Risk sharing rules and investment in groups

In this study, we consider a game among n investors, who individually choose to borrow a certain amount to invest in a risky project. We assume that the success probabilities for the risky projects are independent and that the individuals can agree upon a fully enforceable sharing rule. We define four major rules, namely Full Liability (FL), Loss Sharing (LS), Profit Sharing (PS) and Equal Sharing (ES), which differ in terms of the sharing of profits and losses across all investors. We compute the equilibrium investment levels and expected social welfare levels and investigate coalition formation structure under these rules. Our theoretical findings show that the game has a unique dominant strategy Nash equilibrium under each rule. Regarding the total equilibrium investment levels, although the ordering of the rules depends on the parameter values, we show a clear supremacy of ES and LS rules over FL and PS rules. Furthermore, through employing numerical analyses, we demonstrate the dominant structure of ES rule over other sharing rules in terms of individual, utilitarian and egalitarian social welfare levels. Lastly, we find that, with certain constraints on model parameters, two agents with identical risk aversion levels are able to form stable coalitions under each rule.