Experiments that investigate the spontaneous emergence of money in laboratory societies rely on indefinitely repeated helping games with random matching (Camera et al., 2013; Camera and Casari, 2014). An important open issue is the lack of a general proof of existence of an equilibrium capable of supporting the efficient allocation under private monitoring, without money. Here, we fill this gap by offering a general proof, as well as by characterizing the efficient non-monetary equilibrium. This technique can be extended to study games with simultaneous actions.
Camera, G., & Gioffré, A. (2019). Cooperation in indefinitely repeated helping games: existence and characterization. ESI Working Paper 19-28. Retrieved from https://digitalcommons.chapman.edu/esi_working_papers/288/