Team Theory and Person-by-Person Optimization with Binary Decisions

In this paper, we extend the notion of person by person optimization to binary decision spaces. The novelty of our approach is the adaptation to a dynamic team context of notions borrowed from the pseudo-boolean optimization field as completely local-global or unimodal functions and sub-modularity. We also generalize the concept of pbp optimization to the case where the Decision Makers (DMs) make decisions sequentially in groups of m, we call it mbm optimization. The main contribution are certain sufficient conditions, verifiable in polynomial time, under which a pbp or an mbm optimization algorithm leads to the team-optimum. As a second contribution, we present a local and greedy algorithm that allows the DMs to select a small neighborhood which guarantees them to behave as if they had complete information. As a last contribution, we also show that there exists a subclass of sub-modular team problems, recognizable in polynomial time, for which the convergence is guaranteed if the pbp algorithm is opportunely initialized.