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

A Market-Share Game Two managers want to maximize market share. Strategies are pricing decisions. Simultaneous moves. One-shot game.

The Market-Share Game in Normal Form Manager 2 Manager 1 What is the Nash Equilibrium???

Market-Share Game Equilibrium Manager 2 Manager 1 Nash Equilibrium

What do we see? Game theory can be used to analyze situations where “payoffs” are non monetary! Here we were looking at market shares Typically we will focus on environments where businesses want to maximize profits. Typical payoffs are measured in monetary units.

Is the Nash Equilibrium always best? Firm B Firm A What is the Nash equilibrium? Low Price – Low Price Is it the best? Could collude and both charge high prices What if we “agree” to charge high prices, but then firm A cheats? Firm A will increase profits (can’t rat them out because collusion is illegal) Everyone fears cheating…we don’t agree.

Examples of Coordination Games Coordination games  should we produce things to coordinate with our rivals, or do something completely different Laser disks vs. DVDs Industry standards size of floppy disks. size of CDs. National standards electric current. traffic laws.

A Coordination Game in Normal Form Player 2 Player 1

A Coordination Problem: Three Nash Equilibria! Player 2 Player 1 More than one Nash equilibrium!! Anytime we do the same…we maximize our profits.

Key Insights: Not all games are games of conflict. Communication can help solve coordination problems. Sequential moves can help solve coordination problems.

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.

Infinitely Repeated Games It appears that Collusion is not possible in a one-shot game, but what if we can build trust??? Need to look at the STREAM of payoffs when they make their current decision Cheat or not cheat What was the formula for PV??

If profits are the same in every period

Can collusion work if firms play the game each year, forever? 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. Trigger causes a FUTURE cost of cheating Remember the deal is  Don’t advertise!!

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 Gain 20 the first period but 2 after cheating episode 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! If Immediate Benefit - PV of Future Cost > 0 Pays to “cheat”. If Immediate Benefit - PV of Future Cost  0 Doesn’t pay to “cheat”.

Key Insight Collusion can be sustained as a Nash equilibrium when there is no certain “end” to a game. Doing so requires: Ability to monitor actions of rivals. Ability (and reputation for) punishing defectors. Low interest rate. High probability of future interaction.

Real World Examples of Collusion Garbage Collection Industry OPEC NASDAQ Airlines

Can we do it? (demonstration problem 10-6) Price Firm B Low High Firm A 0,0 50,-40 -40,50 10,10 Suppose firm A and firm B repeatedly face the situation presented below and the interest rate is 40 percent. The firms agree to charge a high price each period provided neither firm has cheated on this agreement in the past. What are firm A’s profits if it cheats on the collusive agreement? What are firm A’s profits if it does not cheat on the collusive agreement? Does an equilibrium result where the firms charge the high price each period?

Cheat  get 50 now and zero after that Not Cheat  get 10 forever Since 50 (cheat) > 35 (not cheat we would end up CHEAT

Factors affecting collusion Collusion is easier when firms know… Who their rivals are (so then they know who to punish) Who their rivals’ customers are (so they can steal them by charging lower prices if they have to punish the rival) When their rivals deviate from the agreement Be able to punish successfully for deviations from agreement The end of the game is not known If there is no tomorrow  there is no punishment  everyone will cheat

Chapter 10 Homework Numbers 2, 4, and 14