Game Theory : the Slow Pace of Fast Change

In The Slow Pace of Fast Change, the framework of game theory is applied to two sets of questions: the pace of progress in a connected world and strategies for taking innovations to market. Markets are, for all practical purposes, games of strategic choice among the many connected players responsible for innovation's adoption and diffusion. I argue in the book that the adoption process for innovations involving such connected players is a cycle of chicken-and-egg decisions—which makes game theory particularly compelling as a way to frame and break into this cycle. The power of the science of strategy in practical application to strategic choice in real-world markets was recognized in the academic fields of "new" industrial organization and industry structure approaches to business strategy; we certainly discovered the benefits of its actionable insights in our own work.

I have found, though, that much of the awareness of the discipline in the "real world" is relatively little or obscured, often beneath labels used in somewhat narrow contexts: prisoner's dilemma, price wars, coopetition, win-win negotiation or competitive simulation. Oddly enough, I have also found the practice of game theory wider and deeper than most people appreciate. More often than not, experienced executives make decisions that reflect a sharply tuned game-theoretic mindset, developed not through using tools or training but through an evolutionary process of repeated learning from the past. Many are surprised—like M. Jourdain in Moliere's Le bourgeois gentilhomme, who was stunned to hear that he'd been speaking prose all his life—that they had been acting as if they were expert game theorists, when in their minds it was all "common sense." That said, the common sense does come at the tail end of an experiential, and often risky, learning process. But that is, in essence, the beauty of the field - it bottles common sense, so that you can anticipate it instead of having to learn it the hard way. Even for those who do not need the evolutionary benefits of experience shrink-wrapped and have enough of it to last a lifetime, the theory does provide essential value: accumulation of experience often causes many of us to find situations that do not fit a known pattern surprising - and, often, paralyzing from a decision-making perspective. The theory is often quite powerful in resolving such puzzling outcomes, and provides a framework for interpreting them and acting on them.

Alternatively, people often think of the theory simply in terms of a toolset—for, say, deciding under competitive uncertainty or to make predictions about future states of a market. But here again, we unnecessarily circumscribe ourselves. Indeed, to truly benefit from it as a framework to understand the world or to change it, game theory is even more powerful if one absorbs it as a mindset rather than just a toolset. To appreciate its breadth as mindset, it is very instructive to trace the staggering diversity of contexts in which the theory has provided insights. Few, even those in the field, are aware of this breadth. For its use in the context of innovations and the networked world, you can read The Slow Pace of Fast Change. For an excellent discussion of its application to business strategy, read Adam Brandenburger and Barry Nalebuff's Coopetition (Doubleday, New York, 1996); for a non-technical introduction to its key areas, read Prajit Dutta's Strategies and Games, (MIT Press, Boston, 1999).

Here, however, are just a few of the applications that take us much further afield from the more familiar terrain.

Interpreting Past History as a Framework for Making History Going Forward

Several years ago, game theory conferences were abuzz with a breakthrough in a puzzle that had survived two thousand years: the nagging question was one from the Talmud, a Babylonian compilation of laws and customs, which specified the division of a dead man's estate among his three wives in apparently contradictory ways. When the man dies and leaves an estate worth a 100 units, the Talmud recommends equal division; if the estate of 100 triples, it recommends proportional division based on each wife's contributions; but if the estate were only worth 200, the suggested division rule follows no reasonable pattern. While it would be hard to say that this contradiction is a crisis even remotely close in importance to those bedeviling present-day Babylonia, it is definitely older than most of the multiple contradictions in which the region is abundant. The solution was that the apparent Talmudic contradiction could be rationalized as a well-understood outcome of a "cooperative" game (See Steven Landsburg's note on this in Slate, April 10, 1998, "Let the Rabbi Split the Pie"; the original work by Robert Aumann and Michael Maschler is written for a technical audience.) Far from being contradictory, it rests on a consistent and fair set of principles after all. Given the importance of such precedents in issues to deal not only with the division of estates but also to bankruptcy and multi-party negotiation proceedings, these findings do have broader implications; they can also serve an important role of setting precedents and benchmarks, which are often crucial to such proceedings.

