Algorithmic Collusion

Transcription

1 Algorithmic Collusion KAI-UWE KÜHN UNIVERSITY O F EAST ANGLIA, CC P, DICE, AND C EPR STEVE TADELIS UNIVERSITY OF C ALIFORNIA, BERKELEY, NBER AND C EPR Prepared for CRESSE 2017

2 The stories lawyers tell Two Artificial Neural Networks and one Nash equilibrium meet in an online (pub) hub. After a few milliseconds, a unique silent friendship is formed (Ezrachi and Stucke 2017) A somewhat different perspective: Two Artificial Neural Networks meet a multidimensional continuum of subgame-perfect Nash equilibria in an online hub. With unbelievable speed the two Artificial Neural Networks react and say huh?.

3 There was a time in antitrust when everyone was talking about interoperability The Microsoft server case: Save encrypted ЖϠ Microsoft Desktop Non-Microsoft Server E What???? Your server can t do that!

4 Do Algorithms behave badly? In the Spring of 2011, two online retailers offered copies of Peter Lawrence s textbook The Making of a Fly on Amazon for $18,651, and $23,698, respectively. This was the result of both sellers using automated pricing algorithms. Everyday, the algorithm used by seller 1 set the price of the book to be times the price charged by seller 2. Later in the day, seller 2 s algorithm would adjust its price to be times that of seller 1. Prices increased exponentially and remained over one million dollars for at least ten days (!), until one of the sellers took notice and adjusted its price to $ From Bruno Salcedo, Pricing Algorithms and Tacit Collusion, Penn State mimeo, 2015

5 The Standard Collusion Model The Incentive Condition: Benefit from undercutting by one unit Loss from switching to a worse equilibrium in the future

6 The Comparative Statics of Collusion Models Asymmetry between players strongly undermines collusion Intransparency undermines collusion Rapid interaction makes collusion easier (mostly) A host of other things Irreversibility of decisions can make it very hard Folklore about homogeneous goods Etc., etc.

7 The theory does not address the coordination problem We have seen that coordination problems are hard to solve without communication, even in simple static games Repeated games have a very large number of equilibria (a continuum of outcomes, each supported by a continuum of strategies) Firms have to coordinate on complicated contingent strategies Can they do this implicitly? Even many economists believe yes the evidence looks a little different Older literature: 2 action 2 person games often shows significant tacit collusion, however, this does not carry over to more complicated games.

8 Coordination is Hard: Ask A Manager! When contributing to good coordination Is risky, coordination failure often occurs What can one do about it? Incentives? Clear instructions! = Good Management (Brandts and Cooper (2007): It s what you say Not what you pay: An experimental study of manageremployee relationships in overcoming coordination failure, Journal of the European Economic Association. See also Brandts and Cooper 2006, Brandts, Cooper, Fatas 2007) Management is all about coordinating complementary activities!

9 Tacit collusion all but disappears with more than two players Huck et al Huck and Normann 2011 These are perfectly transparent markets! Market transparency does not cause collusion! These are games with high frequency of interaction! This does not cause collusion

10 Even where prices are higher than theory suggests, they are not collusive 300 joint profit max mixed NE mixed NE Random Fixed w/out Fixed with Kühn und Normann: The Coordinated Effects of Mergers: An Experiment, in preparation

11 But communication generates collusion 300 joint profit max mixed NE mixed NE Random Fixed w/out Fixed with Kühn und Normann: The Coordinated Effects of Mergers: An Experiment, in preparation

12 What is Important in Communications? 1 if we both choose [Period 1 High] for the first one we both get ecu 2 Yea 1 [Period 2 High] for period 2 2 and then we both can choose [Period 2 High] for the second one 2 yeah 1 making my decision 2 and don't backstab 1 hey 2 if we both choose [Period 1 High] and then [Period 2 High] we get a dollar for the round 1 so i just got skrewed, awesome 2 haha 1 don't screw me tho 2 i wont u 1 lol yep [Period 1 High] and [Period 2 High] sounds goood 2 sending mine 1 ciao! 1 ^*%&(*^)&(*^(%& 2 im starting to hate people lol 1 ya i know the feeling 2 do you? 1 there are some real jerks out there 2 bcs so did the last person who skrewed me lol 1 haha 2 so whats the plan? 1 [Period 1 High] then [Period 2 High]? 2 yea. but if you [Period 1 Medium] tho i'm putting [Period 2 Low] for the nxt one lol. 1 why would you do that? 2 [Period 1 High] and [Period 2 High]... yes... 1 why would you put anything other than [Period 2 High] for the last one? this game isn't dependant on how bad other poeple do you are giving up money just to spite someone you will never know 2 if you skrew me on the 1st one im skrewing you bak no matter what thats why lol 1 that doesn't make any sense 2 lol so you are planning on putting be *[Period 1 Medium] 1 of course 2 alright 1... lol... 2 dont be stupid bcs i will. put. [Period 2 Low] 1 since i know you are going ot screw me on the second one i'll put [Period 1 High] then [Period 2 High] no point in doing anything else might as well get i'm choosing 1 right.

13 The Power of Verbal Punishment Most used non-proposal category: Admonishments good job, [expletive deleted] you are a bad person I hope someone [expletive deleted] you over as well you know they shoot you for that in Texas Apology/Rationalization: sorry about that I assumed you would have screwed me over like the last person I had The I believed you would cheat defense

14 What does this imply for algorithmic collusion? Algorithms are arguably rational in perusing well-defined programmed objectives But rationality and even common knowledge of rationality does not resolve coordination problems Why would algorithms be better at solving coordination problems without communication? How would algorithms establish a common language that would allow communication and agreement without that being explicitly programmed and the programming be coordinated between the algorithms?

15 Can algorithms spontaneously collude There are some results on adaptive learning: Milgrom and Roberts (1990): Rationalizability, Learning, and Equilibrium in Games with strategic complementarities Adaptive Learning Process: A strategy choice is justified if there is no other strategy that would have done better against every combination of strategies in the smallest interval containing the competitors' recent past play (where recent may be a very long time interval) The theorem says: Every adaptive learning process in a supermodular game converges to the unique one shot Nash equilibrium if there is a unique NE. Otherwise it converges to the set of (one shot) rationalizable actions This means: although the game may be played in continuous time and infinitely often repeated, there is convergence to one shot behaviour despite the fact that there is conditioning on past behaviour of rivals What is missing: coordination on future play in response to the history of play

16 Models in which spontaneous collusion occurs Salcedo (2017) Algorithm becomes perfectly known to the competitor after some time This is critical because it allows to design an algorithm that reacts collusively to that of the rival and punishes potential pro-competitive behaviour which in turn allows the rival to redesign the algorithm Effectively establishes communication and coordination about the algorithm

17 Important insights for policy Some coordination mechanism is needed to allow algorithms to collude Generally this involves exchange of information between the designers of the algorithms Currently highly unrealistic because firms will not share their valuable asset Simple competition rules as they already exist (no talking about prices) have a direct equivalent in algorithms: if algorithms are shared the strategy of how to react to current prices in the future is fully revealed. Should therefore fall directly under current cartel rules These actions are very detectable: designing algorithms for communication with each other involves many programmers and computer engineers. Exchange of algorithms can be at least as easily detected as talking about prices

18 Is there a brave new world of algorithmic collusion? Even self-aware artificial neural networks need to communicate to coordinate on collusion However, a pricing algorithm does not need communications capability For now there seems no reason that coordination on communication capability and coordination of algorithms as such is more difficult to detect than collusion in current markets. However, you should panic once those self-aware artificial neural networks start using time travel for their secret meetings