Managerial Economics & Business Strategy Chapter 10 Game Theory: Inside Oligopoly

Introduction: Prisoner’s Dilemma Ginger and Rocky rob a 7-eleven. Evidence is good on the robbery but not so good on whether it was an armed robbery. Rocky Strategy Don’t Confess Confess 1, 1 7, Free Free, 7 5, 5 Ginger

Introduction: Prisoner’s Dilemma Game Theory on Display (tires example) EC Fines Roche, BASF, Six Other Firms Total of $751.7 million for Price Fixing, WSJ 2001

Game Form A Normal Form Game consists of: Players = managers or firms Strategies or feasible actions = planned decisions Payoffs = profits or losses, market share The order in which players make decisions is important Simultaneous Sequential Type of game is important one-shot repeated games

A Normal Form Game Player 2 12,11 11,12 14,13 Player 1 11,10 10,11 12,12 10,15 10,13 13,14

Normal Form Game: Scenario Analysis Suppose 1 thinks 2 will choose “A”. Player 2 12,11 11,12 14,13 Player 1 11,10 10,11 12,12 10,15 10,13 13,14

Normal Form Game: Scenario Analysis Then 1 should choose “a”. Player 1’s best response to “A” is “a”. Player 2 12,11 11,12 14,13 Player 1 11,10 10,11 12,12 10,15 10,13 13,14

Normal Form Game: Scenario Analysis Suppose 1 thinks 2 will choose “B”. Player 2 12,11 11,12 14,13 Player 1 11,10 10,11 12,12 10,15 10,13 13,14

Normal Form Game: Scenario Analysis Then 1 should choose “a”. Player 1’s best response to “B” is “a”. Player 2 12,11 11,12 14,13 Player 1 11,10 10,11 12,12 10,15 10,13 13,14

Normal Form Game Scenario Analysis Similarly, if 1 thinks 2 will choose C… Player 1’s best response to “C” is “a”. Player 2 12,11 11,12 14,13 Player 1 11,10 10,11 12,12 10,15 10,13 13,14

Dominant Strategy Regardless of whether Player 2 chooses A, B, or C, Player 1 is better off choosing “a”! “a” is Player 1’s Dominant Strategy! Player 2 12,11 11,12 14,13 Player 1 11,10 10,11 12,12 10,15 10,13 13,14

Putting Yourself in your Rival’s Shoes What should player 2 do? 2 has no dominant strategy! But 2 should reason that 1 will play “a”. Therefore 2 should choose “C”. Player 2 Strategy A B C a b c 12,11 11,12 14,13 C Player 1 11,10 10,11 12,12 10,15 10,13 13,14 C A

The Outcome This outcome is called a Nash equilibrium: Player 2 12,11 11,12 14,13 Player 1 11,10 10,11 12,12 10,15 10,13 13,14 This outcome is called a Nash equilibrium: “a” is player 1’s best response to “C”. “C” is player 2’s best response to “a”.

Key Insights Look for dominant strategies Put yourself in your rival’s shoes Nash Equilibrium: doing the best you can given what other players are doing. No player can unilaterally improve his/her payoff by changing his/her strategy. Not all games will have a Nash Equilibrium (monitoring workers example) Some games may have more than 1 Nash Equilibrium

A Market Share Game Two managers want to maximize market share (the payoff is market share) Strategies are pricing decisions Simultaneous moves One-shot game

The Market-Share Game in Normal Form Manager 2 Manager 1 First number in each cell represents the market share for Firm 1, and the second for Firm 2.

Market-Share Game Equilibrium Manager 2 Manager 1 Nash Equilibrium

A Coordination Game Strategy Work Together Don’t Work Together Microsoft Word Strategy Work Together Don’t Work Together $100, $80 $40, $40 $25, $25 $50, $80 Corel WordPerfect

A Coordination Problem: Two Nash Equilibria! Microsoft Word Strategy Work Together Don’t Work Together $100, $80 $40, $40 $25, $25 $50, $80 Corel WordPerfect

Key Insights: Not all games are games of conflict (e.g., industry standards existed for floppy disc sizes, electrical currents, new “industries,” HDTV) Communication can help solve coordination problems. Sequential moves can help solve coordination problems. Government could set a standard to solve coordination problems: electrical current.

An Advertising Game Two firms (Kellogg’s & General Mills) managers want to maximize profits Strategies consist of advertising campaigns Simultaneous moves One-shot interaction Repeated interaction

A One-Shot Advertising Game General Mills Kellogg’s

Equilibrium to the One-Shot Advertising Game General Mills Kellogg’s Nash Equilibrium

Can collusion work if the game is repeated 1 time? General Mills Kellogg’s

No (by backwards induction). In period 2, the game is a one-shot game, so equilibrium entails High Advertising in the last period. The same holds true if we repeat the game any known, finite number of times.

Can collusion work if firms play the game each year, forever? Yes, unless a rival “cheats.” Collusion can be supported with trigger strategies. Consider the following “trigger strategy” by each firm: “Don’t advertise, provided the rival has not advertised in the past. If the rival ever advertises, “punish” it by engaging in a high level of advertising forever after.” In effect, each firm agrees to “cooperate” so long as the rival hasn’t “cheated” in the past. “Cheating” triggers punishment in all future periods. Note: collusion illegal and it is illegal for firms to engage in “trigger-like” behavior to get the collusive outcome.

