Staffing problems with local network externalities

This study examines how an organization assigns agents to interactive jobs embedded in a network. We employ a two-stage linear quadratic game with local complementarities, in which the underlying network represents the interrelated jobs that an organization seeks for staff. Under the assumption that employees have heterogeneous abilities, the organization assigns individuals to jobs in an attempt to maximize aggregate effort or aggregate payoff. Two problems are considered when maximizing the total effort. First, we assume that each agent’s ability is single dimensional and show that the planner should match the ordinal ranking of an agent’s ability level to the job indexed by the same ordinal level in the centrality ranking. Second, we assume that agents are experts in different jobs, implying that each agent’s ability is multidimensional. We show that the optimal staffing problem is essentially an assignment problem that can be solved by the Hungarian algorithm in polynomial time. Finally, we consider an optimal staffing scenario to maximize the total payoff. Finding all permutations of n agents has high computation time complexity. To solve this problem, we design a heuristic algorithm.