Price Competition in the Presence of Social Comparison and Demand Uncertainty

Does the social comparison still intensify the competition among sellers in volatile markets? In this paper, we study the price competition in markets with volatile sizes and, importantly, with sellers that socially compare their profits with each other ex post for any realization of market sizes. While the classic social comparison theory, as well as conventional wisdom, has long suggested that the comparison behavior such as behind aversion (upward comparison) and ahead seeking (downward comparison) will intensify competition, we reveal how social comparisons can totally have opposite-directional impacts once interacting with the market variability. In particular, we show that a stronger behind aversion behavior will still intensify the price competition, yet somewhat surprisingly, the impact of ahead seeking is variability-dependent: there is a threshold on the market size variability such that the competition between sellers will, in fact, be softened if markets are more volatile than such a threshold, and vice versa. Interestingly, the aforementioned predictions go in the other direction when sellers are selling complementary products: we will have the impacts of behind aversion variability-dependent while the ahead seeking is always pro-competitive. Our insights are robust under a general demand structure and demand shock specifications, asymmetry in sellers and markets, and sellers' misperceptions in market variabilities. Our work sheds light on other interactions of strategic complements or substitutes in the presence of social comparisons, e.g., quantity competition and advertising competition