Human history, as is well known, is replete with many other puzzles and phenomena that have begged explanation. Taking a game-theoretic lens to history has helped shed light on many such questions; interestingly, they offer guidance on how to act when similar situations arise going forward. Consider a pivotal period of European history. Much of the economic growth experienced by Europe during the 11th to the 14th century involved trade, particularly over the Mediterranean route. How did such long distance and complex trading persist and grow, despite the challenges of information and geography of those times? In his studies of the Jewish Maghribi traders, (who originated not far from Babylon, the setting of our earlier puzzle) Stanford University's Avner Greif discovered how such merchant communities practiced and scaled up successful businesses. They did so by employing agents who were governed through a model of collectivist punishments. The merchants collaborated on punitive measures on agents who did not act in the merchants' interests. The incentives to commit to such a collective punishment scheme can be explained through a framework of an infinitely repeated game. Several of the lessons of how several generations of Maghribi traders organized themselves and their system can help inform organizational and consensus-building strategies for global corporations today. (For references, see Avner Greif's extensive work in the area, in the Journal of Economic History (1989), American Economic Review (1993), and Journal of Political Economy (1994).

To be convinced that it is well worth our while paying attention to unraveling history's puzzles for strategizing in contemporary societies - and that game theory offers a powerful prism -- one must return, yet again, to Babylonia. Herodotus of Halicarnassus, the Greek historian and storyteller from the 5th century BC, talks of the Babylonian custom of men bidding for wives. It was a powerful social welfare scheme, where the money raised through bids on the most attractive women was used to subsidize transactions involving the least attractive ones. In any event, this practice of competitive bidding as a market phenomenon, whose first recorded application was in Babylon, became more widespread in its use in the ancient Roman empire when soldiers would plant a spear in the atrium auctionarium to invite bids sub hasta (under the spear) on their spoils from various foreign adventures. The Romans proceeded to use this mechanism, which eventually came to be known as an auction, as means of liquidating property. Auction, literally, means "to increase"—and we have witnessed in recent times that there is an increasing and infectious quality to this form of market organization, whether it is in Internet commerce over household trivialities or in bidding wars involving takeovers and mergers. The infectious aspects of this form have historical precedent. The popularity of the auction grew so much that at one point the entire Roman Empire was put up for bid by the Praetorian Guard in 193 AD after they took it over when the incumbent emperor Pertinax was assassinated. After all, how else does one get a fair market valuation when it comes time to find a buyer for the Roman Empire?

We have learned that the mysterious attraction of the auction is that it is the most visible form of the market being transformed into a game. It is perhaps the only means left available when the market simply fails to provide any benchmarks to gauge fair valuations or prices. This game has been repeated over the centuries across various civilizations from the Dutch systems for tulips to English, Japanese, Chinese and Indian auctions in numerous other contexts ranging from land, chattel, grain, art and oil drilling rights. Quaint methods were devised to play the game, from "candle-stick bidding", where the winner is the last person to bid before a candle's wick falls to the "whisper auctions" used in fish markets of Venice. The game theoretic understanding of how auctions work and have worked in the past led to a burgeoning practice of auction market design in contemporary times. It was used to organize billions of dollars worth of transactions involving radio spectrum for multiple generations of wireless communications around the world and to the establishing the rules of play for, arguably, the most successful Internet company in history, eBay. Many of the broadband telecommunications deal strategies mentioned in The Slow Pace of Fast Change draw upon learnings from auctions.

