Definition: A sharing rule is a function that defines the split of gains between a principal and agent. The
gains are usually profits, and the split is usually a linear rule that gives a
fraction to the agent.
For example, suppose profits are x, which might be a random variable. The principal and agent might agree, in advance of knowing x, on a sharing rule s(x). Here s(x) is the amount given to the agent, leaving the principal with the residual gain x-s(x).
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