Abstract
This contribution to applied game theory is the result of an intriguing collaboration between Robert Aumann’s disciple, Uri Weiss, and Karl Popper’s proponent and critic Joseph Agassi (who died at 95, a few weeks after the book was published). It therefore sums up a dialogue between two very distinct intellectual talents: that of the young state-of-the-art game-theory technician, and that of the seasoned, highly original, meta-theoretical commentator on science and its methods. More specifically, Weisse’s critique of various minute lacunas of his game-theory colleagues finds its proper contextualization within the critical rationalist view of the social sciences in general, and within Agassi’s notable philosophy of technology in particular. The result is a sharply argued study of mishandled gray areas between mathematical game theory and its application.
That these two distinct intellectual aptitudes must join hands and cooperate within any serious discussion of game theory is one of the first and most consequential statements that the authors make. Mathematical game theory, they observe, comprises mostly trivial analyses of ideal (and thus non-existent) situations of competition and cooperation. Its application to the real world, however, is unavoidably an ethically and ideologically suffused task wherein the main hero is not, and should not be, the search for dominant strategies guaranteeing maximalization of material gains, but rather the aspirations that we wish and ought to have as a society and a species (including those that dictate which games we should refuse to play, which games are too dangerous, too risky, too violent, and so on). Within mathematical game theory algorithm-like homines economici compete on the only thing that they seem to treasure: having the upper hand. The mathematical context, therefore, dictates their strategies. They go to war if war promises a better yield than a peaceful gesture, and they leave their girlfriend in the blink of an eye if they meet an identical twin with an extra dollar in her purse. This attitude in itself breeds suspicion, which encourages cold-hearted decision making. But in real life values that are less amenable to exact calculations often play, and should play, a more dominant role. Indeed the authors are right to observe that the very idea of a strategy is all too often a utopic idealization, since most people do not have a well-calculated strategy ready in hand. And so, the meta-game of choosing which game to play, which game to try and avoid and, most importantly, which game to refuse playing is crucial. Social and moral commitments, the authors argue, are thus unavoidably part-and-parcel of game theory proper. We must get rid of the pretense to know in advance and in each context, the game that we are in, and so (too often) what strategy we must choose, for it too is an utopistic fantasy. Instead, we must realize that game theory proper is an active negotiation about who we are and who we hope to avoid becoming.
To illustrate this point, as well as the standard reaction of game theory experts to it, let us briefly recall the paradigm of game theory: the so-called “prisoner’s dilemma.” I will assume here that you are familiar with its general rules. Let me just note in passing that it is not a game at all, but rather a game type, indeed an infinite set of games that follow a misleadingly similar pattern, which often yields profoundly varying results: minute changes in the rules and values often have radical effects on recommended strategies and on the consequences to be drawn from them about real-life decisions. (Also, it is perhaps useful to remember that the heroes of the “game,” the interrogees who face the dilemma, are not prisoners: some of them, you will recall, may end up free.) Now, as any basic game theory introduction explains: the dominant and thus rational strategy of the one-round best-known (family of) version(s) of this game is defection. Indeed, the risk of being optimistic about your peers’ intentions is so great, and the means for increasing mutual trust are so inadequate that mutual overall betrayal is famously the end result of the rationally played prisoner’s dilemma. This is the case even when the game is played many times over. In other words, game theory boasts to demonstrate mathematically that in certain real-life contexts, particularly in those where trusting fellow players is very risky, betraying them is possibly very beneficial, and means for enforcing mutual trust do not exist, the most rational result is a gloomy sub-optimal Nash equilibrium (all rational players will stick to their sub-optimal choice in a long series of endless defections). But less rational, yet far more conscientious and trustworthy participants will cooperate, thus getting far better results. The authors, therefore, argue against accepting the standard and gloomy verdict as applying to real-life lessons. Instead, game theory should include guiding principle for seeking minor social changes that would increase cooperation in various real-life contexts. This seems basic commonsense. Yet it stands in contrast to many discussions of game theory experts.
A good starting point for realizing what is at stake here, and what the authors suggest, is to recall the naïve observation often made by game theory students upon first encountering one of the familiar versions of the “prisoner’s dilemma.” Nowhere in real life, they point out, do human interrogees face anything like the mathematical dilemma. What then do we gain by studying it? Unlike computer programs which simulate successful and less successful playing strategies in carefully monitored computer labs, human interrogees have a past, a code of values, an identity, and a self-image to maintain, all of which deeply influence their decision to trust or betray their peers. Maybe they care for each other. Perhaps, for instance, the interrogees are a father and his beloved son. This situation may easily turn a seemingly zero-sum “prisoner’s dilemma” into a pareto circumstance: the son goes free, and the loving father gets a maximum sentence, and yet he smiles with content feeling that he achieved his goal. Or perhaps the interrogees do not know each other at all, but simply fear being labelled “a snitch” by their jail companions? Is it not rational to fear going to prison with such a dangerous label on your back?
