This year’s Economics Nobel was awarded to Milgrom and Wilson. Notwithstanding their characterizations by media as contributors to auction theory, both of them primarily worked in pure and applied game theory. Auction theory is actually an application of games, Milgrom found solutions for some very peculiar and exotic auctions , for example, auction of Radio frequencies to private companies. This was a very original application because of the unusual object being auctioned (air) and the difficulty of designing an efficient auction mechanism to maximize the gain to the auctioneer(the government).
Regardless of their contributions to auction theory, I want to point out how game theory evolved over time and what started as a very promising approach to analyzing human behavior turned out to have severe limitations – not because not enough research was done, but on the contrary a lot of research was done by some very brilliant people (including Milgrom!)
This could be illustrated perhaps by discussing Milgrom and Roberts (not Wilson) 1982 paper in Econometrica. Milgrom is not a lucid writer of articles, nor are most of the theoretical economists in our time. So I really started teaching from the article from early 1990’s possibly because I did not quite understand it before that time.
Let’s take one small part of the US antitrust Law and show how game theory evolved and policy changed over time
The Law simply says prevention of entry of new firms by charging a lower price (the technical term is limit-pricing) is illegal ( this is different from predatory –pricing where an incumbent firm charges price below cost to prevent entry – that is a more serious accusation)
Pre-game theory: Anytime a large corporation lowered price substantially, someone would accuse it of limit-pricing. Indeed, companies like Amazon could not have possibly survived during those times. (1950’s/60’s) The Justice department would have busted them open!
Post Game theory – initial stage – Research on entry games revealed that limit-pricing can not possibly be part of a subgame –perfect equilibrium. In fact, the threat of limit-pricing is not credible , because should entry occur, the incumbent firms will then concede entry because it is always more profitable to do so. In a marriage when one spouse is weak, the other one knowingly cheats because divorce is not a credible threat on the part of the weak spouse. So, even for large corporations (who play the role of weak spouses here), preventing entry by lowering price for the entire market loses more money rather than allowing entry of new firms and co-existing with them.
In the light of what I said above, if we observe a large incumbent company lowering price, it is because it has a better technology and it wants to capture the market by exploiting its superior technology. So, Amazon.com or Alibaba.com does not try to kick out other retailers, it succeeds to capture the market by being the most efficient selling portal on the internet . Whether its actions are socially justifiable, ethical, etc, is another story.
So, the policy of the government regarding enforcement of Anti-trust Law was changed sometime in late 1970’s. Technically, limit –pricing was still illegal, but practically it was much harder to prove, because an incumbent firm will always claim to have better technology. Anti-trust law was applied more to other non-price actions like creating effective entry barriers . IBM and AT&T were broken up during these times in massive anti-trust cases, but none were accused of limit-pricing.
Post-Game Theory –Later stage
Milgrom and Roberts took the entry game analysis one step further. They introduced two possible avatars of incumbent firms – one high cost and one low-cost (with a better technology) . They argued that if the entering firm does not know which avatar it is playing against, then the high-cost firm can mimic the low cost firm and charge the low cost firm’s price. Depending on the possible scenarios of losses and profits (which is quite complex), there could be an equilibrium where high cost avatar successfully mimics the low cost avatar, the low-cost avatar concedes the mimicry (because it costs him more not to) and the entrant does not enter because if it does, then, the probability of the avatar being low cost and the consequent loss is greater than just not entering at all!
So we can have successful limit-pricing under incomplete information! But then the Anti-trust policy now becomes much more complex, every single situation has to be investigated carefully to see if limit-pricing has occurred, or it is the low-cost firm selling at its normal price. A bonanza for anti-trust economists who got rich from 1990-2010 because every case became more and more complex. Economists’ testimony on both sides of a case often involved complex game theory models and supporting data and/or refutation of the other side’s models and data. Millions of dollars were earned during this time in consultant fees. Some of my friends/colleagues got rich, and I am sure Milgrom himself availed of these opportunities sometime during his distinguished career.
A lot of extensions were done on Milgrom and Roberts’ paper , of course, opening up even more complex scenarios about when limit-pricing can happen.
So as more complex games were solved successfully by people like Milgrom (and not so successfully by people like me), it ultimately became clear that in a complex game with super-sophisticated players, the set of equilibria is too rich – which means we can not build a policy framework based on game theory .
Milgrom and others wrtote a lot of papers on firm behavior that was applied to all aspects of antitrust and government regulatory agency problems. In fact, the limit-pricing result is only one of many significant contributions of Milgrom, used by me for illustration here.
Pretty much this is where it stands in the entire field of anti-trust nowadays. The economics consultants in each antitrust case or mergers and acquisitions case make a boatload of money on each side
As game theory has been too successful , it still helps us to understand the basic issues, but does not provide enough guidance for complex situations – besides indicating that many things can happen with sophisticated players under an environment of incomplete information! – which is something we knew already before all this began sixty years ago hahaha!!
Well, at least we micro people do not make consistently wrong predictions like some, (not all) monetary policy guys. But, I was hoping we could do maybe a little better!!
By the way, this comment does not even come close to an evaluation of Milgrom’s scholastic works which are far broader in scope than antitrust policies. Please see the link below:
