A note on the take-it-or-leave-it bargaining procedure with double moral hazard and risk neutrality

In this note we study a take-it-or-leave-it bargaining procedure between two risk neutral individuals engaged in the joint stochastic production of a commodity. Each individual has to exert effort, that is, to provide a one-dimensional input which is unobserved to the other individual. The output-contingent sharing rule is constrained to lead to nonnegative consumption for both individuals, a limited liability constraint. The individuals enter joint production in one of two possible occupations, or tasks, the p-agent and the a-agent, which differ in their incentive intensity. Hence, incentives are asymmetric. The p-agent makes a take-it-or-leave-it offer to the a-agent, and has therefore all the contractual power, modulo providing the a-agent an exogenously given reservation utility.