, $20K We’ll come back to infinitely repeated games in the future Duff (Chapter 13) Beer Defect $20K, $15K $16K, $16K Finitely repeated prisoner’s dilemma Fudd Beer For now, think of this as a 10- round, finitely repeated game r, c Cooperate Defect Both know that there are only 10 rounds Still simultaneous choice each round Cooperate $18K, $18K $15K, $20K Can Duff (or Fudd) play “nice” Duff in early rounds to build up a Beer reputation for cooperation to elicit the cooperation of the Defect $20K, $15K $16K, $16K other in future rounds?  Finitely repeated prisoner’s dilemma Fudd Beer 1 2 3 4 5 6 7 8 9 10 Duff D D D D D D D D D D r, c Cooperate Defect Fudd D D D D D D D D D D There’s no incentive to cooperate in the last round… Cooperate $18K, $18K $15K, $20K Duff …ergo, there’s no incentive to Beer cooperate in the first round Defect $20K, $15K $16K, $16K  Finitely repeated prisoner’s dilemma Fudd Beer 1 2 3 4 5 6 7 8 9 10 Duff D D D D D D D D D D r, c Cooperate Defect Fudd D D D D D D D D D D Even in a finitely-repeated prisoner’s dilemma, cooperation Cooperate $18K, $18K $15K, $20K is still difficult to obtain Duff (We’ll come back to this issue Beer later for infinitely-repeated games) Defect $20K, $15K $16K, $16K Sequential games Fudd Beer One player chooses first, Produce Produce followed by the other r, c 3,000 units 4,000 units Let’s consider this a one-time interaction (for now) Produce $18K, $18K $15K, $20K 3,000 units Duff Suppose that Duff is the first- Beer mover (i.e., the “leader”) Produce $20K, $15K $16K, $16K 4,000 units Sequential games Payoffs: Duff, Fudd $18K, $18K Fudd $15K, $20K Duff $20K, $15K Fudd $16K, $16K Sequential games But Duff has many, many more options than just 3,000 vs. 4,000 Duff knows that after it produces, Fudd faces a residual demand and acts like a monopoly for that residual demand, producing one-half the difference between the competitive output level and Duff’s output 1 𝑞𝑞𝐹𝐹 = (𝑄𝑄𝐶𝐶 − 𝑞𝑞𝐷𝐷 ) 2 The following is known as the Stackelberg model of duopoly  Stackelberg duopoly Oligopolistic beer industry Price $14 Duff knows that after it $13 $12 produces, Fudd is going to $11 produce exactly ½ the difference $10 $9 between that and competitive $8 market output of 𝑄𝑄𝐶𝐶 = 12 $7 $6 For example, $5 1 $4 Competitive 𝑞𝑞𝐷𝐷 = 10 ⇒ 𝑞𝑞𝐹𝐹 = 12 − 10 = 1 equilibrium 2 $3 1 𝑝𝑝𝑐𝑐 = $2 𝑀𝑀𝑀𝑀 = 𝐴𝐴𝐴𝐴 𝑞𝑞𝐷𝐷 = 8 ⇒ 𝑞𝑞𝐹𝐹 = 12 − 8 = 2 2 $1 Market demand 1 $0 𝑞𝑞𝐷𝐷 = 6 ⇒ 𝑞𝑞𝐹𝐹 = 12 − 6 = 3 2 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Quantity (1,000s)  Stackelberg duopoly Oligopolistic beer industry Price $14 Duff knows that after it $13 $12 produces, Fudd is going to $11 produce exactly ½ the difference $10 $9 between that and competitive $8 market output of 𝑄𝑄𝐶𝐶 = 12 $7 𝑅𝑅𝐷𝐷𝐷𝐷 $6 $5 $4 Competitive equilibrium Thus, Duff’s residual demand $3 𝑝𝑝𝑐𝑐 = $2 𝑀𝑀𝑀𝑀 = 𝐴𝐴𝐴𝐴 (𝑅𝑅𝐷𝐷 ) is half-as-steep as the 𝐷𝐷 $1 Market demand linear inverse demand curve $0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Quantity (1,000s)  Stackelberg duopoly Oligopolistic beer industry Price $14 Duff as some corresponding twice- $13 $12 as-steep marginal revenue $11 schedule (𝑀𝑀𝑅𝑅𝐷𝐷 ) $10 $9 Chooses 𝑞𝑞𝐷𝐷 such that 𝑀𝑀𝑅𝑅𝐷𝐷 = 𝑀𝑀𝐶𝐶𝐷𝐷 $8 $7 Here, 𝑞𝑞𝐷𝐷 = 6,000 𝑅𝑅𝐷𝐷𝐷𝐷 Stackelberg duopoly $6 𝑝𝑝𝑆𝑆𝑆𝑆 = $5 equilibrium Fudd reacts by producing Competitive 1 $4 equilibrium 𝑞𝑞𝐹𝐹 = 12 − 6 = 3,000 $3 2 𝑝𝑝𝑐𝑐 = $2 $1 𝑀𝑀𝑅𝑅𝐷𝐷 = 𝑀𝑀𝐶𝐶𝐷𝐷 𝑀𝑀𝑀𝑀 = 𝐴𝐴𝐴𝐴 Total market output = 9,000 𝑀𝑀𝑅𝑅𝐷𝐷 Market demand $0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Quantity (1,000s) Duff Fudd  Stackelberg duopoly Oligopolistic beer industry