A Classroom Competition in Risk Taking

Today we have a guest post from Kyle Haynes, assistant professor of political science at Purdue University. He can be reached at kylehaynes [at] purdue [dot] edu.

Thomas Schelling’s (1966) groundbreaking work on “brinkmanship” explains how deterrent threats are made credible between nuclear-armed opponents. Schelling argued that although rational leaders would never consciously step off the ledge into nuclear Armageddon, they might rationally initiate a policy that incurs some risk of events spiraling into an inadvertent nuclear exchange. Whichever state can tolerate a greater risk of accidental disaster could then escalate the crisis until the adversary, unwilling to incur any additional risk, concedes. For Schelling, this type of crisis bargaining is a competition in risk taking. I use the following simulation to teach this concept:

The simulation begins by randomly splitting the entire class into pairs of students. One student in each pair is designated as Player 1 (P1), the other as Player 2 (P2). At the beginning of each game the instructor places nine white table tennis balls and a single orange table tennis ball into an empty bowl or small bucket. In Round 1 of the game, P1 must decide whether to concede the first extra credit point to P2, or to “stand firm” and refuse to concede. If P1 concedes, P2 receives one point and P1 receives zero points. If P1 stands firm, the instructor will blindly draw a single ball from the ten in the bowl. If the instructor draws a white ball, both players survive, and the game continues to the next round. If the instructor draws an orange ball, then “disaster” occurs and both players lose two points.

If the game continues to the second round, the instructor removes a white ball from the pot and replaces it with another orange ball—there are now eight white balls and two orange balls. It is P2’s turn to decide whether to stand firm or concede. If P2 concedes, P1 receives one point. If P2 stands firm and the instructor draws a white ball, both players survive, and the game continues to Round 3. If, however, the instructor draws an orange ball, both players lose two points.

For Round 3, it is again P1’s turn to decide how to act. But again before a decision is made, the instructor replaces another white ball with an orange one so that there are three orange balls and seven white balls in the pot.

The game continues along this path either until an orange ball is drawn, or the number of rounds set by the instructor have been played. When the game ends, record the points earned by each player. Return to the original ratio of white and orange balls, and begin the next game. After several iterations have been played, total points earned are tallied for each student and the instructor can dole out whatever reward they choose in proportion to the points students have earned.

The players’ relative tolerance of risk is the primary determinant of who will win points. The player that is more willing to risk mutual disaster is likely to continue standing firm while the more risk-averse player will concede whenever he or she decides that the probability of mutual disaster is unacceptably high.

After the exercise, instructors should ask students how the different iterations of the game varied over time and across student pairings. If, for instance, one player acquires a reputation for high risk tolerance, others might begin conceding to her early in the game in order to avoid disaster. Alternatively, players might begin playing more aggressively over time simply out of spite. This is a valuable opportunity to highlight the non-rational components of bargaining.

Instructors might also want to adjust certain parameters at different points to illustrate how specific factors affect the bargaining process. For example, the inherent uncertainty of conflict escalation can be simulated by randomly varying the number of balls drawn after a player opts to stand firm.

In my experience, this simulation has proven highly effective at helping students grasp the logic of brinkmanship and apply it to real-world cases.