November 2017

Classical Thinking and Game Theory, Part II

By Carlos Fuentes

This is the second 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. The first installment of the series appeared in the August 2017 issue of Innovators & Entrepreneurs.

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 War 1 (The History), and then apply it to analyze the strategic interactions of those who participate in the US 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 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.

The Players

By a faction, I understand a number of citizens, whether amounting to a majority or a minority of the whole, who are united and actuated by some common impulse of passion, or of interest, adverse to the rights of other citizens, or to the permanent and aggregate interests of the community—Federalist Paper No. 10, James Madison

Players are individuals or groups (e.g., firms) capable of making decisions and influencing outcomes. Although followers—say, army soldiers or employees—have a role, leaders are the key participants. This trivial observation is often overlooked. In the business space, corporations are often seen as homogenous entities whose decisions reflect the will of management, staff and owners. A moment of reflection shows that reality is different: although administrative staff and top management work for the same company, their ability to influence outcomes is not the same, their compensation schemes are vastly dissimilar, and in general their payoffs have little in common. Furthermore, the interests of top management can be, and usually are, in conflict with the interests of owners whose business knowledge is limited. Economists coined a term for this type of game with asymmetric information: the principal-agency problem. 2 

How can real players be identified? Understanding motivations and payoffs is often the key. They range from a sense of patriotic duty, to disinterested care for the wellbeing of others, to desire for status, to envy, to hunger for power, to monetary gain. The following penetrating question helps uncover the players’ true identity: cui bono? 3

Once leaders are singled out, the strategist, if the opportunity arises, should try to remove rivals from the game, diminish their power, or otherwise make them less effective. 4The means are countless and can include attempts at moral and religious suasion, much as the Spartans did against Pericles, and some politicians continue to do today with success. Force, disguised with different attires, is the preferred agent when the strong meets the weak.

In The History there are leaders like Pericles who, according to Thucydides, was highly incorruptible; his nephew, the risk-taking and self-serving Alcibiades, who switches sides twice during the war; the wealthy, patriotic and unimaginative Nicias; and many others with their own motivations to favor or oppose the war. Thucydides implicitly asserts that human actions are better understood within their context, which encompasses socio-economic conditions, prospects of gain, ability to influence, risk profile and motivations.

A Useful Conceptual Framework: The Tragedy of the Commons

Happy will it be if our choice should be directed by a judicious estimate of our true interests, unperplexed and unbiased by considerations not connected with the public good. But this is a thing more ardently to be wished than seriously to be expected—Federalist Paper No. 1, Alexander Hamilton

This section discusses The Tragedy of the Commons, an analytical framework in Game Theory that has justly become famous. It was described by biologist Garrett Hardin from the University of California at Santa Barbara in his article by the same name published in Science. 5 Hardin depicts the following situation, particular in its details, but applicable to many real-world problems, where individual interest and freedom to choose lead to societal catastrophe. 6 Mayhem, it turns out, can be avoided by restricting the individual choices that affect others. The conclusion is unavoidable, but contradicts the widely-held belief that “the invisible hand” maximizes the benefits to society. How can this be? The answer lies in the common misunderstanding of Adam Smith reasoning 7—the result of careless reading of his writings, or worse yet, relying on hearsay to form opinions 8:

“It is not from the benevolence of the butcher, the brewer or the baker that we expect our dinner, but from their regard to their own self-interest… [Every individual] intends only his own security, only his own gain. And he is in this led by an invisible hand to promote an end which was no part of his intention. By pursuing his own interest, he frequently promotes that of society more effectually than when he really intends to promote it.”

