August 2017

Classical Thinking and Game Theory, Part I

By Carlos Fuentes

“We can say this of most people: that they are ungrateful and unreliable; they lie, they fake, they are greedy for cash and they melt away in the face of danger.”
—“The Prince,” Machiavelli

“Men are ambitious, vindictive, and rapacious.”
—Federalist Paper No. 6, Alexander Hamilton

This is the first installment in a series of four articles that were summarized in “A Rigged Game,” published in the July/August 2017 issue of Contingencies, itself a follow up to “Winning or Losing the Game?” (Contingencies, July/August 2016), where a mathematical model was introduced to analyze the economic consequences of integrated delivery models. Two common themes are discernible in these pieces:

  1. Interactions arise in a wide array of contexts and the fundamental strategic principles must be commensurately broad;
  2. The analytical power of such principles is linked to our ability to adapt them to the situation at hand and employ them as reasoning tools.

Game theory can be used to develop mathematical models, as it was done in “Winning or Losing the Game?” or to create conceptual frameworks—the “soft” approach— for analysis. Conceptual frameworks are the hallmark of strategists, most of whom never had any formal training in Game Theory but have fostered the ability to use them effectively, no doubt because such frameworks are rooted in common sense and a deep understanding of human nature.

The purpose of this series of articles is to illustrate the “soft” approach of game theory using Thucydides’ master work, The History of the Peloponnesian War1 (The History), and then appling it to analyze the strategic interactions of those who participate in the U.S. health care system, understand the root causes of the problem (cost, access, quality, efficiency), and draw conclusions about plausible mid- and long-term outcomes. Due to space considerations, the study of Thucydides’ work is limited to a few sections of the First Book of his magnum opus where he introduces his views on human nature, analyzes the causes of the war between Athens and Sparta, and recounts the justifications invoked by the belligerents. A few concepts of Game Theory are discussed to demonstrate how they are embedded in Thucydides’ thought. This approach should give an indication of how war colleges, military academies and courses on diplomacy approach the master.

Why is a work on history written 2,500 years ago still critically relevant to the serious student of strategy? Why has this book been used to analyze situations of paramount importance such as World War One and the Cold War? Why are the ideas expressed by Thucydides so pertinent to strategic interactions? Thucydides himself gave the answer in 1.22 (Chapter 1, section 22): “I shall be content if [my history] is judged useful by those who will want to have a clear understanding of what happened—and, such is the human condition, will happen again at some time in the same or a similar pattern. It was composed as a permanent legacy, not a show-piece for a single hearing.” To paraphrase Thucydides, human nature creates broad patterns of conduct that are amenable to analysis.

The Game

A great many men have imagined states and princedoms such as nobody ever saw or knew in the real world, for there’s such a difference between the way we really live and the way we ought to live that the man who neglects the real to study the ideal will learn how to accomplish his ruin, not his salvation2—“The Prince,” Machiavelli

A fundamental requirement to act strategically is to understand the rules of the game—the real game, not the imagined one—and gather information about the players. If the opportunity arises, the strategist can modify the game in her favor by defining some of its rules, changing the payoffs through the shaping of perceptions, and even driving out strong opponents. Thucydides’ masterful narrative interweaves these elements throughout his book. In 1.33 he describes how the Corcyreans tried to convince the Athenians to take their side by making invocations to justice, gratitude, admiration and self-interest3: “if you accept our case, it will prove a good opportunity for you, in many ways to your advantage. First you will be giving aid to an injured party […] this would bring you the admiration of most other people, the gratitude of those you will be helping, and an increase in your own strength.” In 1.37 the Corinthians counter with amoral arguments: “In truth, the motives for this policy [Corcyrean neutrality] were more sinister than virtuous: [the Corcyreans] did not want any ally as witness of their crimes, or to embarrass them if called in aid […] This specious neutrality of theirs is no wish to avoid implication in the misdeeds of others, but rather a pretext for their own unimpeded misdoing—violence where they have the power, cheating if they can get away with it, no shame at any advantage gained […] They say of course that they were willing in the first place to go to arbitration. But arbitration proposed when you have the upper hand and a secure position is an empty pretense.” Although gratitude, justice and other virtues are part of the Thucydidean universe, they play a minor role in determining outcomes. Thucydides is unmoved by the professed good intentions aimed at confusing other players, but recognizes that these attempts are common and sometimes effective. In 1.23 Thucydides expresses his opinion on the cause of the war: “In my view the real reason, true but unacknowledged, which forced the war was the growth of Athenian power and Spartan fear of it; but the openly proclaimed grievances on either side causing the breach of the treaty and the outbreak of war were as follows… ”4 There is little doubt that the passage of time and emotional detachment allow us to understand the conflict as one driven by material interests, yet none can fail to notice how easily personal interests cloud our thinking in many areas, even in those that are considered factual and scientific such as economics, where practitioners can embrace diametrically opposed views.5 The same lack of objectivity is present in the health care debate.

