Using the U.S. vs North Korean conflict to illustrate and teach Bayes-Nash equilibria

One of the challenges in an undergraduate game theory class is to explain to students the notions of a Bayes-Nash equilibrium (BNE) and a Perfect Bayes-Nash equilibrium (PBNE). Traditionally, if introduced at all, BNE and PBNE are explained by using situations of strategic interaction with an economic context, i.e. entry games with incomplete information, Cournot competition with cost uncertainty, auction games and so on. One notable exception to this is Harrington’s Games, Strategies, and Decision Making, which besides applications to economic problems also uses a number of examples from history, literature, film, and sports to introduce the main concepts of game theory. In this paper we follow the idea that the teaching of undergraduate game theory in general and in particular the notions of BNE and PBNE can be successfully enhanced by constructing a model of and analyzing “current events”, that students are familiar with and “care” about. Specifically, we model the current tension between the U.S. and North Korea as a game with incomplete information, assuming that both countries have private information regarding their willingness or reservation to engage in a military conflict or seek a diplomatic solution We then illustrate the brinksmanship game between the two countries in both its strategic and in its extensive form and solve for the BNE outcomes as well as the probability that a military conflict will be avoided. Having introduced the basic elements of a game with incomplete information we proceed to modify the game in such a way that allows for signaling by North Korea and therefore requires an updating of the U.S.’s beliefs based upon the received signal, i.e. we introduce the notion of, and solve for the PBNE, or BNE with consistent beliefs. The examples presented in this paper require no prior knowledge of economic theory and have been proven to be successful in a class room setting.