Strategic delegation analysis was limited to sales delegation cases, until Jansen et al. (2007) and Ritz (2008) presented the case of market share delegation. In this paper, we adopt a simplified version of the market share parameter to deal with the cost asymmetry between firms. It shows that both output decision and incentive contract are affected by market size and cost difference. In addition, the new form of market share delegation not only preserves the spirit of Jansen et al. and Ritz, but also becomes useful in dealing with most multi-stage games of concerned issues as well. Furthermore, for the cost-efficient firm, the not-so-competitive action makes the profit of the market-share delegation firm more than that of the sales delegation firm.