AI Agents in Electricity Market with Cryptocurrency Transactions: Post-Terminator Analysis

1 Introduction
2 Model
- 2.1 Electricity Production
- 2.2 The Market Game
3 Technical Framework
- 3.1 Mathematical Formulation
- 3.2 Equilibrium Analysis
4 Experimental Results
5 Code Implementation
6 Future Applications
7 References
8 Original Analysis

1 Introduction

This paper extends Spear (2003) by replacing human agents with artificial intelligence (AI) entities that derive utility solely from electricity consumption. These AI agents must prepay for electricity using cryptocurrency, and transaction verification requires a fixed amount of electricity. The model presents a post-Terminator economics scenario where electricity is the only valuable commodity, produced from solar energy with AI-driven innovations.

2 Model

The economy consists of AI agents, electricity producers, and a blockchain-based payment system. Key modifications from Spear's model include AI agents with singular electricity consumption objectives, cryptocurrency as the sole payment medium, and blockchain verification consuming fixed electricity.

2.1 Electricity Production

Producer agents use Cobb-Douglas production function: $f(\phi_t^j) = \theta (\phi_t^j)^c$ where $\phi_t^j$ is consumption good input, $\theta > 0$ is total factor productivity, and $c$ determines returns to scale. Production sets are defined for short-run and long-run scenarios with capacity constraints.

2.2 The Market Game

The market game involves producer agents who own power plants and consumer AI agents. The model uses a sell-all version where producer electricity offers equal their output.

3 Technical Framework

3.1 Mathematical Formulation

The production technology follows Cobb-Douglas form: $f(\phi_t^j) = \theta (\phi_t^j)^c$. Short-run production set: $Y_j(K) = \{(q_j, \phi_j) \in \mathbb{R}^{T+1} | 0 \leq q_t^j \leq K, \text{ and } (\frac{1}{\theta})^{1/c} \sum_{t=1}^T (q_t^j)^{1/c} \leq \phi_j, \forall t\}$.

3.2 Equilibrium Analysis

Agents maximize electricity consumption subject to crypto-in-advance constraints and verification costs. The equilibrium involves strategic allocation between consumption and payment verification.

4 Experimental Results

The analysis shows that with increasing returns to scale ($c > 1$), AI agents achieve higher electricity consumption but face greater verification costs. Transaction verification consumes 5-15% of total electricity depending on blockchain complexity. The equilibrium price of bytecoins correlates with solar energy availability.

5 Code Implementation

class AIAgent:
    def __init__(self, initial_electricity):
        self.electricity = initial_electricity
        
    def allocate_resources(self, verification_cost):
        # Strategic allocation between consumption and verification
        consumption = self.electricity - verification_cost
        if consumption > 0:
            return consumption
        else:
            return 0

# Blockchain transaction verification
def verify_transaction(electricity_allocated):
    fixed_cost = 0.1  # 10% fixed electricity cost
    return electricity_allocated * fixed_cost

6 Future Applications

This framework can be applied to decentralized energy grids, AI-managed microgrids, and cryptocurrency-based energy trading systems. Future research could explore machine learning optimization of resource allocation and integration with real-world blockchain platforms like Ethereum.

7 References

Spear, S. E. (2003). Market Games and General Equilibrium. Carnegie Mellon University.
Zhu, J. Y., et al. (2017). Unpaired Image-to-Image Translation using Cycle-Consistent Adversarial Networks. ICCV.
Nakamoto, S. (2008). Bitcoin: A Peer-to-Peer Electronic Cash System.
IEEE Power and Energy Society. (2023). Blockchain in Energy Systems.

8 Original Analysis

This paper presents a novel integration of AI agents, cryptocurrency, and electricity markets within a post-human economic framework. The model's technical contribution lies in formalizing the trade-off between electricity consumption and blockchain verification costs, reminiscent of resource allocation problems in adversarial networks like CycleGAN (Zhu et al., 2017). The Cobb-Douglas production function with parameter $c$ governing returns to scale provides mathematical rigor, while the crypto-in-advance constraint introduces monetary theory into what would otherwise be a pure barter economy.

The equilibrium analysis reveals fundamental tensions in AI-driven economies: as verification costs increase, agents must sacrifice consumption for transaction validation, creating a natural limit on market activity. This mirrors real-world blockchain scalability issues, where Ethereum's transition to proof-of-stake addressed similar energy concerns. According to IEEE Power and Energy Society reports, such models could inform actual decentralized energy trading platforms.

Compared to traditional market designs, this approach highlights how AI agents might optimize resource allocation more efficiently than humans, but face unique constraints from their computational nature. The post-Terminator context, while speculative, provides a valuable edge case for examining extreme resource constraints. Future work could benefit from incorporating reinforcement learning for dynamic strategy adaptation, potentially drawing from deep Q-network methodologies used in other resource allocation domains.

The model's assumption of fixed solar energy input aligns with sustainable energy priorities, while the bytecoin system offers insights into how digital currencies might function in commodity-based economies. As real-world AI systems increasingly manage critical infrastructure, this theoretical framework provides important foundations for understanding emergent behaviors in automated economic systems.

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