Advertisement

Autonomous Agents and Multi-Agent Systems

, Volume 28, Issue 6, pp 956–985 | Cite as

Multiagent resource allocation with sharable items

  • Stéphane AiriauEmail author
  • Ulle Endriss
Article

Abstract

We study a particular multiagent resource allocation problem with indivisible, but sharable resources. In our model, the utility of an agent for using a bundle of resources is the difference between the value the agent would assign to that bundle in isolation and a congestion cost that depends on the number of agents she has to share each of the resources in her bundle with. The valuation function determining the value and the delay function determining the congestion cost can be agent-dependent. When the agents that share a resource also share control over that resource, then the current users of a resource will require some compensation when a new agent wants to join them using the resource. For this scenario of shared control, we study the existence of distributed negotiation protocols that lead to a social optimum. Depending on constraints on the valuation functions (mainly modularity), on the delay functions (such as convexity), and on the structural complexity of the deals between agents, we prove either the existence of a sequences of deals leading to a social optimum or the convergence of all sequences of deals to such an optimum. We also analyse the length of the path leading to such optimal allocations. For scenarios where the agents using a resource do not have shared control over that resource (i.e., where any agent can use any resource she wants), we study the existence of pure Nash equilibria, i.e., allocations in which no single agent has an incentive to add or drop any of the resources she is currently holding. We provide results for modular valuation functions, we analyse the length of the paths leading to a pure Nash equilibrium, and we relate our findings to results from the literature on congestion games.