Price $14 Total market output = 9,000 $13 $12 Market price 𝑝𝑝𝑆𝑆𝑆𝑆 = $5 $11 $10 Duff’s profit 𝜋𝜋𝐷𝐷 = $18,000 $9 $8 Fudd’s profit 𝜋𝜋𝐹𝐹 = $9,000 $7 𝑅𝑅𝐷𝐷𝐷𝐷 Stackelberg duopoly $6 equilibrium 𝑝𝑝𝑆𝑆𝑆𝑆 = $5 Competitive $4 equilibrium $3 𝑝𝑝𝑐𝑐 = $2 𝑀𝑀𝑀𝑀 = 𝐴𝐴𝐴𝐴 $1 𝑀𝑀𝑅𝑅𝐷𝐷 = 𝑀𝑀𝐶𝐶𝐷𝐷 𝑀𝑀𝑅𝑅𝐷𝐷 Market demand $0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Quantity (1,000s) Duff Fudd  Stackelberg duopoly Oligopolistic beer industry Price $14 Stackelberg duopoly lies between $13 $12 Cournot-Nash and competition $11 Perfect $10 = Monopoly oligopoly $9 𝑝𝑝𝑚𝑚 = $8 Efficiency? Cournot-Nash duopoly $7 Stackelberg duopoly 𝑝𝑝𝐶𝐶𝐶𝐶 = $6 equilibrium 𝑝𝑝𝑆𝑆𝑆𝑆 = $5 Competitive $4 equilibrium $3 𝑝𝑝𝑐𝑐 = $2 𝑀𝑀𝑀𝑀 = 𝐴𝐴𝐴𝐴 $1 𝑀𝑀𝑅𝑅𝑚𝑚 Market demand $0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Quantity (1,000s)  Oligopoly *All three of these conditions must Oligopolistic beer industry hold for the conclusion… Price $14 If (1) both firms are identical and $13 $12 (2) costs are constant and (3) $11 Perfect market demand is linear*, then: = Monopoly $10 oligopoly 1 $9 𝑄𝑄𝑚𝑚 = 𝑄𝑄𝑐𝑐 Cournot-Nash duopoly 2 𝑝𝑝𝑚𝑚 = $8 $7 Stackelberg duopoly 2 𝑝𝑝𝐶𝐶𝐶𝐶 = $6 equilibrium 𝑄𝑄𝐶𝐶𝐶𝐶 = 𝑄𝑄𝑐𝑐 𝑝𝑝𝑆𝑆𝑆𝑆 = $5 3 Competitive $4 equilibrium $3 3 𝑝𝑝𝑐𝑐 = $2 𝑀𝑀𝑀𝑀 = 𝐴𝐴𝐴𝐴 𝑄𝑄𝑆𝑆𝑆𝑆 = 𝑄𝑄𝑐𝑐 4 $1 𝑀𝑀𝑅𝑅𝑚𝑚 Market demand $0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Quantity (1,000s)  How to outsmart a Cournot oligopolist Oligopolistic beer industry Price $14 Suppose Duff & Fudd are in $13 $12 Cournot-Nash equilibrium $11 Perfect 𝑞𝑞𝐷𝐷 = 𝑞𝑞𝐹𝐹 = 4,000 These are all the = Monopoly $10 $9 oligopoly 𝜋𝜋𝐷𝐷 = $16,000 same numbers used previously 𝑝𝑝𝑚𝑚 = $8 Cournot-Nash duopoly 𝜋𝜋𝐹𝐹 = $16,000 $7 Stackelberg duopoly 𝑝𝑝𝐶𝐶𝐶𝐶 = $6 equilibrium Duff knows Fudd is behaving 𝑝𝑝𝑆𝑆𝑆𝑆 = $5 $4 Competitive according to the Cournot $3 equilibrium assumption, i.e., Fudd treats 𝑝𝑝𝑐𝑐 = $2 $1 𝑀𝑀𝑀𝑀 = 𝐴𝐴𝐴𝐴 Duff’s output as given Market demand $0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Can Duff outsmart Fudd and be Quantity (1,000s) better off?  How to outsmart a Cournot oligopolist Oligopolistic beer industry Price $14 If Duff produces the monopoly $13 $12 output level 𝑞𝑞𝐷𝐷 = 6,000, then $11 Perfect Fudd responds by producing = Monopoly $10 $9 oligopoly 𝑞𝑞𝐹𝐹 = 3,000. Price is 𝑝𝑝 = $5. 𝑝𝑝𝑚𝑚 = $8 Cournot-Nash duopoly 𝜋𝜋𝐷𝐷 = $18,000 $7 𝑝𝑝𝐶𝐶𝐶𝐶 = $6 Stackelberg duopoly 𝜋𝜋𝐹𝐹 = $9,000 equilibrium 𝑝𝑝𝑆𝑆𝑆𝑆 = $5 Competitive (This is the Stackelberg $4 equilibrium equilibrium.) $3 𝑝𝑝𝑐𝑐 = $2 Thus, a Cournot oligopolist can 𝑀𝑀𝑀𝑀 = 𝐴𝐴𝐴𝐴 $1 Market demand $0 always be better off by NOT 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 behaving like a Cournot Quantity (1,000s) oligopolist… How to outsmart a Cournot oligopolist Thus, the Principle of Or, as Nobel laureate economist Outsmarting George Stigler (1964, p. 44) put Any economic analysis is it: incomplete if the individual agents therein can change their behavior “A satisfactory theory of oligopoly to better their situation… cannot begin with assumptions What is the implication of the concerning the way in which each Principle of Outsmarting…? firm views its interdependence with its rivals.” To what “assumptions” is Stigler referring? 08 Practice questions 08 Practice questions Unless otherwise instructed, use standard assumptions. 1. Why does everybody talk so loudly at parties? Use simple game theory to explain. 2. Why are group projects with randomly-assigned partners so frustrating for bright, motivated college students? Use simple game theory to explain. 3. Why are group projects with randomly-assigned partners so beloved by dull, unmotivated college students? Use simple game theory to explain. 