Reputation and Strategic Irrationality

Lecture 11 Game Plan „ Reputation and “strategic irrationality” „ Course feedback Credibility and Reputation “This is our very soul … our whole life. For them, it’s just another field.” - Edwin Land, Polaroid founder, reacting to Kodak’s entry into instant photography Kodak’s assessment „ Kodak took care to enter gently Kodak film and cameras were incompatible with Polaroid’s „ So Polaroid could still milk profits from its established customer base „ With Kodak’s deep pockets, there was no way they would leave „ Thus, Polaroid was going to give in „ Polaroid’s Growl Polaroid responded by not giving in immediately, and saying that it would never give „ How should Kodak react to such statements? Why? „ Reputation in Repeated Games Enter Don’t 0, 3 „ „ Fight -2, -2 Accom 1, 1 Suppose incumbent monopolist always faces 80% chance that another entrant will come along Does this change things? Reputation in Repeated Games Enter Don’t 0, 3 „ „ -2, -2 Accom 1, 1 Fighting costs 3 today If Fighting deters next entrant and the one after that, etc.. it has benefit 2 in every future period „ „ Fight benefit 2(.8+.82+…)=2(1/.2 – 1) = +8 Fighting rational if it preserves “reputation” “Craziness” to Deter Entry 0, 3 Pr(Crazy) = 1/4 1, 1 Don’t Crazy Accom 1 3 Sane “Crazy” = having incentive to fight Enter Fight Enter Fight 4 4 Don’t 0, 3 Accom 1, 1 -2, 10 -2, -2 Enter whenever Pr(Crazy) < 1/3 Not Crazy Enough … 0, 3 Pr(Crazy) = 1/4 1, 1 Don’t Crazy Accom 1 3 Sane Enter Fight Enter Fight 4 4 Don’t 0, 3 Accom 1, 1 -2, 10 -2, -2 Enter whenever Pr(Crazy) < 1/3 Responding to “Craziness” Crazy 0, 3 1, 1 -1, 2 0, 0 Don’t Accom Leave Accom 1 3 Sane Enter Fight Stay Fight Enter Fight Stay Fight -3, 10 4 4 Don’t Accom Leave Accom 0, 3 1, 1 -1, 2 0, 0 -3, -3 ƒ What is the sequential equilibrium of this game? Crazy(?) Incumbent: Rules „ Incumbent learns whether it is “Crazy” or “Sane” „ „ 1. 2. 3. 4. “Crazy” incumbents love to fight Sequence of decisions Entrant – Enter? If so, Incumbent – Fight? If so, Entrant – Stay? If so, Incumbent – Fight? „ In last stage, only Crazy want to Fight. Get Crazy! We will play in sets of five people „ „ one Entrant four Incumbents The Entrant may Enter any/all of the four markets One of the four Incumbents is Crazy! Get Crazy! „ First, each Incumbent will learn whether it is Crazy or Sane • not allowed to credibly reveal this „ „ „ „ Next, Entrant decides which (if any) of the four markets to enter In markets with entry, Incumbents decide whether to fight In markets with fighting, Entrant decides whether to stay In markets with Entrant staying, Incumbent decides whether to Fight Sane Act Crazy „ Some (but not all!) Sane must Fight „ „ „ „ if all Fight, entrant will Stay for sure if none Fight, entrant will Leave for sure So, Sane must be indifferent to Fighting This requires that the entrant must Leave with probability 1/2 after Fight The Million Dollar Question: Will Entrant Enter? 0, 3 1, 1 -1, 2 1 Don’t Crazy 1 3 Sane Accom 0, 0 2 Accom Leave Enter Fight Stay1 2 Fight Enter Fight Stay Fight -3, 10 4 4 1 Don’t Accom Leave 1 0, 3 1, 1 2 Accom 2 -1, 2 0, 0 -3, -3 Entrants Blink „ Some (but not all!) entrants must Leave „ „ „ „ if all Leave, Sane will Fight for sure if none Leave, Sane will Accom for sure Entrant must be indifferent to Leaving This requires that incumbent be Crazy with probability 1/3 conditional on Fight „ so 50% of 75% Sane will Fight The Million Dollar Question: Will Entrant Enter? 0, 3 1, 1 -1, 2 1 Don’t Crazy 1 1 Fight Enter 2 Don’t Accom 1 0, 3 3 1, 1 Accom Leave 4 4 2 Fight Enter 3 Sane Accom 0, 0 2 Stay1 2 Fight Stay Fight -3, 10 3 3 1 3 Leave 1 2 Accom 2 -1, 2 0, 0 -3, -3 Entrant Stays Out „ What happens if entrant enters? „ „ „ „ all Crazy Fight (25%) plus 2/3 of the Sane Fight (50%) only get Accomodation 25% Entrant should stay out What tips the balance is that Entrant must worry about both: 1. Crazy opponents 2. Sane opponents acting crazy (!) Summary „ Reputation can help establish credibility in repeated games if losing reputation is costly: lost “mystique” „ others know you aren’t Crazy „