### Abstract

Defining the dilemma game by the proposition, A game cannot sustain an increase of cooperation strategy in its strategy distribution, we deduced that the substance of a dilemma can be expressed by a productive summation of the static factor and the dynamic factor independently. A static factor is an element of the game's structure that influences a possible dilemma, which relates to a game's structural deviation from a situation where the cooperation strategy can be weakly dominant over other strategies. In contrast, a dynamic factor refers to a strategy distribution's influence on the dilemma by affecting the game dynamics. In a 2 × 2 game, the existence of a dilemma can be determined only by a static factor. That is, whether or not a dilemma occurs is related only to the structural effect of the game. On the other hand, in a more-than-two-strategies game, both static and dynamic factors determine the occurrence of a dilemma, and the static factor cannot solely explain the occurrence of a dilemma.

Original language | English |
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Pages (from-to) | 105-114 |

Number of pages | 10 |

Journal | BioSystems |

Volume | 90 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jul 1 2007 |

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### All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Modelling and Simulation
- Biochemistry, Genetics and Molecular Biology(all)
- Applied Mathematics

### Cite this

**Relationship between dilemma occurrence and the existence of a weakly dominant strategy in a two-player symmetric game.** / Tanimoto, Jun; Sagara, Hiroki.

Research output: Contribution to journal › Article

*BioSystems*, vol. 90, no. 1, pp. 105-114. https://doi.org/10.1016/j.biosystems.2006.07.005

}

TY - JOUR

T1 - Relationship between dilemma occurrence and the existence of a weakly dominant strategy in a two-player symmetric game

AU - Tanimoto, Jun

AU - Sagara, Hiroki

PY - 2007/7/1

Y1 - 2007/7/1

N2 - Defining the dilemma game by the proposition, A game cannot sustain an increase of cooperation strategy in its strategy distribution, we deduced that the substance of a dilemma can be expressed by a productive summation of the static factor and the dynamic factor independently. A static factor is an element of the game's structure that influences a possible dilemma, which relates to a game's structural deviation from a situation where the cooperation strategy can be weakly dominant over other strategies. In contrast, a dynamic factor refers to a strategy distribution's influence on the dilemma by affecting the game dynamics. In a 2 × 2 game, the existence of a dilemma can be determined only by a static factor. That is, whether or not a dilemma occurs is related only to the structural effect of the game. On the other hand, in a more-than-two-strategies game, both static and dynamic factors determine the occurrence of a dilemma, and the static factor cannot solely explain the occurrence of a dilemma.

AB - Defining the dilemma game by the proposition, A game cannot sustain an increase of cooperation strategy in its strategy distribution, we deduced that the substance of a dilemma can be expressed by a productive summation of the static factor and the dynamic factor independently. A static factor is an element of the game's structure that influences a possible dilemma, which relates to a game's structural deviation from a situation where the cooperation strategy can be weakly dominant over other strategies. In contrast, a dynamic factor refers to a strategy distribution's influence on the dilemma by affecting the game dynamics. In a 2 × 2 game, the existence of a dilemma can be determined only by a static factor. That is, whether or not a dilemma occurs is related only to the structural effect of the game. On the other hand, in a more-than-two-strategies game, both static and dynamic factors determine the occurrence of a dilemma, and the static factor cannot solely explain the occurrence of a dilemma.

UR - http://www.scopus.com/inward/record.url?scp=34447096355&partnerID=8YFLogxK

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U2 - 10.1016/j.biosystems.2006.07.005

DO - 10.1016/j.biosystems.2006.07.005

M3 - Article

VL - 90

SP - 105

EP - 114

JO - BioSystems

JF - BioSystems

SN - 0303-2647

IS - 1

ER -