Learning to Trust: Uncovering Unobserved Multi-Period Behavioral Strategies from Observed Stage Game Actions Using Finite Automata

We introduce a methodology to infer players' unobserved multi-period strategies from their observed stage game actions in economic decision-making experiments. We use finite-state automata to model multi-period strategies by employing an algorithm that synthesizes a minimal state automaton from a sequence of inputs and outputs. The inputs and outputs are the players' and their opponents' behavior, and the automaton is the decision rule. We use this methodology to examine new experimental data from finitely and infinitely repeated trust games. We synthesize an automaton for every behavioral observation in the experiment. Although we are able to infer that over 70 unique finite-state automata strategies are used in he infinite horizon game, over 90 percent of the data may be explained by a very small number of behaviorally interpretable strategies. We find that subjects who are in a position to initiate trust use a harsh punishment strategy infrequently (when trust is not reciprocated) in early play, but learn predominantly to use this strategy over time. By contrast, players who are in a position to reciprocate trust do not learn to reciprocate (perhaps because the harsh punishment strategy does not emerge until near the end of the session). In fact, these players appear to be exhibiting "gambler's fallacy" behavior by forming incorrect subjective probabilities that the infinite game will end. Our inference methodology is able to capture this behavior by generating automata that count the number of periods of play. We conclude that our strategy inference technique enables us to better our understanding of the nature of strategic behavior in trust games.