Higher-order beliefs in a sequential social dilemma

Strategic players must form beliefs about how others will react at future decision nodes. How often do such beliefs form a consistent hierarchy where subjects believe others hold beliefs similar to their own? We introduce a simple four-player sequential social dilemma where actions reveal first and higher-order beliefs. The unique sub-game perfect Nash equilibrium (SPNE) for self-interested players is observed less than 5% of the time, even though our diagnostic treatments show that a majority of our subjects are self-interested, higher-order rational and have accurate first-order beliefs. In our data, strategic play deviates substantially from Nash predictions because first-order and higher-order beliefs are inconsistent for most subjects, that is most subjects believe that other's beliefs differ from their own beliefs. We construct and operationalize an epistemic model of belief hierarchies to estimate that less than 10% of subjects have consistent first and higher-order beliefs.