A key lesson from the rich history of auction experience continues to inform every form of auction design today. The winner of the auction of the Roman Empire was a wealthy senator, Didius Julianus, who posted the winning bid of 6,250 drachmas per member of the Praetorian Guard to assume the coveted title of emperor of Rome. It was unclear if he lost his shirt in getting to that point - he certainly lost his head: he was beheaded a few months after his victory. Game theorists to this date recognize the curse that visits with the winner of any auction - as do experienced bidders -- and carefully design its rules to mange this phenomenon. This is the winner's curse, or the regret that the winner experiences after being informed of victory, because it means that on average one could have won by a lower bid. Fear of the curse, generally makes bidders want to shade their bids to avoid over-bidding - much to the auctioneer's chagrin.

Much of contemporary auction market engineering begins with design principles that anticipate such undesirable behaviors related to this curse. These forms of engineering of auction markets have resulted in tremendous economic implications, where companies such as eBay have made millions of dollars of additional revenues, and government treasuries around the world have earned billions of dollars by auctioning radio spectrum. An example of the kinds of design improvements suggested by an awareness of the winner's curse problem is the idea of keeping the bidding process public and running the auction with an ascending price. This gives each bidder a reference point - the last bid posted - and provides a bound on the fear of over-paying. This, in turn, makes bidders less conservative and helps increase the values generated in the auction. For references see Paul Milgrom Auction Theory for Privatization, Cambridge University Press, forthcoming, or Bhaskar Chakravorti, William Sharkey, Yossef Spiegel, and Simon Wilkie "Auctioning the airwaves," Journal of Economics and Management Strategy, 1994.

On the flip-side, it has been argued that such precision design of the rules of the game has also promoted aggressive bidding and the entire wireless communications industry has been ridden with debt as a result. This, it has been argued, contributed to a telecommunications industry slowdown amounting to losses in the trillions. Needless to say, a better understanding of the games played in earlier civilizations have made subtle, and yet substantial, differences to our lives in contemporary times.

Playing Games in Basic Sciences

It is not just in the "soft" situations, socio-economic, political or business games, for which the game theoretic framework is useful. Game theory has influenced thinking in the basic sciences as well. Consider some questions that have arisen in biology: why do so many animals display wasteful physical characteristics with no apparent biological purpose? Examples that are often cited are: the spectacular, but extravagant and unnecessary, plumage of a peacock's tail, or why gazelles repeatedly leap in place again and again when they spot a predator in the savannah, or why so many deciduous trees indulge in nutritionally costly coloration. The last of these may be a no-brainer for the hordes of tourists who take to the back roads of New England in the fall, but the coloration, especially the red, is nutritionally costly for the trees - an inefficiency that ought to have been ironed out over the course of evolutionary adaptations. The explanation given by evolutionary biologists to all of these and a host of other such questions is a theory of signaling based on games of asymmetric information. (See Carl T. Bergstrom, The Theory of Honest Signaling, in http://octavia.zoology.washington.edu/handicap/)

Recent work by biologists Sam Brown and W.D. Hamilton on the last of these questions, for example, establishes three arguments. (See S.P. Brown and W.D. Hamilton, "Autumn tree colors as a handicap signal," Proceedings of the Royal Society of London, B (2001), 268: 1489-1493.) The first is that fall coloration, other than its cosmetic appeal, indeed, does seem on the surface to be an excessive use of scarce natural resources. Second, aphids, a group of tree pests, are known to avoid trees with bright reds and yellows when seeking to colonize trees during the fall season. Third, it is also the case that trees with bright fall colors also have invested in higher proportions of chemicals that are bad for aphids. What is going on between the trees and the aphids? According to the biologists, there is a game between the trees and the aphids of asymmetric information and an investment in signaling to close the gap. The colors are an expensive signal from the trees (that have access to such information) to the aphids (without access to this information) to stay away.

Granted, in a biological context, the players are not necessarily making conscious strategic choices—their behaviors are as if such choices have survived over the course of evolution. A. Michael Spence won a Nobel prize for his theory of such expensive signaling games among players that do make strategic choices—a model that is immediately adaptable to explain not just the autumn leaves, but the peacock and the gazelle as well.

