Dynamic Noncooperative Group Formation with Size Advantage and Group Reputation

Abstract

We analyze a noncooperative dynamic game of group formation with group reputation. It is inspired by observations of adoption patterns in some retail markets. Firms are partitioned into name groups, or affiliation networks, in each period. In a group, all firms share the same group reputation among consumers. After a failed firm exits, an entrant firm chooses which name to adopt or to create a new name. There is no cost of choosing any name, but group size and history matter. Existing firms cannot change names nor prevent an entrant from joining their group, and thus the name choice at the time of entry is a long-term choice.Consumers observe only failure events and not firm actions. Every period there is a small turnover of consumers and newcomers do not have information about group histories. If firm groups have the same record to a consumer, larger groups are much more attractive than smaller groups, which we model as following Lanchester's Square Law (Lanchester, 1916).Empirical patterns show synergy effects: entrants tend to choose one of the existing names, and particularly the biggest untainted name. Second biggest group is not chosen when the biggest group is untainted.We found that, in customer-efficient equilibria, where firm failures are rare because all firms make effort constantly, new name creation does not occur when there is an untainted name group to join. However, a universal name group (that all firms have the same name) is not an absorbing state. Eventually there is a failure and after that a creation of a new name occurs. These are consistent with the empirical patterns. The dynamic process of group structure is recurrent among two name groups and a universal name group, in our stationary size market.