Keywords

Multiagent resource allocation Congestion games 

References

  1. 1.
    Ackermann, H., Röglin, H., & Vöcking, B. (2009). Pure Nash equilibria in player-specific and weighted congestion games. Theoretical Computer Science, 410(17), 1552–1563.CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    Airiau, S., & Endriss, U. (2010). Multiagent resource allocation with sharable items: Simple protocols and Nash equilibria. In Proceedings of the 9th international joint conference on autonomous agents and multiagent systems (AAMAS-2010) (pp. 167–174).Google Scholar
  3. 3.
    Bachrach, Y., & Rosenschein, J. S. (2008). Distributed multiagent resource allocation in diminishing marginal return domains. In Proceedings of the 7th international conference on autonomous agents and multiagent systems (AAMAS-2008).Google Scholar
  4. 4.
    Byde, A., Polukarov, M., & Jennings, N. R. (2009). Games with congestion-averse utilities. Proceedings of the 2nd international symposium on algorithmic game theory (SAGT-2009) (pp. 220–232). Berlin: Springer.CrossRefGoogle Scholar
  5. 5.
    Chevaleyre, Y., Dunne, P. E., Endriss, U., Lang, J., Lemaître, M., Maudet, N., et al. (2006). Issues in multiagent resource allocation. Informatica, 30, 3–31.zbMATHGoogle Scholar
  6. 6.
    Chevaleyre, Y., Endriss, U., Estivie, S., & Maudet, N. (2007). Reaching envy-free states in distributed negotiation settings. In Proceedings of the 20th international joint conference on artificial intelligence (IJCAI-2007).Google Scholar
  7. 7.
    Chevaleyre, Y., Endriss, U., & Maudet, N. (2010). Simple negotiation schemes for agents with simple preferences: Sufficiency, necessity and maximality. Journal of Autonomous Agents and Multiagent Systems, 20(2), 234–259.CrossRefGoogle Scholar
  8. 8.
    Cramton, P., Shoham, Y., & Steinberg, R. (2006). Combinatorial auctions. Cambridge, MA: MIT Press.zbMATHGoogle Scholar
  9. 9.
    Dunne, P. E. (2005). Extremal behaviour in multiagent contract negotiation. Journal of Artificial Intelligence Research, 23, 41–78.zbMATHMathSciNetGoogle Scholar
  10. 10.
    Dunne, P. E., & Chevaleyre, Y. (2008). The complexity of deciding reachability properties of distributed negotiation schemes. Theoretical Computer Science, 396(1–3), 113–144.CrossRefzbMATHMathSciNetGoogle Scholar
  11. 11.
    Dunne, P. E., Wooldridge, M., & Laurence, M. (2005). The complexity of contract negotiation. Artificial Intelligence, 164(1–2), 23–46.CrossRefzbMATHMathSciNetGoogle Scholar
  12. 12.
    Endriss, U., & Maudet, N. (2005). On the communication complexity of multilateral trading: Extended report. Journal of Autonomous Agents and Multiagent Systems, 11(1), 91–107.Google Scholar
  13. 13.
    Endriss, U., Maudet, N., Sadri, F., & Toni, F. (2003). On optimal outcomes of negotiations over resources. In Proceedings of the 2nd international joint conference on autonomous agents and multiagent systems (AAMAS-2003). New York: ACM Press.Google Scholar
  14. 14.
    Endriss, U., Maudet, N., Sadri, F., & Toni, F. (2006). Negotiating socially optimal allocations of resources. Journal of Artificial Intelligence Research, 25, 315–348.MathSciNetGoogle Scholar
  15. 15.
    Mas-Colell, A., Whinston, M. D., & Green, J. R. (1995). Microeconomic theory. New York: Oxford University Press.zbMATHGoogle Scholar
  16. 16.
    Milchtaich, I. (1996). Congestion games with player-specific payoff functions. Games and Economic Behavior, 13(1), 111–124.CrossRefzbMATHMathSciNetGoogle Scholar
  17. 17.
    Milchtaich, I. (2004). Social optimality and cooperation in nonatomic congestion games. Journal of Economic Theory, 114(1), 56–87.CrossRefzbMATHMathSciNetGoogle Scholar
  18. 18.
    Osborne, M. J., & Rubinstein, A. (1994). A course in game theory. Cambridge, MA: MIT Press.zbMATHGoogle Scholar
  19. 19.
    Penn, M., Polukarov, M., & Tennenholtz, M. (2009). Asynchronous congestion games. In M. Lipshteyn, V. Levit, & R. McConnell (Eds.), Graph theory, computational intelligence and thought. Lecture notes in computer science (Vol. 5420, pp. 41–53). Berlin: Springer.Google Scholar
  20. 20.
    Penn, M., Polukarov, M., & Tennenholtz, M. (2009). Congestion games with load-dependent failures: Identical resources. Games and Economic Behavior, 67(1), 156–173.CrossRefzbMATHMathSciNetGoogle Scholar
  21. 21.
    Rosenthal, R. W. (1973). A class of games possessing pure-strategy Nash equilibria. International Journal of Game Theory, 2(1), 65–67.CrossRefzbMATHMathSciNetGoogle Scholar
  22. 22.
    Saha, S., & Sen, S. (2007). An efficient protocol for negotiation over multiple indivisible resources. In Proceedings of the 20th international joint conference on artificial intelligence (IJCAI-2007) (pp. 1494–1499).Google Scholar
  23. 23.
    Sandholm, T. W. (1998). Contract types for satisficing task allocation: I Theoretical results. In Proceedings of the AAAI spring symposium: Satisficing models.Google Scholar
  24. 24.
    Shapley, L. S., & Monderer, D. (1996). Potential games. Games and Economic Behaviour, 14(1), 124–143.CrossRefzbMATHMathSciNetGoogle Scholar
  25. 25.
    Shapley, L. S., & Scarf, H. (1974). On core and indivisibility. Journal of Mathematical Economics, 1(1), 23–37.CrossRefzbMATHMathSciNetGoogle Scholar
  26. 26.
    Voice, T., Polukarov, M., Byde, A., & Jennings, N. R. (2009). On the impact of strategy and utility structures on congestion-averse games. In Proceedings of the 5th international workshop on Internet and network economics (WINE’09) (pp. 600–607).Google Scholar

Copyright information

© The Author(s) 2013

Authors and Affiliations

  1. 1.LAMSADEUniversité Paris DauphineParis Cedex 16France
  2. 2.Institute for Logic, Language, and ComputationUniversity of AmsterdamAmsterdamThe Netherlands

Personalised recommendations