Biological games have a long tradition in the field of evolutionary biology to explain cooperative and conflicting behaviors of species. It turns out, such games can occur at the microscopic level as well. Paul Turner and Lin Chao of the University of Maryland recently discovered that an RNA virus may be engaging in an evolutionary variant of the prisoners' dilemma game. (See Paul Turner and Lin Chao "Prisoner's dilemma in an RNA virus," Nature (1999), 398: 441-443.)

Extensions of simple two-player games have attracted interest in several other areas of basic science. Recently we did some work on the future of an intriguing area of cross-disciplinary development that cuts across physics, applied mathematics, computer science, among others: quantum computing. The questions (apart from the obvious one of what exactly is quantum computing) that are in the minds of many are two-fold: what use is quantum computing, and how far away are we from the development of a quantum computer? In this context, I spoke with David Meyer of the University of California at San Diego. He has the distinction of being one of the early exponents of "quantum games" initiated in 1999 using a story involving Star Trek's Captain Picard in a showdown with Q on the bridge of the Starship Enterprise. Their encounter is through a game of coin flips. In Meyer's game, Q wins by using quantum mechanics to prepare a coin that can come up heads and tails at the same time, and Picard loses because he can only perform the classical action of flipping the coin on one of its sides (see David Meyer "Quantum strategies", Physics Review Letters, 82, 1052-1055). It is believed by many in this emerging field that the quantum extensions of classical game theory is shedding light on physical phenomena; cumulatively, it will contribute to the efforts to develop a quantum computer. If this ambitious effort does succeed, our abilities to process information and compute would increase to levels currently unimaginable.

Games of War and of the War on Terrorism

Game theory's application to war is well-known. Conversely, war has been applied to the theory of games; one often mirrors the other. Many people in business spout and speak of the war strategist Sun-Tzu, as their original game theorist (though most game theorists may have never heard of him, such is the magic of silos in a connected world). In Mabinogion, a collection of Welsh folk tales, two kings fight a war and play chess on the side. The game of chess is a reflection of the ongoing events on the battlefield. The recent play-by-play television coverage of the war in Iraq has been eerily similar in its visuals and digital quality as video games, thereby transforming not just the strategic structure but the appearance of war as well to that of a game for the armchair warrior. Of course, in the battlefield, war has far more serious consequences, but the basic principles of game theory still apply in war-fighting strategy.

John von Neumann, one of the founding fathers of game theory was, at one point, a strategic advisor to General Leslie R. Groves to select Japanese cities as bombing targets during the Second World War. The problem was an inherently game-theoretic one: if the US always chose their targets in the commonly known order of importance, the Japanese would anticipate it and would defend their cities appropriately. The key was to balance importance and surprise - an element that the Japanese themselves had used to great effect at Pearl Harbor. A sheet of paper, dated May 10, 1945, in the Library of Congress provides von Neumann's lists of potential bombing targets. One of them reads: Kyoto, Hiroshima, Yokohama, Kokura. Kyoto was spared, apparently, for its historical significance. The terrifying consequence for the next city on the list is part of history today.

Frequently, the signaling games we spoke of earlier is applied during wartime or as a mechanism to pre-empt outright war. The principle of mutually assured destruction and escalation of nuclear capabilities during the height of the Cold War was a classic application of the well-known prisoner's dilemma game combined with signaling. While building up nuclear arsenals amount to an expensive and tangible signal, sometimes such signals are sent in less tangible ways - almost in the form of "cheap talk", a way to send signals not through new investments but by relying on past reputations. White House Chief of Staff H.R. Haldeman, famously, recorded in his diary in October 1969 about Nixon's "madman theory" of indicating a ratcheting up of the readiness level of nuclear forces. If his military moves made Moscow and Hanoi concerned enough, the theory goes, it might lead to the former using its leverage over the latter to be more cooperative in peace talks planned in Paris.

