Directed Matching with Endogenous Markov Probability: Clients or Competitors?

We analyze the problem of strategic poaching of consultants by clients with particular reference to the business consulting industry. This article presents a market equilibrium in a mixed economy where three categories of agents, consulting groups, client firms and consultants strategically interact with each other. At each date the consulting group faces a new client firm that requires a task to be implemented. We show that under very general conditions, when a matching pair of clients and consultants meets, a dominant strategy will be played, where the consultant is captured by the client and the consulting group matches (whenever possible) the client's request. The novelty of this model is that the quality of the consulting services does not only depend on the consulting group's assignment strategy , but also on the capturing behavior of the clients. In this sense, the clients impose a consumption externality on each other, which is a source of inefficiency in this otherwise competitive market.