Higher order beliefs and emotions in games

Emotions affect the valence of outcomes and yield action tendencies. Many emotions are triggered by beliefs. It is therefore important to develop a methodology to incorporate the role of emotions in mathematical models of human interaction by analyzing how hierarchical beliefs affect the subjective values of outcomes and actions in games. Such methodology is now called “psychological game theory” after the seminal work of Geanakoplos et al. (Games Econ. Behav., 1989). The initial approach was to make the utility of outcomes (endnodes) depend on hierarchical beliefs and adapt the standard “rational-expectations” equilibrium analysis to such “psychological” games. I argue that a more radical departure from standard game theory is advisable. In many applications of standard (“non-psychological”) game theory, standard “rational-expectations” equilibrium analysis is questionable and lacks thorough foundations. The problem is even more serious in “psychological” games. Such problems can be addressed, at least in part, referring to the foundations of game theory. I suggest that serious predictions/explanations by means of game theory of real life and lab phenomena where emotions matter must face up front the following issues: (i) information about psychological features of agents is incomplete and hardly representable with common prior models; (ii) behavior in sequential games does not result from the choice of strategies, but rather from the choice of actions within the context of plans, which are—essentially--beliefs about one’s own behavior; (iii) stable behavior in recurrent interaction should be explained as a self-confirming equilibrium, where agents’ beliefs about relevant unknowns are typically wrong, but they are confirmed by available evidence; (iv) behavior in non-recurrent interactions should be (coarsely) predicted by a few steps of iterated deletion of non-best replies subject to some plausible restrictions on low-order beliefs; (v) “decision utility” (action tendencies) sometimes cannot be derived from “experience utility” (outcome values). This is illustrated by a wealth of applications.