Sometimes the value of the signal is not to convey information or intent but to confuse to the point of deterrence in order to avoid further uncertainty. An unclassified 1995 Pentagon briefing document (Essentials of Post-Cold War Deterrence, obtained under the FOIA by Hans Kristensen, Case # 96-55) released under the Freedom of Information Act says: "Because the value that comes from the ambiguity of what the US may do to an adversary if the acts we seek to deter are carried out, it hurts to portray ourselves as too fully rational and cool-headed. The fact that some elements may appear to be potentially 'out of control' can be beneficial to creating and reinforcing fears and doubts within the minds of an adversary's decision-makers…That the US may become irrational and vindictive if its vital interests are attacked should be part of the national persona we project to all adversaries." This most game-theoretic of documents was written long before the events that have rocked the world since September 11, 2001. Opinions are divided on whether the US administration acted rationally in its ensuing campaigns and linking of different crises in other parts of the world, such as Afghanistan and Iraq. Some even described the administration as being "out of control." A game-theoretic framing of the situation would suggest that, as recommended in the Pentagon document, a willingness to appear "out of control" can, indeed, be rationalized as a deliberate strategy.

A different application of game theory sheds light on mysterious behavior by other players in the geopolitical game. Consider North Korea's Kim Jong-il, frequently considered the most irrational leader on the planet (in a field with many highly eligible contenders), who could, in fact, be playing a very carefully calculated and rational game of announcing his nuclear intentions. The US has limited negotiating power, according to this logic, because its options are few. UN sanctions do not matter much to a regime that had millions of its citizens die from famine rather than relent on earlier demands. A military attack would have devastating consequences even from a limited retaliation (before military strikes can neutralize them) from North Korea on neighboring Seoul, 50 miles across the border, or on densely populated Japan that lies within range of over a hundred of its No-dong missiles. The ultimate ace in the deck for President Kim is his own confusing signals about nuclear capabilities and general "out of control" behavior. A key lesson from game theory is the realization that adversaries may have very rational reasons to act in apparently irrational ways. Assume, until shown otherwise, that their moves are calculated just as one's own are—even if their objectives, knowledge and constraints may be very different.

On the home-front, the shifting dynamics on the geopolitical stage are having an impact on counter-terrorism measures and homeland security. Here, too, game theory finds application. I shall describe some of our own work in a separate piece, but it is interesting to see these ideas catching on with several other groups. An example is the Institute for Strategic Threat Analysis and Response at the University of Pennsylvania, where ongoing research uses network theory and game theory to determine the best places to intervene in several situations, such as airline baggage screening and smallpox vaccination programs. The problem, for example, with airline baggage screening is that an airline in determining whether to install a baggage checking system voluntarily must balance the cost of doing so with the reduction in the risk of an explosion from luggage not only from the passengers who check in with it, but from the bags transferred from other airlines. The incentive to invest in security is greatly diminished if other airlines fail to adopt protective measures - leading to a "tragedy of the commons" game, where no party, in a multi-party effort, steps forward and invests. The relative pinch of these costs is even greater in an environment where airlines are already struggling with a downturn in the travel industry. An idea being explored is public subsidies to the largest airlines - which can then increase the incentives to the others to make their investments since it would significantly contribute to a lowering of a risk of explosion from transferred luggage. For a reference, check the Institute website http://www.seas.upenn.edu/~istar/research/index.html.

Games of Match-Ups and Match-Making

The situation on the geopolitical stage has often been described as a dangerous match - a Game of Chicken. This is a game most closely associated with Thomas Schelling's classic, Strategy of Conflict. This refers to the sport of teenagers in cars racing in opposite directions towards each other till one of them—the "chicken" swerves out of the way, and loses. Schelling describes the potent strategies in such games as ones that involve sending credible signals of intent to stay the course—for example, if one of the drivers were to throw the steering wheel out of the window. The Game of Chicken has, not surprisingly, found its way into the plots of many movies. One of the most comprehensive sites on game theory on the web, Gametheory.net, cites Cry-Baby, Footloose, Rebel Without a Cause, and, of course, Thirteen Days, a dramatization of the Cuban missile crisis—to name only a few.

