Optim Lett (2011) 5:333–346 DOI 10.1007/s11590-010-0213-y ORIGINAL PAPER Team optimization problems with Lipschitz continuous strategies Giorgio Gnecco · Marcello Sanguineti Received: 10 October 2009 / Accepted: 14 June 2010 / Published online: 1 July 2010 © Springer-Verlag 2010 Abstract Sufficient conditions for the existence and Lipschitz continuity of optimal strategies for static team optimization problems are studied. Revised statements and proofs of some results appeared in the literature are presented. Their extensions are discussed. As an example of application, optimal production in a multidivisional firm is considered. Keywords Statistical information structure · Team utility function · Value of a team · Optimal production in a firm 1 Introduction In team optimization problems, a group of decision makers (DMs), each having at disposal some information and various possibilities of decisions, aims at maximizing a common goal, expressed via a team utility function. Each DM takes a decision as a function, called strategy, of its available information. In the model that we adopt in this paper, the information is expressed via a probability density function, so we have a statistical information structure [14, Chapter 3]. We consider static team optimization The authors were partially supported by a grant “Progetti di Ricerca di Ateneo 2008” of the University of Genoa, project “Solution of Functional Optimization Problems by Nonlinear Approximators and Learning from Data”. G. Gnecco · M. Sanguineti (B ) Department of Communications, Computer, and System Sciences (DIST), University of Genoa, Via Opera Pia 13, 16145 Genova, Italy e-mail: marcello@dist.unige.it G. Gnecco e-mail: giorgio.gnecco@dist.unige.it 123