2 A Market-Share Game Two managers want to maximize market share. Strategies are pricing decisions.Simultaneous moves.One-shot game.
3 The Market-Share Game in Normal Form Manager 2Manager 1What is the Nash Equilibrium???
4 Market-Share Game Equilibrium Manager 2Manager 1Nash Equilibrium
5 What do we see?Game theory can be used to analyze situations where “payoffs” are non monetary!Here we were looking at market sharesTypically we will focus on environments where businesses want to maximize profits.Typical payoffs are measured in monetary units.
6 Is the Nash Equilibrium always best? Firm BFirm AWhat is the Nash equilibrium?Low Price – Low PriceIs it the best?Could collude and both charge high pricesWhat 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.
7 Examples of Coordination Games Coordination games should we produce things to coordinate with our rivals, or do something completely differentLaser disks vs. DVDsIndustry standardssize of floppy disks.size of CDs.National standardselectric current.traffic laws.
8 A Coordination Game in Normal Form Player 2Player 1
9 A Coordination Problem: Three Nash Equilibria! Player 2Player 1More than one Nash equilibrium!!Anytime we do the same…we maximize our profits.
10 Key Insights: Not all games are games of conflict. Communication can help solve coordination problems.Sequential moves can help solve coordination problems.
11 An Advertising GameTwo firms (Kellogg’s & General Mills) managers want to maximize profits.Strategies consist of advertising campaigns.Simultaneous moves.One-shot interaction.Repeated interaction.
12 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 decisionCheat or not cheatWhat was the formula for PV??
14 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 cheatingRemember the deal is Don’t advertise!!
15 Suppose General Mills adopts this trigger strategy. Kellogg’s profits? Cooperate = /(1+i) + 12/(1+i)2 + 12/(1+i)3 + …= /iValue of a perpetuity of $12 paidat the end of every yearCheat = 20 +2/(1+i) + 2/(1+i)2 + 2/(1+i)3 + …= /IGain 20 the first period but 2 after cheating episodeGeneral MillsKellogg’s
16 Kellogg’s Gain to Cheating: Cheat - Cooperate = /i - ( /i) = /iSuppose i = .05Cheat - Cooperate = /.05 = = -192It doesn’t pay to deviate.Collusion is a Nash equilibrium in the infinitely repeated game!If Immediate Benefit - PV of Future Cost > 0Pays to “cheat”.If Immediate Benefit - PV of Future Cost 0Doesn’t pay to “cheat”.
17 Key InsightCollusion 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.
18 Real World Examples of Collusion Garbage Collection IndustryOPECNASDAQAirlines
19 Can we do it? (demonstration problem 10-6) PriceFirm BLowHighFirm A0,050,-40-40,5010,10Suppose 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?
20 Cheat get 50 now and zero after that Not Cheat get 10 foreverSince 50 (cheat) > 35 (not cheat we would end up CHEAT
21 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 agreementBe able to punish successfully for deviations from agreementThe end of the game is not knownIf there is no tomorrow there is no punishment everyone will cheat