Smith’s message is simple. However, the popular conclusion (that unfettered ability to choose is optimal for society regardless of consequences to others) remains an article of faith to many who have never understood the context of Smith’s writings. To appreciate the serious limitations of the “invisible hand” it is important to realize that Smith saw the market as the effective regulator of the use of resources: the assumption is that if I acquire or use something, the price I pay compensates society fairly for the resources consumed to create such good or service. And here is the rub: the “invisible hand,” at best, applies to markets with a robust price system. 9 It turns out that there are instances, many of them crucially important to society, where a price system does not exist, or if it exists it does not work properly. A famous example is the pollution produced by factories. In this case, manufacturers never pay a commensurate price for the environmental destruction they generate. Another example, one that has been studied carefully, is the US health care system, where some of the major determinants of prices are the ability of one party to extract concessions from others, and the opportunity to game the system. 10  Furthermore, in many instances, the relation between price and quality is elusive at best 11, information is imperfect—in some cases really imperfect and asymmetric—competition is far from perfect, and so on. Given the poor track record of the US health care system it is clear that the “invisible hand,” instead of maximizing societal benefits has produced an inefficient scheme that benefits certain powerful groups at the expense of the many.

Are there conditions that allow or force better results? In researching the subject (and in the process winning the 2009 Nobel Prize in Economics), Professor Elinor Ostrom from Indiana University developed a list of conditions that foster cooperation but, she concluded, “the dilemma never fully disappears, even in the best operating systems. … Instead of thinking of overcoming or conquering tragedies of the commons, effective governance systems cope better than others.” Students of strategy, applying common sense or mathematical models, have come to the same conclusion from different angles. In 1.14 Thucydides, using the case of a miscellaneous confederacy where various tribal groups promote their own concern, explains how individual interests can cause the common ruin: “Each [party] thinks that its inertia [self-interest] will do no harm, and that it is someone else’s responsibility rather than theirs to make some provision for their future: the result is that with all individually sharing this same notion they fail as a body to see their common interest going to ruin.” Alexander Hamilton held similar views when he wrote in Federalist Paper No. 1 that “among the most formidable of the obstacles which the new Constitution will have to encounter may readily be distinguished the obvious interest of a certain class of men in every State to resist all changes which may hazard a diminution of the power, emolument, and consequence of the offices they hold under the State establishments; and the perverted ambition of another class of men, who will either hope to aggrandize themselves by the confusion of their country, or will flatter themselves with fairer prospects of elevation from the subdivision of the empire into several partial confederacies than from its union under one government.”

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

1  Thucydides (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.

2  See “Game Theory, Principal-Agent Problem & Arthur Anderson” (

3  For whose benefit?

4  Leadership is of paramount importance and one of the strategic “Centers of Gravity” identified by the famous Prussian General Carl von Clausewitz in his seminal book “On War.”  See “A Lesson From the Greeks,” Contingencies, November/December 2014, p. 33.

5 Science, 162, pp. 1243-48 (1968)

6  For a description of The Tragedy of the Commons see “In Defense of Machiavelli,” Contingencies, November/December 2009, p. 30.

7  Adam Smith mentions the “invisible hand” only three times in his writings, yet the catchy phrase has become extremely popular and misunderstood.

8  Actuaries are less likely to lack objectivity, or so we believe. After all, we subscribe to Ruskin’s maxim: “The work of science is to substitute facts for appearances and demonstrations for impressions.” On the subject of uninformed thinking, Thucydides stated in 1.20 that, “All men show the same uncritical acceptance of the oral traditions handed on to them […] This shows how little trouble most people take in their search for the truth—they happily resort to ready-made opinions.”

9  There are many cases where price systems exist, but individual freedom is pernicious to society: illegal drugs, prostitution, gambling and more.

10  For instance, providers compensated on a fee-for-service basis charge more for the same service than providers under capitated arrangements or salaries simply because the former have the ability to do so—nothing to do with the quality or the quantity of the service.  In a similar fashion, drug manufacturers set prices based on their negotiating strength, not necessarily on the value drugs provide to society, the cost to manufacture them, or, on occasion, supply and demand (because demand is relatively inelastic). 

11  In health care, efforts to adjust prices with quality have produced mediocre results. Outcomes may improve over time, but only up to a point, certainly well below the ideal, partly because the system can be gamed.