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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 belief-dependent 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.