The Decision Science Journal of Innovative Education

Using Game Theory to Introduce Ethics in Decision Sciences

Gerard M. Campbell

Information Systems and Operations Management

Charles F. Dolan School of Business

Fairfield University

Fairfield, CT 06824

USA

e-mail: gcampbell@mail.fairfield.edu

phone: (203) 254-4000 x-3118

fax: (203) 254-4105

Recent high-profile corporate scandals have highlighted the need for an increased emphasis on ethics throughout business school curricula. For those teaching courses related to decision sciences, introductory-level game theory can provide an excellent vehicle for raising awareness of ethical issues within a quantitative modeling framework. Game theory has been around for decades, but most decision science and management science textbooks do not cover it. Fortunately, a variety of instructional materials are freely-available on the web to supplement standard texts.

This teaching brief describes how web-based materials can be used to introduce game theory and ethics in a two-hour module taught during two class periods. Its contents are suitable for use at either the graduate or undergraduate level, and, as a self-contained module, it can be positioned almost anywhere within a course. It also has the advantage of not requiring extensive preparation by instructors who have had no formal training in game theory or ethics. The module includes seven steps, but steps 1, 3, and 7 may be eliminated if class time is a serious constraint. For advanced undergraduate or graduate courses, an ethics-related reading assignment, such as Gallo (2004), could be distributed to read as homework before the module begins.

Step 1: A fun way to begin the discussion of game theory is to use the “motivating experiment” described by Mobius (2003). The following rules of the game should be written on the board:

“On a piece of paper, write an integer between 0 and 100 to represent your best guess of what 2/3 of the average of all students’ guesses will be. The student closest to 2/3 the average of all guesses without going over will receive $5.00. In case of a tie, all students with the best guess will each receive $5.00.”

The prospect of receiving cash from the instructor generates a lot of excitement. Theoretically, all students could guess zero, and the instructor would owe $5.00 to each student. However, based on reported results from numerous universities, the instructor has little to worry about – 2/3 the average is likely to end up being between 15 and 20. A spreadsheet is useful for establishing the winner(s), who will happily accept their prize.

Step 2: After playing the introductory game, the board is used to present the following definition and explanation of terms, adopted from Mobius (2003):

“Definition: Game theory is a formal way to analyze interaction among a group of rational agents who behave strategically. This definition contains a number of important concepts which are discussed in order: Group: In any game there are multiple decision makers, who are referred to as players. If there is a single player, the game becomes a decision problem. Interaction: What one individual player does directly affects at least one other player in the group. Otherwise, the game is simply a series of independent decision problems. Strategic: Individual players account for this interdependence. Rational: While accounting for this interdependence, each player chooses her best action …”

Step 3: After presenting the definition, the movie “A Beautiful Mind” (2002) can be discussed. In the movie, Russell Crowe portrayed John Nash, a major contributor to the field of game theory. A memorable scene occurs when Nash is in a Princeton-area bar with several of his male friends, all seeking female companionship. A group of women is there, including an especially gorgeous blonde. In a major “light-bulb” moment, Nash realizes that the best way for all his friends to attain female companionship is for none of them to pursue the blonde. In the movie, Nash’s “beautiful mind” uses this as inspiration for Nobel Prize winning research in the field of game theory. The definition of game theory can again be referenced as the scene is discussed (or, better yet, shown). Although the discussion is not mathematical, it helps students realize the applicability of game theory to an interesting real-life setting.

Step 4: At this point, the time is right for another quantitative example. The widely-known “prisoner’s dilemma” game can be introduced as follows: Two men are suspected of committing a serious crime together (e.g., armed robbery). Each is held in a separate cell, so they do not know what the other is doing. Each is aware of the following “payoff matrix,” which shows how long they would spend in jail [in the form of (years for suspect X, years for suspect Y)] under four different confession scenarios:

After discussing how the prisoner’s dilemma fits the definition of game theory, students can be asked what decision they would make if they were one of the suspects. Issues of trust and “honor among thieves” may be considered, but confessing will typically emerge as the preferred choice. As an aside, the game’s real-life cops-and-robbers roots can be noted. For my classes, I read excerpts from an article about a broker’s aide pleading guilty in a case related to Martha Stewart’s ImClone stock sale. While it did not correspond exactly to the prisoner’s dilemma problem on the board, it was close enough to demonstrate real life applicability. Another tie-in students might know about is the show “Friend or Foe” on the Game Show Network.

Step 5: After finishing with the basic prisoner’s dilemma, a more interesting variant, known as the “repeated prisoner’s dilemma,” can be introduced. For this, students can use web-connected computers to visit a website (http://serendip.brynmawr.edu/bb/pd.html) to play ten iterations of the prisoner’s dilemma against a computer “opponent.” The online game uses a payoff matrix similar to that shown earlier, but payment is in desirable “gold coins” instead of undesirable years in prison, and “Cooperate” and “Cheat” replace “Don’t Confess” and “Confess.” This version has the advantage of not involving unscrupulous criminals, whose cooperative choice of not confessing is morally questionable. Despite the differences, the online version of the game is easily recognized as similar to the basic version presented earlier. The students will not know the computer has been programmed to use the well-known “tit-for-tat” strategy, where it starts by cooperating and continues by doing whatever its opponent did on the previous iteration. It will not take long for most to realize that a high score for ten iterations can be obtained by cooperating for the first nine iterations and then cheating on the last.

