Should a Stackelberg-dominated supply-chain player help her dominant opponent to obtain better system-parameter knowledge?

Abstract

A manufacturer (Manu) supplies a product to a retailer (Reta). The uncertain knowledge of the dominant player (which may be either Manu or Reta) about a system parameter is represented by a subjective probability distribution. At the time when the dominant player is designing the supply or purchase contract, should the dominated player help the dominant player to improve his imperfect system-parameter knowledge? Can the dominant player induce the dominated player to share her superior knowledge by using (or by threatening to use) sophisticated “channel-coordinating” contract formats? It is likely that one would surmise from the literature that the answer to both questions is “yes”. However, this chapter shows that very often the correct answer is “no”. Specifically, for the basic cost and market parameters, we show that the dominated player is (1) always motivated to mislead the dominant player to have a biased mean value for his subjective distribution; and (2) motivated, over a wide range of likely conditions, to increase the variance of the dominant player’s subjective distribution. Moreover, the dominant player cannot narrow this range of confusion-encouraging conditions by using a more sophisticated contract format such as a “menu of contracts.” Our results highlight the need to develop arrangements that can actually motivate a dominated player to share knowledge honestly.