#### Coordination of a Supply Chain with Risk-Averse Agents

**Abstract: **The extant
supply chain management literature has not addressed the issue of coordination
in supply chains involving risk-averse agents. We take up this issue and
begin with defining a coordinating contract as one that results in a
Pareto-optimal solution acceptable to each agent. Our definition
generalizes the standard one in the risk-neutral case. We then develop
coordinating contracts in three specific cases: (i) the supplier is risk
neutral and the retailer maximizes his expected profit subject a a downside risk
constraint, (ii) the supplier and the retailer each maximizes his own
mean-variance trade-off, and (iii) the supplier and the retailer each maximize
his own expected utility. Moreover, in case (iii) we show that our
contract yields the Nash Bargaining solution. In each case, we show how we
can find the set of Pareto-optimal solutions, and then design a contract to
achieve the solutions. We also exhibit a case in which we obtain
Pareto-optimal sharing rules explicitly, and outline a procedure to obtain
Pareto-optimal solutions.