Defection on the last iteration is a phenomenon worthy of discussion. The following excerpt [from Davis (1983), page 151] can be read to show related examples in nature:

“To maintain a cooperative relationship in a sequence of prisoner’s dilemmas, there must be a good chance that defections will be punished and cooperation rewarded. In ant colonies that are stationary, symbiotic relationships are common; in honeybee colonies that are constantly moving, they are unknown. If there is a good prospect that the relationship will break up tomorrow, defection will become more likely today.”

Implications for decision-making can be highlighted by emphasizing that, in business, you frequently do not know who you will encounter again in the future.

To show that opponents using different strategies cannot be handled as easily as those using tit-for-tat, another website can be visited. Students could be instructed to visit http://gametheory.net, select “interactive materials,” then “repeated prisoner’s dilemma.” Here, five different opponents employing different strategies can be found, and the simple strategy of always cooperating until the last play will not work well against all of them. As students explore different strategies of their own devise, some may discover something along the lines of tit-for-tat. After the students have had a chance to develop their own strategies, tit-for-tat (with cooperation first) can be formally introduced as a strategy that has proven to be remarkably robust under a wide variety of conditions. The instructor might also refer to the disarmament game used in organizational behavior classes, where “tit-for-tat” also applies.

Step 6: Here, the discussion focuses more directly on ethics. The relationship between tit-for-tat and the “eye for an eye” philosophy can be noted. The class can also discuss how tit-for-tat relates to teachings of world religions and strict adherence to the “golden rule” of doing unto others as you would have them do unto you. The real world versus utopia might come out in the discussion, along with the importance of knowing who you are playing against and maintaining your own reputation as a fair player. If time permits, the class might also consider the opposing views on the relationship between game theory and ethical decision-making expressed in Higgins (2002) and Milne (2002), two short articles available on-line.

In discussing how ethics relates to decision-making and quantitative models, Gallo (2004) highlights the “responsibility principle” proposed by the philosopher Jonas, which suggests that points of view of all stake-holders need to be considered. Theys and Kunsch (2004) propose “the importance of co-operation for ethical decision-making,” and they support it with results based on the prisoner’s dilemma game. These principles of responsibility and cooperation are useful in the discussion of ethical decision-making.

Step 7: To further the discussion of ethics, another website ( www.spectacle.org/995/ ) can be visited to view an online issue of “The Ethical Spectacle” (1995). This issue presents numerous short articles related specifically to the prisoner’s dilemma. Topics include: business, litigation, love, politics, software development, and welfare. Students can be assigned articles to read and verbally summarize for the rest of the class. The articles are useful for demonstrating the wide applicability of game theory, and for highlighting concerns of responsibility and cooperation in decision-making.

To complete the module on game theory and ethics, the instructor might read the excerpt shown below from an article entitled “The High of Being Nice” (Readers Digest, 2002, p. 47), which summarizes recent research conducted at Emory University.

“The scientists used magnetic resonance imaging to scan the brains of 36 women while they played the ‘Prisoner’s Dilemma Game’ …. The researchers found that most of the time the women chose to cooperate. Whenever they did work together, the scientists could see stimulation in two parts of the brain associated with pleasure. ‘This suggests that people find it rewarding to cooperate with each other,’ says neuroscientist Gregory Berns. ‘Mutual small acts of kindness really do make you feel better.’”

Are people “hard-wired” to behave ethically? It is an interesting question to address towards the end of the module, particularly in light of the earlier material related to evolutionary biology.

Game theory can lend itself to much more than the two hour treatment described here. Entire courses can be found in economics and philosophy departments at many universities, but the topic has generally not been included in decision science and management science texts. This teaching brief has described how freely-available websites can be used to introduce game theory and ethical decision-making. As of May 2003, this module had been used in a junior-level Management Science course and a sophomore-level Business Ethics course. There was strong student participation each time the module was used, and written student feedback was very positive, as shown in the Appendix.

For classrooms without student web access, an alternative to the two-hour module described here is a one-hour module with web exercises assigned as homework. For this, a half-hour towards the end of one class could be used for steps 1-4; step 5 and the articles from step 7 could be assigned as homework; and a half hour at the beginning of the next class could be used for step 6 and the discussion part of step 7.

Davis, Morton D., Game Theory, A Nontechnical Introduction, Dover Publications, Inc., New York, 1983.

Gallo, Giorgio, “Operations research and ethics: Responsibility, sharing and cooperation,” European Journal of Operational Research, Vol. 153, pp. 468-476, 2004.

Readers Digest, “The High of Being Nice,” Medical Update, p. 47, October 2002.

Theys, M. and Kunsch, P.L. “The importance of co-operation for ethical decision-making with OR,” European Journal of Operational Research, Vol. 153, pp. 485-488, 2004.

In two classes where the module was used, an assessment form was distributed at the end of the module asking students to rate the extent to which stated objectives were achieved. On a five-point scale, with five being the best, the mean ratings of the two classes for each objective are shown below, along with examples of written student comments.

1) To introduce basic concepts of game theory, and to show how it Fall ’02 Spr ‘03

2) To use the Prisoner's Dilemma problem as a means of considering Fall ’02 Spr ‘03

the perspectives of different stakeholders affected by a decision. 4.50 4.44

3) To illustrate how ethical considerations and moral values can Fall ’02 Spr ‘03

“The module was very informative and triggered many new ideas in the topic of ethics.”

“I liked using the computer to play games. It was interactive and fun. The games

“I became very interested in this module. If there was a class called Game Theory,