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Direct Sum Matrix Game with Prisoner's Dilemma and Snowdrift Game

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  • Chengzhang Ma
  • Wei Cao
  • Wangheng Liu
  • Rong Gui
  • Ya Jia

Abstract

A direct sum form is proposed for constructing a composite game from two games, prisoner's dilemma and snowdrift game. This kind of direct sum form game is called a multiple roles game. The replicator dynamics of the multiple roles game with will-mixed populations is explored. The dynamical behaviors on square lattice are investigated by numerical simulation. It is found that the dynamical behaviors of population on square lattice depend on the mixing proportion of the two simple games. Mixing SD activities to pure PD population inhibits the proportion of cooperators in PD, and mixing PD activities to pure SD population stimulates the proportion of cooperators in SD. Besides spatial reciprocity, our results show that there are roles reciprocities between different types of individuals.

Suggested Citation

  • Chengzhang Ma & Wei Cao & Wangheng Liu & Rong Gui & Ya Jia, 2013. "Direct Sum Matrix Game with Prisoner's Dilemma and Snowdrift Game," PLOS ONE, Public Library of Science, vol. 8(12), pages 1-7, December.
  • Handle: RePEc:plo:pone00:0081855
    DOI: 10.1371/journal.pone.0081855
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    References listed on IDEAS

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    1. Yongkui Liu & Xiaojie Chen & Lin Zhang & Long Wang & Matjaž Perc, 2012. "Win-Stay-Lose-Learn Promotes Cooperation in the Spatial Prisoner's Dilemma Game," PLOS ONE, Public Library of Science, vol. 7(2), pages 1-8, February.
    2. Hisashi Ohtsuki & Christoph Hauert & Erez Lieberman & Martin A. Nowak, 2006. "A simple rule for the evolution of cooperation on graphs and social networks," Nature, Nature, vol. 441(7092), pages 502-505, May.
    3. Martin A. Nowak & Karl Sigmund, 1998. "Evolution of indirect reciprocity by image scoring," Nature, Nature, vol. 393(6685), pages 573-577, June.
    4. Schlag, Karl H., 1998. "Why Imitate, and If So, How?, : A Boundedly Rational Approach to Multi-armed Bandits," Journal of Economic Theory, Elsevier, vol. 78(1), pages 130-156, January.
    5. M.A. Nowak & K. Sigmund, 1998. "Evolution of Indirect Reciprocity by Image Scoring/ The Dynamics of Indirect Reciprocity," Working Papers ir98040, International Institute for Applied Systems Analysis.
    6. Helbing, Dirk, 1992. "Interrelations between stochastic equations for systems with pair interactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 181(1), pages 29-52.
    7. Martin A. Nowak & Karl Sigmund, 2005. "Evolution of indirect reciprocity," Nature, Nature, vol. 437(7063), pages 1291-1298, October.
    8. Schlag, Karl H., 1998. "Why Imitate, and If So, How?, : A Boundedly Rational Approach to Multi-armed Bandits," Journal of Economic Theory, Elsevier, vol. 78(1), pages 130-156, January.
    9. Christoph Hauert & Michael Doebeli, 2004. "Spatial structure often inhibits the evolution of cooperation in the snowdrift game," Nature, Nature, vol. 428(6983), pages 643-646, April.
    10. Xiaojie Chen & Yongkui Liu & Yonghui Zhou & Long Wang & Matjaž Perc, 2012. "Adaptive and Bounded Investment Returns Promote Cooperation in Spatial Public Goods Games," PLOS ONE, Public Library of Science, vol. 7(5), pages 1-8, May.
    11. Arnon Lotem & Michael A. Fishman & Lewi Stone, 1999. "Evolution of cooperation between individuals," Nature, Nature, vol. 400(6741), pages 226-227, July.
    12. Shijun Wang & Máté S Szalay & Changshui Zhang & Peter Csermely, 2008. "Learning and Innovative Elements of Strategy Adoption Rules Expand Cooperative Network Topologies," PLOS ONE, Public Library of Science, vol. 3(4), pages 1-9, April.
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