Of course, Hollywood does not quite do justice to game theory's applications - or even to its theory for that matter. Consider the closest it gets to explain what was the mysterious discovery for which John Forbes Nash actually received the Nobel Prize for in the Academy award winner, A Beautiful Mind. In an application that would potentially have more far-reaching consequences than most of the ones talked of thus far, there is a memorable, and quite a bit odd, scene from the movie in which the fictional John Nash, played by actor Russell Crowe, and fellow male students are eyeing a group of women in a bar. The group includes a single blonde among several brunettes; while all the men prefer the blonde over the others, they would rather get to know a brunette than have no woman at all. Nash's solution? "If everyone competes for the blonde, we block each other and no one gets her. So then we all go for her friends. But they give us the cold shoulder, because no one likes to be second choice. Again, no winner. But what if none of us go for the blonde. We don't get in each other's way, we don't insult the other girls. That's the only way we win. That's the only way we all get (a girl)." (From A Beautiful Mind: The Shooting Script, Akiva Goldsman, 2002). Anyone who has followed this advice must be cursing John Nash and all game theorists by now. Not only is the fictional Nash wrong, the solution is not a Nash equilibrium, the mysterious and yet famous discovery that is central to the field and earned him a Nobel.

To see why, going for a brunette is not a best choice, if Nash after having delivered this specious advice were to assume that his gullible friends would follow it and head for the brunettes, then his own best strategy is to go for the blonde. Conversely, if his friends were to assume that Nash apart from being a bit odd is also a fink and would go for the blonde, they would each be best served by going for the brunettes themselves, if they can resist the urge to clobber him for cloaking poor logic in something that sounds deep. Moral of the story: there is a nugget in the movie's blonde-in-bar sequence after all—if you believe everybody else will follow flawed advice, it is a best choice to be the only one to profit by not following it.

Ironically, game theorists ought to be pretty good at this stuff, believe it or not. Match-making is in itself a lively area of work in game theory. Harvard's Al Roth was asked by the Board of Directors of the National Resident Matching Program (NRMP), which matches 20,000 residents to jobs every year to help design a new algorithm that matches residents to hospitals. The need for a new matching algorithm grew out of two years of acrimony and controversy involving exchanges in Academic Medicine in 1995 and groups such as the American Medical Student Association, the Public Citizen's Health Research Group, the AMA, and others. It was alleged that the NRMP was biased and flawed and that "there was an element of perfidy in the reluctance of the NRMP to make the changes demanded and in the history of how the match had been constructed and advertised to past generations of participants." (See Alvin Roth and Elliott Peranson, "The Effects of the Change in the NRMP Matching Algorithm, JAMA The Journal of the American Medical Association, September 3, 1997.) Much of the controversy had grown out of a reading - a partial misunderstanding by the medical community—of the large body of work in game theory on two-sided matching markets—of which Prof. Roth is one of the leading exponents.

"The first few years of operation in the new match design seem to have been extremely smooth…the organization of the match no longer appears to be a source of significant controversy," according to Roth, quoted in (Hal Varian, "Avoiding the pitfalls when economics shifts from science to engineering", New York Times, August 29, 2002.) He also showed through experiments that the controversies may have been misplaced - the old algorithm was not that different from the new "ideal" algorithm in its performance. While the fictional Nash fumbled in matching up his buddies, followers of the real Nash have been doing much better in putting the perennial angst of match-making to rest.

And, besides, even if you cannot decide and end up with more than one match, you can call your neighborhood game theorist to decide how to share among the multiple matches. At the very least you can call on a rabbi who will have a very intuitive Talmudic rule in hand.

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