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Network Cost-Sharing Games: Equilibrium Computation and Applications to Election Modeling

  • Rahul Swamy
  • Timothy Murray
  • Jugal Garg
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11346)

Abstract

We introduce and study a variant of network cost-sharing games with additional non-shareable costs (NCSG+), which is shown to possess a pure Nash equilibrium (PNE). We extend polynomial-time PNE computation results to a class of graphs that generalizes series-parallel graphs when the non-shareable costs are player-independent. Further, an election game model is presented based on an NCSG+ when voter opinions form natural discrete clusters. This model captures several variants of the classic Hotelling-Downs election model, including ones with limited attraction, ability of candidates to enter, change stance positions and exit any time during the campaign or abstain from the race, the restriction on candidates to access certain stance positions, and the operational costs of running a campaign. Finally, we provide a polynomial-time PNE computation for an election game when stance changes are restricted.

Keywords

Network cost-sharing game Nash equilibrium Hotelling-Downs 

References

  1. 1.
    Brill, M., Conitzer, V.: Strategic voting and strategic candidacy. In: AAAI (2015)Google Scholar
  2. 2.
    Brusco, S., Dziubiński, M., Roy, J.: The Hotelling-Downs model with runoff voting. Game Econ. Behav. 74(2), 447–469 (2012)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Ding, N., Lin, F.: On computing optimal strategies in open list proportional representation: the two parties case. In: AAAI (2014)Google Scholar
  4. 4.
    Downs, A.: Economic theory of political action in a democracy. J. Pol. Econ. 65(2), 135–150 (1957)CrossRefGoogle Scholar
  5. 5.
    Duggan, J., Fey, M.: Electoral competition with policy-motivated candidates. Games Econ. Behav. 51, 490–522 (2005)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Feldman, M., Fiat, A., Obraztsova, S.: Variations on the Hotelling-Downs model. In: AAAI (2016)Google Scholar
  7. 7.
    Feldotto, M., Leder, L., Skopalik, A.: Congestion games with mixed objectives. In: Chan, T.-H.H., Li, M., Wang, L. (eds.) COCOA 2016. LNCS, vol. 10043, pp. 655–669. Springer, Cham (2016).  https://doi.org/10.1007/978-3-319-48749-6_47CrossRefGoogle Scholar
  8. 8.
    Fotakis, D., Kontogiannis, S., Spirakis, P.: Symmetry in network congestion games: pure equilibria and anarchy cost. In: Erlebach, T., Persinao, G. (eds.) WAOA 2005. LNCS, vol. 3879, pp. 161–175. Springer, Heidelberg (2006).  https://doi.org/10.1007/11671411_13CrossRefzbMATHGoogle Scholar
  9. 9.
    Funk, C., Rainie, L.: Climate change and energy issues. Pew Research Center (2015)Google Scholar
  10. 10.
    Hotelling, H.: Stability in competition. Econ. J. 39(153), 41–57 (1929)CrossRefGoogle Scholar
  11. 11.
    Kallenbach, J., Kleinberg, R., Kominers, S.D.: Orienteering for electioneering. Oper. Res. Lett. 46, 205–210 (2018)MathSciNetCrossRefGoogle Scholar
  12. 12.
    McKelvey, R.D., Wendell, R.E.: Voting equilibria in multidimensional choice spaces. Math. Oper. Res. 1(2), 144–158 (1976)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Obraztsova, S., Elkind, E., Polukarov, M., Rabinovich, Z.: Strategic candidacy games with lazy candidates. In: IJCAI, pp. 610–616 (2015)Google Scholar
  14. 14.
    Osborne, M.J.: Candidate positioning and entry in a political competition. Games Econ. Behav. 5(1), 133–151 (1993)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Rosenthal, R.W.: A class of games possessing pure-strategy Nash equilibria. Int. J. Game Theory 2(1), 65–67 (1973)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Sabato, I., Obraztsova, S., Rabinovich, Z., Rosenschein, J.S.: Real candidacy games: A new model for strategic candidacy. In: AAMAS, pp. 867–875 (2017)Google Scholar
  17. 17.
    Sengupta, A., Sengupta, K.: A Hotelling-Downs model of electoral competition with the option to quit. Games Econ. Behav. 62(2), 661–674 (2008)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Shen, W., Wang, Z.: Hotelling-Downs model with limited attraction. In: AAMAS (2016)Google Scholar
  19. 19.
    Syrgkanis, V.: The complexity of equilibria in cost sharing games. In: Saberi, A. (ed.) WINE 2010. LNCS, vol. 6484, pp. 366–377. Springer, Heidelberg (2010).  https://doi.org/10.1007/978-3-642-17572-5_30CrossRefGoogle Scholar
  20. 20.
    Takamizawa, K., Nishizeki, T., Saito, N.: Linear-time computability of combinatorial problems on series-parallel graphs. J. ACM 29(3), 623–641 (1982)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.University of Illinois at Urbana-ChampaignUrbanaUSA

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