Demonstrating the Possibility of Pareto Inferior Nash Equilibria

One of the serious challenges when teaching game theory to undergraduate students is to explain the occurrence of a multiplicity of equilibria and the relat-ed problem of equilibrium selection. Many equilibria are simply considered to be totally “unreasonable” and “senseless” by many students and worth their atten-tion only because they fit the technical definition of an equilibrium as given in the textbook, which implies it might be useful to know how to find these equi-libria only because of the final exam. A particular example of such “absurd” equilibria is the occurrence of Pareto-dominated equilibria, as in the bimatrix game Matching Colors (Figure 1). The (red, red) equilibrium with a payoff of 100 to each payer is not considered to be a serious possibility by most students. Even when they understand how it fits the definition of a Nash equilibrium (NE), they believe only exceptionally bounded-ly rational people would fall for it. (In some sense, it seems that many students are kibitzers [Binmore 1992, 397], people who watch games but do not play themselves and who tend to believe they know the right moves better than the players themselves.) Possible explanations referring to historical accidents and the dynamics of social norms appear somewhat abstract and receive mainly skep-tical reactions in the classroom. This seems a typical situation in which a class