### Abstract

We report computer simulation experiments based on our agent-based simulation tool to model a new N-per-son game based on John Conway's Game of Life. The individual agents may choose between two behavior options: cooperation or defection. The payoff (reward/penalty) functions are given as two parabolas: one for each option. After a certain number of iterations, the behavior of the agents stabilizes to either a constant value or oscillates around such a value. The simulation's goal is to investigate the effects of intermediate behavior on a society of agents. We have performed a systematic investigation of this game for all six possible cases of the mutual positions of parabolic payoff functions crossing each other at two points: x 5 0.3 and 0.7 where x is the ratio of the cooperation choice to the total number of agents in the agent's neighborhood. The global ratios X(t) of the total number of cooperators in the entire array of agents as functions of time (itera-tions) and the solutions of the game X_{final} as functions of X_{0} were observed for each case for Pavlovian, greedy, and conformist agents. The solutions have predictable tendencies only when the neighborhood is the entire array of greedy or conformist agents. In all other cases unexpected properties emerge.

Original language | English (US) |
---|---|

Pages (from-to) | 50-60 |

Number of pages | 11 |

Journal | Complexity |

Volume | 15 |

Issue number | 3 |

DOIs | |

State | Published - Jan 2010 |

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### Keywords

- Agent-based simulation
- Cooperation
- Game of life
- N-person games

### ASJC Scopus subject areas

- General

### Cite this

*Complexity*,

*15*(3), 50-60. https://doi.org/10.1002/cplx.20289

**Agent-based simulation of an n-person game with parabolic payoff functions.** / Szilagyi, Miklos N; Somogyi, Iren.

Research output: Contribution to journal › Article

*Complexity*, vol. 15, no. 3, pp. 50-60. https://doi.org/10.1002/cplx.20289

}

TY - JOUR

T1 - Agent-based simulation of an n-person game with parabolic payoff functions

AU - Szilagyi, Miklos N

AU - Somogyi, Iren

PY - 2010/1

Y1 - 2010/1

N2 - We report computer simulation experiments based on our agent-based simulation tool to model a new N-per-son game based on John Conway's Game of Life. The individual agents may choose between two behavior options: cooperation or defection. The payoff (reward/penalty) functions are given as two parabolas: one for each option. After a certain number of iterations, the behavior of the agents stabilizes to either a constant value or oscillates around such a value. The simulation's goal is to investigate the effects of intermediate behavior on a society of agents. We have performed a systematic investigation of this game for all six possible cases of the mutual positions of parabolic payoff functions crossing each other at two points: x 5 0.3 and 0.7 where x is the ratio of the cooperation choice to the total number of agents in the agent's neighborhood. The global ratios X(t) of the total number of cooperators in the entire array of agents as functions of time (itera-tions) and the solutions of the game Xfinal as functions of X0 were observed for each case for Pavlovian, greedy, and conformist agents. The solutions have predictable tendencies only when the neighborhood is the entire array of greedy or conformist agents. In all other cases unexpected properties emerge.

AB - We report computer simulation experiments based on our agent-based simulation tool to model a new N-per-son game based on John Conway's Game of Life. The individual agents may choose between two behavior options: cooperation or defection. The payoff (reward/penalty) functions are given as two parabolas: one for each option. After a certain number of iterations, the behavior of the agents stabilizes to either a constant value or oscillates around such a value. The simulation's goal is to investigate the effects of intermediate behavior on a society of agents. We have performed a systematic investigation of this game for all six possible cases of the mutual positions of parabolic payoff functions crossing each other at two points: x 5 0.3 and 0.7 where x is the ratio of the cooperation choice to the total number of agents in the agent's neighborhood. The global ratios X(t) of the total number of cooperators in the entire array of agents as functions of time (itera-tions) and the solutions of the game Xfinal as functions of X0 were observed for each case for Pavlovian, greedy, and conformist agents. The solutions have predictable tendencies only when the neighborhood is the entire array of greedy or conformist agents. In all other cases unexpected properties emerge.

KW - Agent-based simulation

KW - Cooperation

KW - Game of life

KW - N-person games

UR - http://www.scopus.com/inward/record.url?scp=73349093131&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=73349093131&partnerID=8YFLogxK

U2 - 10.1002/cplx.20289

DO - 10.1002/cplx.20289

M3 - Article

AN - SCOPUS:73349093131

VL - 15

SP - 50

EP - 60

JO - Complexity

JF - Complexity

SN - 1076-2787

IS - 3

ER -