Vertical exclusion with downstream risk aversion or limited liability

An upstream firm with full commitment bilaterally contracts with two ex ante identical downstream firms. Each observes its own cost shock, and faces uncertainty from its competitor's shock. When they are risk neutral and can absorb losses, the upstream firm contracts symmetric outputs for production efficiency. However, when they are risk averse, competition requires the payment of a risk premium due to revenue uncertainty. Moreover, when they enjoy limited liability, competition requires the upstream firm to share additional surplus. To resolve these trade-offs, the upstream firm offers exclusive contracts in many cases.