Misguided invocations to high authorities6, sometimes effective, sometimes not so, are typically used to justify a position, discredit the opponent and in general to gain an advantage. This type of “arguments” is conspicuous in politics but equally prevalent in other realms such as business dealings. In 1.126-1.138, Thucydides reports on propaganda to justify the war: “During this time [the Spartans] sent delegations to Athens making various complaints, to ensure that they had the strongest justification for going to war if the Athenians made no concession. The first Spartan embassy demanded that the Athenians should drive out ‘the curse of the goddess’ […] They pretended that their prime object was to serve the honor of the gods, but in fact they knew that the curse was attached to Pericles [the leading Athenian general …] Their hope was to discredit him in the eyes of his fellow citizens […] The Athenians made the counter-demand that the Spartans should drive out the curse of Taenarum […] The Athenians further demanded that they should drive out the curse of the goddess of the Bronze House.” Thucydides remarks that although Spartan and Athenian leaders did not lend any credence to the curses, each party hoped that by presenting itself with a façade of morality, public opinion would be swayed in a favorable direction or at least such morality could camouflage the true objectives—the interests of city-states and, above all, the concerns of powerful individuals.

Trickery masked with a veneer of good intentions is present in the Peloponnesian War. An instance that is eerily reminiscent of the American political system occurs in 1.87 when Sthenelaidas, one of the ephors (elected magistrates) that favors hostilities asks the question to the assembly on whether or not Sparta should go to war but with a twist: instead of deciding by acclamation, as Spartans traditionally did, he requests each member to publicly express his opinion7, in fact, making appear weak and unpatriotic those who opposed the war. This type of stratagem is not uncommon in games people play.

There are many contemporary examples of successful attempts at creating “smoke screens.” One of the most revealing is the tobacco companies use of propaganda to convince the public that there was no evidence that linked smoking to lung cancer and later to create doubt about such link. To be more convincing, tobacco companies enlisted the endorsement of the American Medical Association8 and doctors who were featured in a large number of advertisements9.

Realist assessments of the conflict are part of the Thucydidean narrative although they seldom make parties deviate from their positions of self-interest. Invocations to justice are useless except when the parties have equal power to compel and see an advantage to negotiate. In 1.75 the Athenians justify their position by stating that “no one can be blamed for looking after their own best interests when the stakes are so high” and then again in 1.76 where they remark that “we have done nothing surprising or contrary to human nature in accepting an empire […] Nor again did we start anything new in this, but it has always been the way of the world that the weaker is kept down by the stronger. And we think we are worthy of our power. There was a time when you thought so too, but now you calculate your own advantage and talk of right and wrong—a consideration which has never yet deterred anyone from using force to make a gain when opportunity presents.”

Carlos Fuentes, MAAA, FSA, FCA, MS, MBA, is president of Axiom Actuarial Consulting. He can be reached at

1Thucydides (460-400 BC) is arguably the greatest historian of all times. See “The History of the Peloponnesian War,” translated by Martin Hammond, Oxford University Press, 2009. References to Thucydides’ work follow the standard convention.

2In this quote, Machiavelli anticipates the distinction between normative and analytical political theories.

3Athens was the most powerful naval city-state; Corcyra the second. The Athenians decided to defend the Corcyreans against the Corinthians with the intention of securing their naval supremacy. The Athenians could not have foreseen that years later, in the middle of the war, Corcyra would implode due to struggles between internal factions, thus becoming a useless ally. War is unpredictable.

4The Corinthians complained that the Athenians were blockading their colony, Potidea. The Athenian grievance against the Peloponnesians was that they had incited the revolt of an allied and tributary city.

5A famous example is afforded by fierce disagreements between John Maynard Keynes, one of the greatest economists in history, and Fredrick von Hayek, one of the champions of laissez faire capitalism. The disagreements are as strong today as they were almost one hundred years ago.

6Authorities often invoked in the US include the Founding Fathers, the Constitution, its amendments, the Christian Sacred Books. Examples of the use of moral, patriotic or religious arguments for personal gain abound such as defending pornography through the First Amendment. Cases where public opinion is manipulated can be seen daily on television and in many (but not all) political debates in which politicians and non-politicians participate.

7'Those of you who think that the treaty has been broken and the Athenians are guilty should stand up and move over here and those who think otherwise should move over there.'