Farsighted Clustering with Group-Size Effects and Reputations

We formulate a new model of strategic group formation by farsighted players in a seller–buyer setting. In each period, sellers are partitioned into groups/brands. At the end of each period, one seller may fail and exit the market by exogenous shock. When there is a vacant slot in the market, an entrant seller comes and chooses which existing group to join or to create a new group. There is a trade-off: larger groups enjoy more-than-proportional benefits of group size thanks to, for example, their visibility to attract customers and their negotiation power in factor markets. However, larger groups are more likely to experience member failure, which is a reputation loss. We find that when the rate of reputation loss is small, clustering is inevitable, but as the rate of reputation loss increases, the largest group with a bad reputation does not attract an entrant, dissolving a cluster. With a limited group-size benefit and a high rate of reputation loss, all entrants create a new group; that is, no clustering occurs. A mathematically interesting result is that, even though the model itself is stationary and symmetric, depending on the parameters, there may be multiple pure-strategy, symmetric stationary equilibria, or there may be no such equilibrium. The economic implications include that group reputation may prevent clustering and that similar markets can have different cluster structures.