A Theory of Experiments: Invariance of Equilibrium to the Strategy Method and Implications

Abstract

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. We formalize the mapping from the monetary payoff game to this actual game and delineate necessary and sufficient conditions for strategic equivalence to apply. We use results from the past literature and our own experiments and report three results. First, not accounting for bias in estimation when decisions at one information set can influence utility at another information set can render significant differences in decision-making. Second, the bias can be large and equivalent to other treatment effects being measured. Third, subtle interventions on salience can magnify these differences by a similar amount.