Spatial reciprocity for discrete, continuous and mixed strategy setups

Satoshi Kokubo, Zhen Wang, Jun Tanimoto

Research output: Contribution to journalArticlepeer-review

36 Citations (Scopus)


The existence of cooperation in the social dilemma has been extensively studied based on spatial structure populations, namely, the so-called spatial reciprocity. However, vast majority of existing works just simply presume that agents can offer the discrete choice: either the cooperative (C) or defective (D) strategy, which, to some extent, seems unrealistic in the empirical observations since actual options might be continuous, mixed rather than discrete. Here, we propose discrete, continuous and mixed strategy setups in the social dilemma games and further explore their performance on network populations. Interestingly, it is unveiled that there is actually considerable inconsistency in terms of equilibrium among different strategy games. Furthermore, we reveal how different cooperative arrangements among these three strategy setups can be established, depending on whether the presumed dilemma subclass is a boundary game between prisoner's dilemma game and Chicken game or between prisoner's dilemma game and Stag-Hunt game.

Original languageEnglish
Pages (from-to)552-568
Number of pages17
JournalApplied Mathematics and Computation
Publication statusPublished - May 15 2015

All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Applied Mathematics


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