A Theory of Experiments: Invariance of Equilibrium to the Strategy Method of Elicitation and Implications for Social Preferences

Most papers that employ the strategy method (SM) use many observations per subject to study responses to rare or off-equilibrium behavior that cannot be observed using direct elicitation (DE), but ignore that the strategic equivalence between SM and DE holds for the monetary payoff game but not the game participants actually play, which is in terms of utilities. To illustrate the severity of this issue, we formalize the mapping from the monetary payoff game to this actual game. A theorem provides necessary and sufficient conditions for strategic equivalence to apply. When the domain of preferences includes commonlymodeled motivations, such as intentions or disappointment aversion, or less-common ones, such as self-image or duty, strategic equivalence fails and thus the invariance to the method of elicitation does not apply. We use results from the past literature and our own experiments to investigate how well this theorem explains when results with SM and DE differ. We manipulate the salience of off-equilibrium considerations in our own experiments to demonstrate that SM and DE are not strategically equivalent, contrary to conventional wisdom. Three results emerge. First, not accounting for the bias in the estimation when decisions at one information set can influence the utility at another information set can render significant differences in decision-making. Second, the bias can be large and equivalent to some of the other causal effects being measured. Third, subtle interventions on salience can magnify these differences by a similar amount.