4. Karl Marx argued that the capitalist class (i.e., the owners of the business enterprises) works tirelessly to make sure that the government acts according to the collective interests of the capitalist class. Apply simple game theory to evaluate this claim. Explain. 5. “Perfect competition is a prisoner’s dilemma into which, fortunately for society as a whole, many firms are led, as though by an invisible hand.” (McCloskey, 1985, p. 440). Provide a comment. 6. Consider the example in the slides about the Cournot-Nash duopoly between Duff Beer and Fudd Beer. Suppose Duff and Fudd each simultaneously attempt to outsmart the other. What is the result and why is it interesting? Explain. 08 Practice questions 7. Two oligopolists agree on a handshake to produce the perfect cartel equilibrium. TRUE, FALSE, or UNCERTAIN: This agreement is stable. Explain. 8. Two oligopolists agree on a handshake to produce the perfect cartel equilibrium. Each tells the other his most embarrassing secret, under the explicit threat that this will be revealed to all should the he defect on the agreement. TRUE, FALSE, or UNCERTAIN: This agreement is stable. Explain. 9. Suppose you are one of the oligopolists in problem 8.8. Can you outsmart the other? Explain. 10. Suppose you are the other oligopolist in problem 8.9. Can you outsmart the other? Explain. 11. Do your answers to 8.9 and 8.10 change your answer to 8.8 at all? Explain. 12. Two oligopolists are producing at the Cournot-Nash equilibrium. TRUE, FALSE, or UNCERTAIN: This behavior is stable. Explain. 13. Before getting married, two individuals sign the following prenuptial agreement. Should one spouse cheat on the other, the cheater owes the cheated $10,000,000 in alimony after the resulting divorce. TRUE, FALSE, or UNCERTAIN: The fidelity of each spouse is guaranteed. Explain. 08 Practice questions 14. My cousin believes that, since 1969, hundreds (or, more likely, thousands) of people have conspired together to suppress the fact that the Apollo 11 moon landing was faked in a Hollywood studio. Is he more likely RIGHT or WRONG in this belief? Use simple game theory to explain. 15. Your professor wants you to study for the upcoming midterm, so he threatens to make the exam really difficult—the most difficult exam you’ll ever take in your life! Is such a threat credible? Explain. 16. What do you think to be the big, overarching lesson of this slide deck, if any? Explain. 17. TRUE, FALSE, or UNCERTAIN: Outsmarting in an oligopoly industry serves a similar function as does entry in a competitive industry. Explain. 18. In late 19th century and early 20th century Germany, cartel agreements were enforceable by law. How do you suppose this affected the structure of historical German industry? Explain.  08 Practice questions Price Oligopolistic widget industry $42 For the following questions, consider the graph $40 $38 to the left. The widget industry is a duopoly of $36 two identical firms: Ace Widget Company and $34 Best Widgets, Inc. There is a significant barrier $32 to entry. $30 $28 19) Find the profit of each if they were able to $26 successfully cartelize. $24 $22 Market demand 20) Find the profit of each at the Cournot-Nash $20 equilibrium. $18 $16 21) Find the profit of each at the Stackelberg $14 equilibrium. (Ace is the “leader”.) $12 $10 22) Find the profit of each if they both $8 simultaneously try to outsmart the other. $6 $4 𝑀𝑀𝑀𝑀 = 𝐴𝐴𝐴𝐴 $2 $0 0 3 6 9 12 15 18 21 24 27 30 33 36 39 Quantity (1,000s)