The Search for Coalition Formation in Costly Environments

We study the dynamics of forming coalitions of self-interested autonomous buyer agents, for the purpose of obtaining a volume discount. In our model, agents, representing coalitions of various sizes, may choose to be acquainted with other agents, hopefully ending up with a joint coalition structure, which will improve the overall price. Upon encountering potential partnering opportunities for extended coalitions, the agent needs to decide whether to accept or reject them. Each coalition partnership encapsulates expected benefit for the agent; however the process of finding a potential partner is associated with a cost. We explore the characteristics of the agent’s optimal strategies in the equilibrium and develop the equations from which these strategies can be derived. Efficient algorithms are suggested for a specific size-two variant of the problem, in order to demonstrate how each agent’s computation process can be significantly improved. These algorithms will be used as an infrastructure from which the general case algorithms can be extracted.