Stable Farsighted Coalitions in Competitive Markets

Abstract

In this paper, we study dynamic alliance formation among agents in competitive markets. We look at n agents selling substitutable products competing in a market. In this setting, we look at models with deterministic as well as stochastic demand, and use a two stage approach. In Stage 1, agents form alliances (coalitions), and in Stage 2, coalitions make decisions (price and inventory) and compete against each other. Stage 2 is modeled as a competitive game. In Stage 1, to analyze the stability of coalition structures, we use two notions from cooperative games - the Largest Consistent Set (LCS) and the Equilibrium Process of Coalition Formation (EPCF). These two notions allow players to be farsighted. While intuition would suggest that an alliance structure from which a defecting coalition may benefit is not stable, we show that this is not necessarily the case when the agents consider possible reactions of others to their actions. In particular, one such example is that of the grand coalition, which we show to be stable in the farsighted sense, even though players benefit myopically by defecting from it. This intuition can be valuable to firms contemplating strategic alliances with partners in a competitive market. We are also able to characterize some additional stable coalition outcomes. Using these characterizations, we are able to derive some intuition on the impact of the size of the market (n), the degree of competition, the effect of cost parameters, and the variability of the demand process on the prices, inventory levels, and structure of the market. We discuss the possible strategic implications of our results to firms in a competitive market and to new entrants.

Keywords: Coalitions, cooperative games, coalition stability

JEL Classification: C71