Pair Formation within Multi-Agent Populations

We present a simple model for the formation of pairs in multi-agent populations of type A and B which move freely on a spatial network. Each agent of population A (and B) is labeled as Ai (and Bj) with i = 1, . . . , NA (and j = 1, . . . , NB) and carries its own individual list of characteristics or ‘phenotype’. When agents from opposite populations encounter one another on the network, they can form a relationship if not already engaged in one. The length of time for which any given pair stays together depends on the compatibility of the two constituent agents. Possible applications include the human dating scenario, and the commercial domain where two types of businesses A and B have members of each type looking for a business partner, i.e. Ai+Bj → Rij. The pair Rij then survives for some finite time before dissociating Rij → Ai +Bj. There are many possible generalizations of this basic setup. Here we content ourselves with some initial numerical results for the simplest of network topologies, together with some accompanying analytic analysis.