Multi-Scale Boundary Effects in Agent-Based Models of Monetary Emergence

Contents

1. Gabatarwa

Wannan bincike ya yi amfani da ƙirar lissafi mai rai don kwaikwayon fitowar kuɗi daga cinikin farko, wanda aka yi wahayi daga hasashen Menger cewa kuɗi na iya tasawa ta kansu a cikin tattalin arzikin musayar kayayyaki. ƙirar ta bayyana al'amuran da za a iya fassara su a matsayin fitowar kuɗi da rushewa, da kuma tasirin gasa. Wani muhimmin bincike shi ne cewa rayuwar kuɗi tana nuna ci gaba mai yawa a kusa da bakin kofa, wanda yake da kamanceceniya da al'amuran gaggawa a cikin kasuwannin hada-hadar kuɗi na hakika.

2. Tsari

This agent-based model comprises N agents, each producing one type of commodity (k=1,...,N). Agent k produces the k-th commodity. The fundamental interactions involve multiple steps, including trading partner search, commodity exchange, preference updating, and production/consumption phases.

2.1 Mu'amalar Agent

Kowane agent yana kula da abubuwan da yake so ya sayo, kuma yana shiga cikin ma'amaloli bisa tsari. Zagaye na ƙunshi N ma'amaloli a jere, yana tabbatar da cewa kowane agent yana da damar shiga.

2.2 Tsarin Ciniki

Tsarin ciniki ya ƙunshi: (1) Neman abokin ciniki, (2) Musayar kayayyaki bisa buƙatun juna, (3) Sabunta abubuwan da ake so saye, da (4) Matakan samarwa da amfani.

3. Tsarin Fasaha

3.1 Bayanin Lissafi

Za a iya siffanta ƙwaƙƙwaran ƙirar ƙirar ta amfani da matrix na fifiko da aikin amfani. Ga wakili i mai vector na fifiko $P_i = [p_{i1}, p_{i2}, ..., p_{iN}]$, inda $p_{ij}$ ke wakiltar fifikon kaya j, ana ba da amfanin ciniki ta hanyar:

$U_{ij} = \sum_{k=1}^{N} p_{ik} \cdot q_{jk} - \sum_{k=1}^{N} p_{jk} \cdot q_{ik}$

A cikin wannan $q_{jk}$ yana nufin adadin kayan k da wakili j ke riƙe da shi.

3.2 Multiscale Analysis

Yi amfani da tsarin ɓarna mai yawa don nazarin halayen ma'auni masu yawa a kusa da ƙofar mahimmanci. Aikin rabo an ayyana shi azaman:

$Z(q,s) = \sum_{\mu} p_{\mu}^q(s) \sim s^{\tau(q)}$

Inda $\tau(q)$ take da alamar yawa, bakan ɓarna mai yawa $f(\alpha)$ ana samun ta ta hanyar canjin Legendre.

4. Experimental Results

4.1 Currency Emergence Patterns

Simulation demonstrates how a commodity spontaneously elevates to monetary status through a process analogous to physical spontaneous symmetry breaking. The bootstrap mechanism ensures universal acceptance of this commodity in all transactions.

4.2 Critical Threshold Behavior

Near critical parameter values, monetary lifespan exhibits multiscale characteristics. This behavior reflects critical phenomena observed in financial markets, particularly resembling complex scaling patterns emerging in foreign exchange dynamics.

5. Aiwatar da Code

Below is a simplified Python implementation of the agent trading mechanism:

class Agent:
    def __init__(self, agent_id, goods_preference):
        self.id = agent_id
        self.preferences = goods_preference
        self.inventory = {i: 1 for i in range(len(goods_preference))}
    
    def calculate_utility(self, other_agent):
        utility = 0
        for good_id, pref in enumerate(self.preferences):
            utility += pref * other_agent.inventory.get(good_id, 0)
        return utility
    
    def engage_transaction(self, other_agent):
        if self.calculate_utility(other_agent) > threshold:
            # 执行商品交换
            self.update_preferences()
            other_agent.update_preferences()
            return True
        return False

def simulate_turn(agents):
    for i in range(len(agents)):
        for j in range(i+1, len(agents)):
            agents[i].engage_transaction(agents[j])

6. Aikace-aikace da Hanyoyin Gaba

This model holds significant importance for understanding financial market dynamics, particularly in decentralized systems such as cryptocurrency markets. Future research directions include:

• Yaɗa zuwa tsarin kuɗi da yawa
• Haɗawa da bayanan kasuwa na ainihi
• Aiwatarwa a tsarin tattalin arziƙin tushen blockchain
• Research on the Impact of Regulation on Monetary Emergence

7. Bincike na Asali

The agent-based model of monetary emergence proposed in this study makes significant contributions to computational economics, particularly in understanding how monetary systems self-organize from simple barter economies. The multiscale effects exhibited by the model near critical thresholds establish a mathematical bridge between economic phenomena and physical critical systems, reminiscent of interdisciplinary approaches in works such as CycleGAN (Zhu et al., 2017) that connect disparate domains through fundamental mathematical principles.

What is particularly striking about this research is its use of modern computational methods to validate Menger's century-old hypothesis. The bootstrapping mechanism identified in the model—where money is accepted precisely because it holds monetary status—resembles network effects observed in contemporary digital currencies. This aligns with the Santa Fe Institute's research on complex adaptive systems, which emphasizes how simple local interactions can generate complex global phenomena.

Multiscale analysis reveals that monetary longevity near critical transitions exhibits fractal characteristics similar to those observed in volatility clustering in financial markets. This connection to real market behaviors, as documented in The European Physical Journal B and Journal of Economic Dynamics and Control, indicates the model captures fundamental aspects of monetary dynamics. The mathematical framework employing partition functions and multifractal spectra provides tools for quantifying economic complexity, applicable to analyzing systemic risk in financial networks.

Idan aka kwatanta da samfuran tattalin arziki na al'ada waɗanda suka dogara da zato na daidaito, wannan hanyar da ta dogara da wakili ta karɓi rashin daidaito na asali da dogaro da tafarki na tsarin tattalin arziki. Ƙarfin samfurin don kwaikwayon fitowar kuɗi da rugujewa ya sa ya dace musamman don fahimtar halayen kuɗin cryptocurrency, inda sabbin nau'ikan kuɗi sukan fito suka ɓace. A nan gaba, haɗa waɗannan binciken tare da bayanan ƙima daga dandamali kamar Ethereum na iya ba da haske mai mahimmanci ga masana tattalin arziki da masu tsara manufofi.

8. References

1. Menger, C. (1871). Principles of Economics
2. Yasutomi, A. (1995). Physica D: Nonlinear Phenomena
3. Górski, A.Z. et al. (2007). Acta Physica Polonica B
4. Zhu, J.Y. et al. (2017). CycleGAN: Unpaired Image-to-Image Translation
5. Arthur, W.B. (1999). Science
6. Lux, T. & Marchesi, M. (1999). Nature
7. Mantegna, R.N. & Stanley, H.E. (2000). Introduction to Econophysics