Psychological Games

Traditional game-theoretic models assume that utilities depend only on actions. This is not sufficient for describing the motivations and choices of decision makers who care about reciprocity, emotions, or social rewards. Psychological games allow utilities to depend directly on beliefs (about beliefs) besides which actions are chosen, and they can capture a wider range of motivations. This Palgrave entry contains several examples and it is indicated where research on psychological games is headed. Traditional game-theoretic models presume that utilities depend on actions. While this framework is quite general (it can, for example, accommodate profit-maximization, altruism, inequity aversion, and Rawlsian maximin preferences) it is not rich enough to adequately describe several psychological or social aspects of motivation which depend directly on beliefs (about beliefs) besides which actions are chosen. The following example illustrates: Karen feels guilty if she lets others down. When paying her landscaper (Jim), this influences her tipping. The more she believes Jim believes he will receive as a tip, the more she gives. More precisely, she gives just as much as she believes Jim believes he will get, in order to avoid the feelings of guilt that will plague her if she gives less. Beyond depicting something arguably realistic, the example illustrates in the simplest possible way how one may have to transcend traditional game theory to model a beliefdependent motivation: Consider a standard game form where Karen chooses a tip t such that 0 ≤ t ≤ w, where w is the number of dollars in her wallet, and where the landscaper has no choice (his strategy set is modeled as a singleton {x}). Karen’s choice of tip thus pins down a strategy profile (t, x). In traditional game theory, payoffs are defined on strategy profiles (or on endnodes induced by strategy profiles), so Karen’s best choice (or choices) would be independent of her belief about Jim’s belief about her choice of tip. This runs counter to the example. Gilboa & Schmeidler (1988) and Geanakoplos, Pearce & Stacchetti (1989) present several examples that illustrate the inadequacy of traditional methods to represent preferences that reflect various forms of belief-dependent motivation. Geanakoplos et al develop a new analytical framework, in which the centerpiece is the notion of a psychological game, which may be seen as a generalization of a traditional game and which can model some of the desired effects. A psychological game differs from a traditional game in that utilities are defined on beliefs (about actions and beliefs), as well as on which actions are chosen. (The term “game with beliefdependent motivation” would be more descriptive than the term “psychological game,” but I stick with the latter which has become established.) The most well-known example of a psychological-games based application is Rabin’s (1993) highly influential model of reciprocity, according to which players wish to act kindly (unkindly) in response to kind (unkind) actions. The key notion of kindness depends on beliefs in a way such that reciprocal motivation can only be described using psychological games. To see why, suppose that I jump out in front of your car blocking your way, so that you can’t cross a bridge and you therefore arrive late to an important meeting. Am I kind? Clearly one cannot say without knowing what my beliefs are. If I believe the bridge is as sturdy as bridges usually are and I am just goofing around, then I am unkind. However, if I believe the bridge is about to collapse then I am kind. Arguably, I would be kind even if I mistook a sturdy bridge for a dangerous one. So, should you be kind or unkind in return? The answer depends on your beliefs about my kindness, and hence on your beliefs about my beliefs. It takes a psychological game to model that. (The example given here is similar in spirit to another example given on p 23 of Rabin (1998). Rabin’s model is normal-form based. See Dufwenberg & Kirchsteiger (2004) for an extension to extensive game forms. See Fehr & Gächter (2000) and Sobel (2005) for general discussions of why reciprocity has important economic consequences.) Reciprocity is but one form of motivation that can be modeled by means of psychological games. Many emotions are good candidates. In his article “Emotions and Economic Theory”, Elster (1998) argues that a variety of emotions have important economic consequences and he laments the attention economists have paid to this. He argues that a key characteristic of emotions is that “they are triggered by beliefs” (p. 49). He discusses anger, hatred, guilt, shame, pride, admiration, regret, rejoicing, disappointment, elation, fear, hope, joy, grief, envy, malice, indignation, jealousy, surprise, boredom, sexual desire, enjoyment, worry, and frustration. He asks (p. 48): “[H]ow can emotions help us explain behavior for which good explanations seem to be lacking?” Psychological games may be useful for providing answers.