Forward induction (FI) thinking is a theoretical concept in the Nash refinement literature which suggests that earlier moves by a player may communicate his future intentions to other players in the game. Whether and how much players use FI in the laboratory is still an open question. We designed an experiment in which detailed reports were elicited from participants playing a battle of the sexes game with an outside option. Many of the reports show an excellent understanding of FI, and such reports are associated more strongly with FI-like behavior than reports consistent with first mover advantage and other reasoning processes. We find that a small fraction of subjects understands FI but lacks confidence in others. We also explore individual differences in behavior. Our results suggest that FI is relevant for explaining behavior in games.

We design a laboratory experiment in which an interested third party endowed with private information sends a public message to two conflicting players, who then make their choices. We find that third-party communication is not strategic. Nevertheless, a hawkish message by a third party makes hawkish behavior more likely while a dovish message makes it less likely. Moreover, how subjects respond to the message is largely unaffected by the third party's incentives. We argue that our results are consistent with a focal point interpretation in the spirit of Schelling.JEL Classification: C72, C92, D82.

We design a novel experiment to study how subjects update their beliefs about the beliefs of others. Three players receive sequential signals about an unknown state of the world. Player 1 reports her beliefs about the state; Player 2 simultaneously reports her beliefs about the beliefs of Player 1; Player 3 simultaneously reports her beliefs about the beliefs of Player 2. We say that beliefs exhibit higher-order learning if the beliefs of Player k about the beliefs of Player $$k-1$$ k - 1 become more accurate as more signals are observed. We find that some of the predicted dynamics of higher-order beliefs are reflected in the data; in particular, higher-order beliefs are updated more slowly with private than public information. However, higher-order learning fails even after a large number of signals is observed. We argue that this result is driven by base-rate neglect, heterogeneity in updating processes, and subjects’ failure to correctly take learning rules of others into account.

When applying to schools, students often submit applications to distinct school systems that operate independently, which leads to waste and distortions of stability due to miscoordination. To alleviate this issue, Manjunath and Turhan (2016) introduce the Iterative Deferred Acceptance mechanism (IDA); however, this mechanism is not strategy-proof. We design an experiment to compare the performance of this mechanism under parallel markets (DecDA2) to the classic Deferred Acceptance mechanism with both divided (DecDA) and unified markets (DA). Consistent with the theory, we find that both stability and efficiency are highest under DA, intermediate under DecDA2, and lowest under DecDA. We observe that some subjects use strategic reporting when predicted, leading to improved efficiency for all participants of the market. Our findings cast doubt on whether strategy-proofness should be perceived as a universal constraint to market mechanisms.

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