Rationing rules for risky claims

We study rationing rules in a scenario where individuals have state-contingent claims over a resource. The rules must allocate shares before the resolution of uncertainty. We begin by characterizing ex-ante rules based on how they handle the inherent uncertainty in individual claims. The key axiom is “No Penalty for Risk”, which states that the rule should not penalize an individual if a situation differs from another only in terms of the presence of risk in the former situation compared to the latter situation’s riskless claim. Regarding ex-post characterizations, our primary axiom is “Indifference to Independent Combination of Gambles”. If an individual has risk-neutral expected utility preferences, any rule that makes them indifferent between a given rationing problem and a corresponding independent combination of gambles between a degenerate gamble and a zero game (any rationing problem with a zero endowment) must be in the ex-post form. Lastly, we provide a partial comparative static result that supports the claim that individuals generally prefer ex-ante rules to ex-post rules when the resource level is low enough.