Abstract

In this paper, we extend the notion of person-by-person (pbp) 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 submodularity. We also generalize the concept of pbp optimization to the case where groups of $m$ decisions makers make joint decisions sequentially, which we refer to as $m$b$m$ optimization. The main contribution is a description of sufficient conditions, verifiable in polynomial time, under which a pbp or an $m$b$m$ optimization algorithm converges to the team-optimum. As a second contribution, we present a local and greedy algorithm characterized by approximate decision strategies (i.e., strategies based on a local state vector) that return the same decisions as in the complete information framework (where strategies are based on full state vector). As a last contribution, we also show that there exists a subclass of submodular team problems, recognizable in polynomial time, for which the pbp optimization converges for at least an opportune initialization of the algorithm.

Keywords

  1. team theory
  2. person-by-person optimality
  3. approximation algorithms

MSC codes

  1. 93A14
  2. 68W15
  3. 90C59
  4. 90C20
  5. 91AXX

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Published In

cover image SIAM Journal on Control and Optimization
SIAM Journal on Control and Optimization
Pages: 3011 - 3028
ISSN (online): 1095-7138

History

Submitted: 1 September 2009
Accepted: 10 August 2012
Published online: 2 October 2012

Keywords

  1. team theory
  2. person-by-person optimality
  3. approximation algorithms

MSC codes

  1. 93A14
  2. 68W15
  3. 90C59
  4. 90C20
  5. 91AXX

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