Hello,
As the next step in seeking constructive criticism for my proposal to the core time pricing model problem, I would like to advance the discussion by clarifying the mathematical and economic properties that a satisfactory solution should ideally exhibit. My intention is to open these characteristics to peer scrutiny and collaborative refinement, particularly in relation to embedding such a model into decentralized pricing systems.
Below are the current properties exhibited by the solution I have derived. I propose this list as a starting point for discussion:
- Decouples agentsâ preference layer from settlement price in a deterministic manner;
- Eliminates traditional price/quantity assumptions, instead modeling preferences as convex functions (as opposed to the more restrictive semi-linear assumptions);
- Ensures smooth and differentiable price evolution, allowing for continuous adjustment;
- Converges to a unique and stable equilibrium price under broad initial conditions;
- Operates in a fully peer-to-peer (P2P) architecture, well-suited for decentralized environments;
- Remains computationally efficient and cheap per transaction, even at scale;
- Achieves Pareto optimality, ensuring no agent can be made better off without making another worse off.
This solution stems from an original research initiative I began in 2000 during my economics studies in Chile. I am currently exploring how its formal structure maps isomorphically onto field elements, preserving core functional relationshipsâa direction that is yielding promising theoretical results.
The full mathematical framework, along with a simulation of its application in a cellular automata scenario (used here as a pedagogically clean presentation of the emergent dynamics), is available here:
GitHub - onedge-network/Emergent_Properties_paper: Repository for the last version of the paper: "Emergent Properties of Distributed Agents with Two-Stage Convex Zero-Sum Optimal Exchange Network"
Notably, even in fully randomized transaction environmentsâwhere agent pairs and parameters are drawn arbitrarilyâthe system exhibits the same convergence behavior. This suggests that the cellular automata is not essential to the mechanism, but rather an illustrative substrate that preserves the modelâs underlying economic properties across generalized conditions.
I look forward to your thoughts, critiques, and ideas on how this list of characteristics might be improved or rigorously tested in other economic or computational settings.
Best regards,