"Betting on nature" or "betting on others": anti-coordination induces uniquely high levels of entropy.

Uncertainty in the form of risk or ambiguity can arise from the interaction with nature and other players, while strategic uncertainty arises only in interactions with others. Here, we systematically compare binary decisions between a safe option and a potentially higher paying but uncertain option in four experimental conditions with the same potential monetary outcomes: coordination vs. anti coordination games, as well as risky and ambiguous lotteries. In each condition, we progressively increase the value of the safe option and measure subjects' certainty equivalents (i.e., the specific safe payoff-threshold that makes a subject indifferent between the two options). We find that anti-coordination games and ambiguous lotteries elicit equally high aversion to uncertainty, relative to the other domains. In spite of this similarity, we find that subjects alternate between the safe and uncertain options much more frequently, thus displaying higher entropy, under anti-coordination relative to any of the other environments. These differences are predicted by theories of recursive reasoning in strategic games (e.g., thinking what others think we think etc.). Indeed, this can occur when interacting with intentional counterparts, but not with nature.