When selfish is socially optimal

Petros G. Voulgaris, Nicola Elia

Research output: Contribution to journalArticlepeer-review


In this paper, we consider cooperative multi-agent systems, where independent agents need to minimize a collective social cost. Given the coupling in the cost, the optimal strategy requires interaction and communications among all the agents in general. In this paper, we unveil important classes of social costs which are optimized by decentralized and selfish solutions, hence eliminating the need for an inter-agent communication network. In particular, we focus on a set of n independent agents coupled only through an overall cost that penalizes the divergence of each agent from the average collective behavior. Adopting input-output methods, we show that optimal decentralized and selfish solutions are possible in a variety of standard input-output cost criteria. These include the cases of l_1, l_2, l_infty induced, and H2 norms for any finite n. Moreover, if the cost includes nondeviation from average variables, the above results hold true as well for l_1, l_2, l_infty induced norms and any n, while they hold true for the normalized, per-agent square H2 norm, cost as n ! 1. The results of the paper demonstrate that selfish behavior can be socially optimal in nontr

Original languageEnglish (US)
JournalIEEE Transactions on Automatic Control
StatePublished - Jan 1 2021

Bibliographical note

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  • Cost function
  • Couplings
  • Decentralized Control
  • Manganese
  • Mean Field Control
  • Networked Control
  • State feedback
  • Uncertainty
  • Urban areas
  • US Government


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