Liquidity externality in a market of buying adjustable agents. (November 2021) - Aal, P.K.; Sousa, K.R. de A.; Salles, L.S.A. de Campos; Koehler, M.
Highlights: An inhomogeneous cellular automata (InCA) can generate an evolutionary dynamic that resembles some economical processes. Some features of the InCA dynamics can be associated to liquidity externalities of real markets. The InCA time series have long memory effects. There is a critical level of liquidity ( qmax ) that would maximizes the business cycles in a real market. This parameter ( qmax ) is intrinsically related to the topology of the economic network that link the individual agents. Abstract: The market dynamics produced by simple interactions among rational investors can generate complex phenomena such as bubbles, crashes, and business cycles. One powerful tool to understand those phenomena might be the use of Cellular Automata (CA) models. In this contribution we investigate spatial aggregations effects associated to the propagation of information contagion waves across a network of non-equivalent adjustable agents. The contagion dynamics is modeled by an inhomogeneous cellular automaton (InCA) as proposed by Weisbuch and Stauffer[ Physica A, 1 (323), 651-662 (2003)]. In this system, a tatonnement process emerges as the individual agents try to adjust their reservation price to follow the externality produced by the state of the neighborhood. Using rescale range analysis we show that the periodic oscillations of InCA average state (that resembles business cycles) have long memory effects (for a determined interval of time). The presence of long memory effects is a usual feature present in many real markets. Our results are obtained after the development of an efficient algorithm to count the cluster of agents with the same state. The application of this algorithm revealed that the number and the size of the agent's cluster increase as adjustment amplitude (the parameter that controls the velocity of the tatonnement process) increases. We then show that there is a value of this amplitude that maximizes the system's tendency to form large and synchronized clusters. By associating this adjustment parameter with the liquidity, we demonstrate that the dynamics of the inhomogeneous cellular automata can mimic liquidity externalities found in real markets.