Financial Interactions and Collective States: Banks, Investors and Firms
Pierre Gosselin, Aïleen Lotz
Abstract: In a previous paper, we applied a field formalism to analyze capital allocation and accumulation within a microeconomic framework of investors and firms. The financial connections were modeled by a field of stakes, representing the links between agents. We showed that the resulting collective states were composed of interconnected groups of agents defined by their connections, their returns and disposable capital. However, within this framework, the collective states exhibited structural instability, as capital shortages in specific sectors could trigger cascades of defaults.
The present model refines this framework by introducing a third type of agent, banks, a type of investor that can create money through loans. We show that money creation neither eliminates systemic instability nor prevents the emergence of defaults. In fact, the effect of banks on system stability and defaults is ambiguous: When banks favor firms over investors, money creation stabilizes the system by providing the necessary capital to prevent initial defaults, whereas when banks favor investors over firms, investors’ influence is strengthened, potentially amplifying instability and defaults. Moreover, regardless of whether they favor investors or firms, banks may facilitate the propagation of defaults once they have started. Ultimately, because banks are themselves investors, the emergence of highly capitalized, high-return banks can directly generate instability in the system.
Beyond these mechanisms, the analysis reveals the structural limits of macroprudential regulation. Highly capitalized, high-return investors and banks may appear more diversified and resilient, yet they constitute the primary source of endogenous instability. The model thus highlights that systemic fragility is inherent to the very structure of financial interdependence and capital flows.
Key words: Financial Markets, Real Economy, Capital Allocation, Statistical Field Theory, Background fields, Collective states, Multi-Agent Model, Interactions.
JEL Classification: B40, C02, C60, E00, E1, G10
Financial Interactions and Collective States: Investors and Firms
Pierre Gosselin, Aïleen Lotz
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.
Key words: Financial Markets, Real Economy, Capital Allocation, Statistical Field Theory, Background fields, Collective states, Multi-Agent Model, Interactions.
JEL Classification: B40, C02, C60, E00, E1, G10
Field Economics: An Introduction
Pierre Gosselin, Aïleen Lotz
Abstract: This paper introduces a novel approach to analyzing economic systems with a large number of agents by applying concepts from field theory. This framework formalizes the probability landscape of the system, capturing both the global collective states and the microeconomic foundations of agent interactions. By identifying the possible collective states of the system, the approach enables a comprehensive understanding of individual dynamics within these states. Furthermore, this perspective challenges traditional economic paradigms, replacing the notion of a single equilibrium with a dynamic view of transitions between collective states.
Key words: Financial Markets, Real Economy, Capital Allocation, Statistical Field Theory, Background fields, Collective states, Multi-Agent Model, Interactions.
JEL Classification: B40, C02, C60, E00, E1, G10