### Abstract

We propose a mathematical model of economic agents to study origin of money. This multi-agent model is based on commodity theory of money, which says that a commodity used as money emerges from barter transaction. Each agent has a different value system which is given by a Heyting algebra, and exchanges one's commodities based on the value system. In each value system, necessity and unnecessity of commodities are expressed by some elements and their compliments on a Heyting Algebra. Moreover, the concept of the compliment is extended. Consequently, the duality of the necessity-unnecessity is weakened, and the exchanges of the commodities are promoted. The commodities which keeps being exchanged for a long time can correspond to money.

Original language | English |
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Title of host publication | AIP Conference Proceedings |

Pages | 380-389 |

Number of pages | 10 |

Volume | 1051 |

DOIs | |

Publication status | Published - 2008 |

Externally published | Yes |

Event | 8th International Conference on Computing Anticipatory Systems, CASYS'07 - Liege Duration: 2007 Aug 6 → 2007 Aug 11 |

### Other

Other | 8th International Conference on Computing Anticipatory Systems, CASYS'07 |
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City | Liege |

Period | 07/8/6 → 07/8/11 |

### Fingerprint

### Keywords

- Barter exchange
- Heyting algebra
- Internal measurement
- Multi-agent
- Theory of money

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*AIP Conference Proceedings*(Vol. 1051, pp. 380-389) https://doi.org/10.1063/1.3020678

**Origin of money : Dynamic duality between necessity and unnecessity.** / Tauchi, Yuka; Kamiura, Moto; Haruna, Taichi; Gunji, Yukio.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*AIP Conference Proceedings.*vol. 1051, pp. 380-389, 8th International Conference on Computing Anticipatory Systems, CASYS'07, Liege, 07/8/6. https://doi.org/10.1063/1.3020678

}

TY - GEN

T1 - Origin of money

T2 - Dynamic duality between necessity and unnecessity

AU - Tauchi, Yuka

AU - Kamiura, Moto

AU - Haruna, Taichi

AU - Gunji, Yukio

PY - 2008

Y1 - 2008

N2 - We propose a mathematical model of economic agents to study origin of money. This multi-agent model is based on commodity theory of money, which says that a commodity used as money emerges from barter transaction. Each agent has a different value system which is given by a Heyting algebra, and exchanges one's commodities based on the value system. In each value system, necessity and unnecessity of commodities are expressed by some elements and their compliments on a Heyting Algebra. Moreover, the concept of the compliment is extended. Consequently, the duality of the necessity-unnecessity is weakened, and the exchanges of the commodities are promoted. The commodities which keeps being exchanged for a long time can correspond to money.

AB - We propose a mathematical model of economic agents to study origin of money. This multi-agent model is based on commodity theory of money, which says that a commodity used as money emerges from barter transaction. Each agent has a different value system which is given by a Heyting algebra, and exchanges one's commodities based on the value system. In each value system, necessity and unnecessity of commodities are expressed by some elements and their compliments on a Heyting Algebra. Moreover, the concept of the compliment is extended. Consequently, the duality of the necessity-unnecessity is weakened, and the exchanges of the commodities are promoted. The commodities which keeps being exchanged for a long time can correspond to money.

KW - Barter exchange

KW - Heyting algebra

KW - Internal measurement

KW - Multi-agent

KW - Theory of money

UR - http://www.scopus.com/inward/record.url?scp=57049114798&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=57049114798&partnerID=8YFLogxK

U2 - 10.1063/1.3020678

DO - 10.1063/1.3020678

M3 - Conference contribution

AN - SCOPUS:57049114798

SN - 9780735405790

VL - 1051

SP - 380

EP - 389

BT - AIP Conference Proceedings

ER -