Cross Holdings and Strategic Manager Compensation. The Case of an Asymmetric Triopoly

We study an asymmetric triopoly in a heterogeneous product market where quantity decisions are delegated to managers. The two biggest firms are commonly owned by shareholders such as index funds while the smallest firm is owned by independent shareholders. Under such a cross-holding owner structure, the owners have an incentive to coordinate when designing their manager compensation schemes. This type of coordination leads to compensation contracts which make the managers less aggressive such that the firms involved in the coordination reduce their output while the outside firm increases its output. The reallocation of production induces a redistribution of profits: the outside firm and the most efficient firm owned by the index funds gain from the coordination while the less efficient firm owned by the index funds might suffer from a loss of profit if cost differences are large. The trade volume in the market is reduced so that shareholder coordination is detrimental to consumer surplus as well as welfare.