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Testing Core Membership in Public Goods Economies

Author Greg Bodwin



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Greg Bodwin

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Greg Bodwin. Testing Core Membership in Public Goods Economies. In 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 80, pp. 45:1-45:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2017)
https://doi.org/10.4230/LIPIcs.ICALP.2017.45

Abstract

This paper develops a recent line of economic theory seeking to understand public goods economies using methods of topological analysis. Our first main result is a very clean characterization of the economy's core (the standard solution concept in public goods). Specifically, we prove that a point is in the core iff it is Pareto efficient, individually rational, and the set of points it dominates is path connected. While this structural theorem has a few interesting implications in economic theory, the main focus of the second part of this paper is on a particular algorithmic application that demonstrates its utility. Since the 1960s, economists have looked for an efficient computational process that decides whether or not a given point is in the core. All known algorithms so far run in exponential time (except in some artificially restricted settings). By heavily exploiting our new structure, we propose a new algorithm for testing core membership whose computational bottleneck is the solution of O(n) convex optimization problems on the utility function governing the economy. It is fairly natural to assume that convex optimization should be feasible, as it is needed even for very basic economic computational tasks such as testing Pareto efficiency. Nevertheless, even without this assumption, our work implies for the first time that core membership can be efficiently tested on (e.g.) utility functions that admit ``nice'' analytic expressions, or that appropriately defined epsilon-approximate versions of the problem are tractable (by using modern black-box epsilon-approximate convex optimization algorithms).
Keywords
  • Algorithmic Game Theory
  • Economics
  • Algorithms
  • Public Goods
  • Coalitional Stability

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References

  1. N. Allouch. The cost of segregation in social networks. Queen Mary Working Paper, 2013. Google Scholar
  2. N. Allouch. On the private provision of public goods on networks. Journal of Economic Theory, pages 527-552, 2015. Google Scholar
  3. C. Ballester, A. Calvó-Armengol, and Y. Zenou. Who’s who in networks. wanted: The key player. Econometrica, 74:1403-1417, 2006. Google Scholar
  4. Y. Bramoulle and R. Kranton. Public goods in networks. Journal of Economic Theory, 135:478-494, 2007. Google Scholar
  5. Parkash Chander and Henry Tulkens. The core of an economy with multilateral environmental externalities. International Journal of Game Theory, 26:379-401, 1997. Google Scholar
  6. V. Conitzer and T. Sandholm. Computing shapley values, manipulating value division schemes, and checking core membership in multi-issue domains. In Proc. National Conference on Artificial Intelligence (AAAI), pages 219-225, 2004. Google Scholar
  7. V. Conitzer and T. Sandholm. Complexity of constructing solutions in the core based on synergies among coalitions. Artificial Intelligence, pages 607-–619, 2006. Google Scholar
  8. Imma Curriel. Cooperative Game Theory and Applications. Springer US, 1 edition, 1997. Google Scholar
  9. X. Deng and C. Papadimitriou. On the complexity of cooperative solution concepts. Mathematics of Operations Research, 19:257, 1994. Google Scholar
  10. F. Y. Edgeworth. Mathematical psychics: An essay on the mathematics to the moral sciences. Reprinted in Diamond, M.A., 1881. Google Scholar
  11. E. Elkind, L. A. Goldberg, P. W. Goldberg, and M. Wooldridge. A tractable and expressive class of marginal contribution nets and its applications. Math. Log. Q., 2009. Google Scholar
  12. Matthew Elliot and Benjamin Golub. A network approach to public goods. In Proc. 14th Electronic Commerce (EC), pages 377-378, 2013. Google Scholar
  13. U. Faigle, S. Fekete, W. Hochstattler, and W. Kern. On the complexity of testing membership in the core of min-cost spanning trees. Internat. J. Game Theory, 26:361-–366, 1997. Google Scholar
  14. D. K. Foley. Lindahl’s solution and the core of an economy with public goods. Econometrica, 38:66-72, 1970. Google Scholar
  15. D. B. Gillies. Solutions to general non-zero-sum games. Contributions to the Theory of Games IV, pages 47-85, 1959. Google Scholar
  16. M. Goemans and M. Skutella. Cooperative facility location games. In Symposium on Discrete Algorithms (SODA), pages 76-85, 2000. Google Scholar
  17. Benjamin Golub. Personal correspondence, 2012. Google Scholar
  18. G. Greco, E. Malizia, L. Palopoli, and F. Scarcello. On the complexity of the core over coalition structures. In International Joint Conference on Artificial Intelligence (IJCAI), 2011. Google Scholar
  19. S. Ieong and Y. Shoham. Marginal contribution nets: A compact representation scheme for coalitional games. In Electronic Commerce (EC), pages 193-202, 2005. Google Scholar
  20. S. Kintali, L. Poplawski, R. Rajaraman, R. Sundaram, and S. Teng. Reducibility among fractional stability problems. In Proc. 50th FOCS, pages 283-292, 2009. Google Scholar
  21. Jonathan Lewin. An interactive introduction to mathematical analysis. Cambridge University Press, 2003. Google Scholar
  22. Y. Li and V. Conitzer. Complexity of stability-based solution concepts in multi-issue and mc-net cooperative games. In Proc. 2014 international conference on Autonomous agents and multi-agent systems (AAMAS). International Foundation for Autonomous Agents and Multiagent Systems, 2014. Google Scholar
  23. Bezalel Peleg and Peter Sudhölter. Introduction to the Theory of Cooperative Games. Springer, 2 edition, 10 2007. Google Scholar
  24. Paul Samuelson. The pure theory of public expenditure. Review of Economics and Statistics, 37(4):350-356, 1954. Google Scholar
  25. H. Scarf. The core of an n person game. Econometrica, 1967. Google Scholar
  26. S. Sung and D. Dimitrov. On core membership testing for hedonic coalition formation games. Operations Research Letters, 35:155-158, 2007. Google Scholar
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