Cooperation with Rivals

The common characteristic of R&D joint ventures between oligopolistic competitors, arms reduction talks, and study groups in law school is cooperation with rivals. Players benefit from cooperation, but any gain by their partner weakens their own position when competing for profits, security, or a high class ranking. I construct a model in which players have different resource endowments and can increase them through bilateral cooperation. The final allocations enter a contest success function and determine each player’s probability of winning a fixed prize. A refinement of Nash equilibrium, Pairwise Stable Nash Equilibrium (PSNE), is defined to deal with the need for mutual consent to establish cooperation. Results show that universal full cooperation is a PSNE in this zero-sum game without repeated play if no player predominates, and the only PSNE if players are free to negotiate side-payments. The model is then applied to trade between the US and China