Suppose General Mills adopts this trigger strategy. Kellogg’s profits? Cooperate = 12 +12/(1+i) + 12/(1+i)2 + 12/(1+i)3 + … = 12 + 12/i Value of a perpetuity of $12 paid at the end of every year Cheat = 20 +2/(1+i) + 2/(1+i)2 + 2/(1+i)3 + = 20 + 2/i General Mills Kellogg’s

Kellogg’s Gain to Cheating: Cheat - Cooperate = 20 + 2/i - (12 + 12/i) = 8 - 10/i Suppose i = .05 Cheat - Cooperate = 8 - 10/.05 = 8 - 200 = -192 It doesn’t pay to deviate. Collusion is a Nash equilibrium in the infinitely repeated game! UGH! General Mills Kellogg’s

Key Insight Collusion can be sustained as a Nash equilibrium when there is no certain “end” to a game. Doing so requires: Know your rival, your rival’s customers, and be able to monitor Ability (and reputation for) punishing cheaters Low interest rate (in this example, i ≤ 5/4) High probability of future interaction In infinitely repeated games there is always a tomorrow to consider. Must weigh the benefits and costs of cheating.

Real World Example of Collusion: OPEC Cartel founded in 1960 by Iran, Iraq, Kuwait, Saudi Arabia, and Venezuela. OPEC's mission is to coordinate and unify the petroleum policies of Member Countries and ensure the stabilization of oil markets in order to secure an efficient, economic and regular supply of petroleum to consumers, a steady income to producers and a fair return on capital to those investing in the petroleum industry. (www.opec.org)

Cournot Game in Normal Form Venezuela Saudi Arabia High Q is never a good strategy for either country; this essentially, means the game is between Med and Low.

One-Shot Cournot (Nash) Equilibrium Venezuela Saudi Arabia

Repeated Game Equilibrium* Venezuela Saudi Arabia (Assuming a sufficiently low interest rate)

Caveat Collusion is a felony under Section 2 of the Sherman Antitrust Act. Conviction can result in both fines and jail-time (at the discretion of the court). OPEC isn’t illegal; thus, US laws don’t apply

Simultaneous-Move Bargaining Game (SMBG) Management and a union are negotiating a wage increase. Strategies are wage offers & wage demands Successful negotiations lead to $600 million in surplus, which must be split among the parties Failure to reach an agreement results in a loss to the firm of $100 million and a union loss of $3 million Simultaneous moves, and time permits only one-shot at making a deal.

The SMBG in Normal Form Union Management

Three Nash Equilibria! Union Management

Fairness SMBG are difficult to predict because of multiple Nash Equilibria. Experimental evidence suggests that bargainers often perceive a 50-50 split to be fair. Union Management

Single Offer Bargaining Now suppose the game is sequential in nature, and management gets to make the union a “take-it-or-leave-it” offer. Do the following: write the game in extensive form Summarize the players Their potential actions Their information at each decision point The sequence of moves and Each player’s payoff

Step 1: Management’s Move 10 5 Firm 1

Step 2: Add the Union’s Move Accept Union Reject 10 Accept 5 Firm Union Reject 1 Accept Union Reject

Step 3: Add the Payoffs Accept 100, 500 Union -100, -3 Reject 10 300, 300 5 Firm Union -100, -3 Reject 1 Accept 500, 100 Union -100, -3 Reject

Step 6: Identify Nash Equilibrium Outcomes Outcomes such that neither the firm nor the union has an incentive to change its strategy, given the strategy of the other

There are 3 Nash Equilibrium Outcomes! Accept 100, 500 Union -100, -3 Reject 10 Accept 300, 300 5 Firm Union -100, -3 Reject 1 Accept 500, 100 Union -100, -3 Reject

Only 1 Subgame-Perfect Nash Equilibrium Outcome! Accept 100, 500 Union -100, -3 Reject 10 Accept 300, 300 5 Firm Union -100, -3 Reject 1 Accept 500, 100 Union -100, -3 Reject

Re-Cap In take-it-or-leave-it bargaining, there is a first-mover advantage (what if union made offer, and firm had to take or leave it?). But... Management should be careful, however; real world evidence suggests that people sometimes reject offers on the the basis of “principle” instead of cash considerations. While the outcome was obvious, the framework can be used to analyze more complicated bargaining issues.

Pricing to Prevent Entry: An Application of Game Theory Two firms: an incumbent and potential entrant Incumbent threatens to start a price war. Is this credible? The game in extensive form:

The Entry Game in Extensive Form -1, 1 Price War Incumbent Enter No Price War 5, 5 Entrant Out 0, 10

One Subgame Perfect Equilibrium Entrant Out Enter Incumbent Price War No Price War -1, 1 5, 5 0, 10

Incumbant VS. Entrant: Incumbant and Credible Threat ($2m), ($2m) Enter Entrant Don’t Enter Expand Q $4m, $0 Incumbent $2m, $2m Enter Don’t Expand Q Entrant Don’t Enter $6m, $0

Incumbant VS. Entrant: Incumbant and Credible Threat Nash and Subgame Perfect Nash: Expand and Don’t Enter ($2m), ($2m) Enter Entrant Don’t Enter Expand Q $4m, $0 Incumbent $2m, $2m Enter Don’t Expand Q Entrant Don’t Enter Note: would see different outcome if entrant goes first (and has started its entry), then incumbant threat not credible. $6m, $0

Insight It does not pay to heed threats made by rivals because not all threats are credible.