A Mathematical Theory of Value: a synthesis on goal-directed agency under resource constraints
arXiv:2606.12502v1 Announce Type: cross Abstract: We propose that value -- the quantity goal-directed agents create, destroy, and exchange -- is a lawful structural quantity in the same category as information. Following Shannon's method, we make one ruthless abstraction: value is the rate at which an agent converts a resource into goal-progress, relative to a frame fixed by its goal. A scale-invariance axiom forces a logarithmic measure, $V=\sum_i k_i \ln e_i$; compounding of a reinvested resource forces the same form via the ergodicity argument of Peters (2019). The two routes are kin rather
This paper represents a theoretical advancement in understanding how artificial intelligence and economic principles converge, building on existing work like Peters (2019) to formalize 'value' in goal-directed systems.
A mathematical theory of value for AI agents could provide foundational insights for designing more efficient, rational, and economically integrated artificial intelligence systems, impacting future AI development and deployment.
This research provides a new theoretical framework for quantifying 'value' within autonomous systems, moving beyond intuitive definitions to a formal, measurable concept akin to information theory.
- · AI researchers
- · AI developers
- · Economic theorists
- · Autonomous system designers
- · Inefficient AI architectures
- · Heuristic-based value systems
It provides a rigorous mathematical basis for evaluating the efficiency and goal-progress of AI agents.
This theory could lead to the development of AI systems with intrinsic economic understanding, influencing resource allocation and decision-making.
It might enable the creation of highly optimized, autonomous economic agents that reshape markets at fundamental levels through a deeper understanding of value creation.
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Read at arXiv cs.AI