<p>This article investigates the reinsurance contract design problem by simultaneously taking into account the joint interests, the conflicting interests and the decisions of the insurer and the reinsurer. To better reflect the insurance practice, we assume that the insurer can reduce her insurance risk by purchasing per-loss reinsurance; the reinsurer can engage in insurance business. During the design of reinsurance contract, the insurer determines the claim risk sharing strategy and the reinsurer determines the reinsurance pricing strategy. We quantify the competition between the insurer and the reinsurer in terms of relative wealth. Under mean-variance criterion, we obtain the explicit optimal reinsurance contract and corresponding optimal value functions. Finally, we carry out numerical experiments to illustrate the theoretical results. We find that compared with the competition degree, risk aversion degree and expected claim, the claim intensity has the most significant impact on the formulation of reinsurance contract; the insurer would pay less, less and more reinsurance premium when the reinsurer engages in insurance business, the insurer considers competition and the reinsurer considers competition, respectively.</p>