We auction scarce rights to play the Proposer and Responder positions in ultimatum games. As a control treatment, we randomly allocate these rights and charge exogenous participation fees. These participation fee sequences match the auction price sequence from a session of the original treatment. With endogenous selection via auctions, we find that play converges to a session-specific Nash equilibrium, and auction prices emerge supporting this equilibrium by the principle of forward induction. With random assignment, we find play also converges to a session-specific Nash equilibrium as predicted by the principle of loss avoidance. While Nash equilibria with low offers are observed, the subgame perfect Nash equilibrium never is.
Shachat, J., & Swarthout, J. (2013). Auctioning the Right to Play Ultimatum Games and the Impact on Equilibrium Selection. Games, 4(4), 738-753. https://doi.org/10.3390/g4040738