Financial Interactions and Collective States: Part I. Investors and Firms

TL;DR

This work extends a prior field-theoretic model of capital allocation by endogenizing the network of financial connections through a dedicated stakes field. Investors organize into interlinked groups, supporting two distinct return regimes (low and high) that drive sectoral dynamics and potential defaults. By formulating a four-tier resolution (averages then sectoral detail) and introducing uncertainty-driven risk propagation, the paper derives conditions for no-default equilibria, default states, and cascades, along with stability and transition pathways. The analysis highlights how uncertainty and cross-sector intermediation can both stabilize or destabilize collective states, foreshadowing how banks and monetary creation (to be addressed in Part II) may alter systemic outcomes and contagion risk.

Abstract

In a previous work, we applied a field formalism to analyze capital allocation and accumulation within a network of investors and firms. In that framework, financial agents could invest in firms or in other investors, and banks-introduced as investors with a credit multiplier-could play a stabilizing or destabilizing role. Collective states emerged from these interactions, reflecting different configurations of capital distribution and stability in the financial system. However, these results relied on the assumption that financial connections were exogenous. The present paper removes this assumption by modeling financial connections as dynamic endogenous variables. Specifically, we extend the framework by introducing a field representation of the network of financial connections. The collective states previously identified are now embedded in a broader class of states, characterized by the structure of investment stakes among investors. We show that these collective states consist of inter-connected groups of agents, along with their returns and disposable capital. The model reveals the emergence of two investor classes: high- and low-return (and capital) agents. High-return investors, in particular, act as a source of instability within the system, enabling transitions between configurations. In each collective state, some sectors may experience defaults. When the collective state exhibits specific structural conditions, defaults may spread across a significant share of the group.