Using Greek Mythology to Teach Game Theory

Beginning of article

I. Introduction

Although Odysseus was destined to lead the Greeks to victory in the Trojan War, he initially tried to avoid joining the Greek cause by acting insane. His attempt to dodge the draft was foiled only by the creation of what is today known as a separating equilibrium. Greek myths make near-perfect examples to use in teaching game theory because the stories are extremely interesting and most students are already familiar with many of the characters. (1)

Game theory is commonly taught in undergraduate classes. Usually economists use business models to illuminate their abstract theories. Game theory professors often regale their students with fascinating tales of how employers use education as a screening device and of how monopolists attempt to restrict competition by acting tough. This article proposes that game theorists should add examples from Greek mythology to their arsenal of game theoretic examples. Greek myths are still studied thousands of years after their creation primarily because they represent fascinating characters in complex situations, and remain interesting and relevant to the human experience. By showing how these myths can be employed to teach game theory, we hope to make a significant contribution to economic pedagogy.

For professional economists game theory is about developing and applying rigorous mathematical models. Once the vast majority of students in an undergraduate game theory class complete their education, however, they will never again encounter a formal game theoretic model. The benefit to undergraduates of studying game theory therefore comes not from their mastering mathematical techniques, but rather from gaining intuitive insights into strategy. Studying how gods and mortals in Greek myths manage and elicit information allows students to gain insight into strategy they wouldn't receive by merely studying what are to them dry business examples.

In most of the remaining sections of this article we present a game theoretic model and then show how a Greek myth illuminates this model. This article assumes that the reader is far more familiar with game theory than with Greek mythology. Therefore, we cover the myths in greater detail then we cover the game theory models.

II. Truth Inducement Through Self-Selection

Separating equilibria are commonly taught in undergraduate economics courses. In a simple separating equilibrium a person is either of type X or Y. No one but this person initially knows his type and this person wants people to think he is of type X. If the individual is rational, asking him what his type is will provide no useful information. One mechanism to induce this individual to reveal his type would be to create a situation where it will be in the self-interests of types X and Y to act differently. If such a mechanism were successful it would create a separating equilibrium through self-selection because the individual himself would be induced to reveal his type.

The most well-known example of a separating equilibrium is Spence's model of education. (2) Consider a simplified version of Spence's model where there are two types of workers, those of high productivity and those of low productivity. Employers want to hire workers of high productivity but they can not directly observe a worker's type. Employers know, however, that it is easier for high productivity workers to graduate from college than it is for low productivity workers to do so. Under these assumptions there might exist a separating equilibrium where only high productivity workers graduate from college.

If only high productivity workers graduate from college then employers will prefer college graduates and completing college will increase a worker's salary. Let B = the benefit in this equilibrium from graduating from college. Since employers can not observe a worker's quality both types of workers would get the same salary increase from college. It will cost the two types of workers, however, different amounts to graduate. Let [C.sup.h] and [C.sup.L] = the cost of attending college for high and low productivity workers respectively. Since, by assumption, it's easier for a high than low quality worker to complete college then [C.sup.h] < [C.sup.L]. For there to exist a separating equilibrium where a worker will graduate from college if and only if he is high quality then [C.sup.h] < B < [C.sup.L].

Odysseus' Recruitment

The myth of Odysseus' recruitment provides an example in Greek mythology of a separating equilibrium achieved through self-selection. Odysseus was a suitor for the hand of Helen, the most beautiful mortal woman in the world. She had many suitors, and to avoid strife they all swore an oath to help her and whomever she chose as her husband. Helen passed over Odysseus in favor of Menelaus, but when the Trojans abducted Helen, Odysseus was still bound by his oath to help Menelaus retrieve her from Troy. The Greeks greatly wanted Odysseus to join their fight because he was extremely cunning. Odysseus, however, perceived that it was not in his self-interest to keep his oath, for he had been warned by an oracle that if he joined the military expedition he would not return home for twenty years, having first lost all his companions. (3) Moreover, he was now happily married to Penelope, with an infant son, Telemachus.

When the Greek leaders came to recruit him, he did not feel compelled by the long-ago oath, and tried to dodge the draft: he feigned insanity, choosing madness to disguise his most notable asset, his intelligence. (4) Odysseus acted insane by plowing his land randomly. Alone among the Greeks Palamedes suspected Odysseus of faking insanity. (5) Palamedes thought Odysseus' type was "sane," while the rest of the Greeks thought his type was "crazy."

To prove Odysseus' sanity Palamedes devised a truth-inducing mechanism that would cause a sane Odysseus and an insane Odysseus to take different actions. In one version of this myth "Palamedes threw Odysseus's son Telemachus in the path of the plow and said, 'Put aside your deception and come with us!"' (6) If Odysseus were insane he would have run over his son with the plow. If, however, Odysseus were sane it would be very costly for him to kill his child. In the myth Odysseus stops short of plowing over Telemachus and, his sanity established, joins the expedition to Troy. Palamedes, relying on a sane Odysseus' emotional attachment to his son, created a separating equilibrium, forcing Odysseus to reveal his type. (7)

In formal game theoretic terms, nature first decided whether Odysseus was sane or crazy. If Odysseus was crazy his response to Palamedes' putting his child in front of the plow would be to kill the child. If Odysseus was sane, then in response to Palamedes' move he could either kill …