Decisions to trust in strategic situations involve ambiguity (unknown probabilities). Despite many theoretical studies on ambiguity in game theory, empirical studies have lagged behind due to a lack of measurement methods, where separating ambiguity attitudes from beliefs is crucial. Baillon et al. (Econometrica, 2018b) introduced a method that allows for such a separation for individual choice. We extend this method to strategic situations and apply it to the trust game, providing new insights. People's ambiguity attitudes and beliefs both matter for their trust decisions. People who are more ambiguity averse decide to trust less, and people with more optimistic beliefs about others' trustworthiness decide to trust more. However, people who are more a-insensitive (insufficient discrimination between different likelihood levels) are less likely to act upon their beliefs. Our measurement of beliefs, free from contamination by ambiguity attitudes, shows that traditional introspective trust survey measures capture trust in the commonly accepted sense of belief in trustworthiness of others. Further, trustworthy people also decide to trust more due to their beliefs that others are similar to themselves. This paper shows that applications of ambiguity theories to game theory can bring useful new empirical insights.

We investigate the credibility of nonbinding preplay statements about cooperative behavior, using data from a high-stakes TV game show in which contestants play a variant on the classic Prisoner's Dilemma. We depart from the conventional binary approach of classifying statements as promises or not, and propose a more fine-grained two-by-two typology inspired by the idea that lying aversion leads defectors to prefer statements that are malleable to ex-post interpretation as truths. Our empirical analysis shows that statements that carry an element of conditionality or implicitness are associated with a lower likelihood of cooperation, and confirms that malleability is a good criterion for judging the credibility of cheap talk.

This paper examines the difference between strategic ambiguity as in game theory and ambiguity arising in individual decisions. We identify a new, non-strategic component underlying all strategic ambiguities, called social ambiguity. We recommend controlling for it to better identify strategic causes. Thus, we shed new light on Bohnet and Zeckhauser's betrayal aversion in the trust game. We first show theoretically that, contrary to preceding claims in the literature, ambiguity attitudes can play a role here. We then show experimentally that social ambiguity, rather than betrayal aversion, can explain our empirical findings. Using our new control, we identify the unique effect of strategic ambiguity. Strategic complexity increases ambiguity perception and thus increases people's likelihood insensitivity when making decisions under strategic ambiguity. Our results show the usefulness of controlling for ambiguity attitudes before speculating on strategic factors.

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