The standard game-theorist reply to this prevalent first impression is swift dismissal, on two very important accounts. First, they brush it aside as a misunderstanding of what mathematical game theory offers: the theory is indifferent to your choice of values or indeed to how rational or irrational you may be, the experts emphatically explain: your values could, for all we care, be altruistic and noble, as long as they are neatly quantifiable. If they are, we can calculate for you a clear-cut rational choice of a strategy within the context of a given game. Clearly, they often add, whether you follow our advice or not is your own affair. Then they note that the real test of all applied mathematical models is empirical. Sure, the experts will hasten to agree with the bewildered student, real life is not pure mathematics, but we never argued that it is. Applied game theory is a technology not a science. It is thus closer to being a tool than to being a theory per se. The test of a tool is its usefulness. The question, therefore, is not whether or not a certain prediction or recommendation of applied game theory accurately represents the ultimate truth about a particular real-life predicament or challenge, but rather: is it a successful, or helpful heuristic approximation? Are predictions based on our neat tool hit the mark sufficiently accurately to be useful?
This standard reply, however, is easily exposed as a skillful form of self-deception, by Weiss and Agassi’s signature move of including by fiat the meta-game of choosing which games to play and which games to avoid into game-theory proper. It is the misleading conviction that given a certain real-life context we are destined to play a given game, that is the target of their criticism. And so realization that game theory is a goal-oriented technology with an attached heuristics and not a neutral truth-seeking science exposes the sleight of hand behind the seemingly innocent promise to calculate rational choices, given every human value, while in actual practice readily applying to all real-life situations a very rough, greedy, and materialistic notion of gain and loss. For even if we set aside the fact that it is far easier to quantify the numerical value of coins than, say, the value of our desire to live in a liberal society where fellow citizens are trustworthy and tolerant, and even if we ignore the fact that, assuming two disparate moral core values, choosing the more rational, by mathematical means is a fiction, there still remains the important fact that it is we who choose what game we are currently playing. It is therefore we who choose what game-theory model to apply given any real-life context. And game theory may therefore provide us with the service of which games are better avoided. What really matters most is not the mathematical (and mostly trivial) aspect of finding the rational strategy, given that we are destined to play a given game. What matters is questioning whether the game that we seem to be playing (or the one that we are told by the game theory expert that we are playing) is indeed the one that we wish to play? This shift of focus by Weiss and Agassi sets aside the utopistic goal of seeking the perfect strategy for any given context. Instead, the center of their rich discussion of game-theory becomes contemplating competing models (competing games, not competing strategies) that we can play given any real-life challenge. It turns our focus on the task of finding minor piecemeal modification to real-life situations that would significantly change the family of games (games, not strategies) that will be relevant to the analysis of a given real-life predicament.
Consider, for example, what would happen if we incorporated into game theory the basic requirement to scrutinize every available social engineering resource at our disposal so as to avoid zero-sum circumstances? Would this not significantly increase our quality of living? Instead of, say, over-fishing in an ocean shared by many countries (in fear of your rivals beating you to it), which might quickly lead to a disastrous Nash equilibrium ending in the irreversible devastation of the environment, policy makers will be required to scrutinize all possible piecemeal engineering modifications of a given social context (agreements, political gestures, modest economic or educational reforms, and so on) that would facilitate trust-giving between opponents, and so avoidance of the harmful conviction that we are doomed to play a prisoner’s dilemma. Successful such modifications would then likely change our very understanding of the game that we are playing: trust-building modifications can easily turn an unhappy Nash equilibrium in a prisoner’s dilemma into a pareto efficient Nash equilibrium in the spirit of the happy conclusion of a generously played “stag hunt.”
This, in essence, is what Weiss and Agassi offer us in their critique of applied game theory. I am not convinced that this is an entirely novel theme in the field of applied game theory, but it is certainly a breath of fresh air, an in the right direction. They scrutinize examples coming from every field of policy making in search of mind-and-mood-altering social and political reforms that encourage the move from suspicion into cooperation. Their aim is not the finding of dominant strategies but rather the increasing of collaborations, and the playful contemplation of viable humane alternatives. These modifications are offered in the spirit of critical rationalism. This means that they aim to be modest in scope and easily testable. They argue that selecting a strategy inadvertently commits one to a specific game, and that, therefore, suspending judgment is often the best available move. They avoid the utopianism so typical to regular game-theory discussions. For example, instead of increasing happiness, they concentrate on the reduction of unhappiness. Instead of the maximalization of gains they contemplate ways of avoiding avoidable losses, especially bankruptcy (and so, like other authors, they often recommend Wald’s maximin principle as complementary to game theory). Instead of finding the best means to win all wars, they offer practical modifications that can decrease misunderstandings between rivals, that might increase suspicion, and so lead to conflicts. Where game-theory economists prefer games that have only a single Nash Equilibrium (since their application is easier) the authors offer to ponder ways of increasing the number of those equilibria (since games with multiple Nash equilibria are closer to real-life, and easily broaden the minds of policy makers), etc.
I regret that the book was not written after the re-election of Trump for presidency. Although the book contains a few interesting comments about the rationality of seemingly irrational tyrants, it would have been interesting to read how the authors would analyze the alarming new developments. Our world is rapidly regressing into the bosom of neo-liberal game theory, where values that are not reducible to power and wealth are being ridiculed as irrational, and long-standing cooperation-increasing agreements are being trampled upon for the sake of dominance. Nevertheless, the book certainly offers a metaphysical and ethical perspective that, if seriously considered, would suggest refreshing ways for tackling this distressing development.