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Abstract

In a series of papers, we applied a field formalism to analyze capital allocation and accumulation within a microeconomic framework of investors and firms. Financial agents could invest in both firms and other investors, while banks, introduced as investors with a credit multiplier, played a stabilizing or destabilizing role. Two types of interactions were considered within the financial sector: financial agents could either lend capital to or buy shares of other investors. We examined the collective states emerging from these interactions. At the macro level, we identified multiple collective states, each characterized by distinct levels of average capital and investor distribution across sectors. These states reflect the inherent instability of financial markets, with some configurations leading to default. At the micro level, we analyzed how returns and defaults propagate within a given collective state, highlighting the critical role of banks in stabilizing or amplifying financial fluctuations. However, these results were derived under 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 relationships. The collective states previously identified are now embedded in a broader class of states, characterized by the structure of investment shares among investors. We show that these collective states consist of interconnected groups of agents, along with their returns and disposable capital. Depending on the strength and form of connections between agents within each group, collective states may be stable or unstable, allowing for 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.