Triple grouping and period-three oscillations in minority-game dynamics

Abstract

Dynamical systems based on the minority game (MG) have been a paradigm for gaining significant insights into a variety of social and biological behaviors. Recently, a grouping phenomenon has been unveiled in MG systems of multiple resources (strategies) in which the strategies spontaneously break into an even number of groups, each exhibiting an identical oscillation pattern in the attendance of game players. Here we report our finding of spontaneous breakup of resources into three groups, each exhibiting period-three oscillations. An analysis is developed to understand the emergence of the striking phenomenon of triple grouping and period-three oscillations. In the presence of random disturbances, the triple-group/period-three state becomes transient, and we obtain explicit formula for the average transient lifetime using two methods of approximation. Our finding indicates that, period-three oscillation, regarded as one of the most fundamental behaviors in smooth nonlinear dynamical systems, can also occur in much more complex, evolutionary-game dynamical systems. Our result also provides a plausible insight for the occurrence of triple grouping observed, for example, in the U.S. housing market.

Reinforcement learning meets minority game: Toward optimal resource allocation

“…Optimal performance of such a system is typically measured by uniform and even utilization of all available resources by the users. Often this is not possible due to the phenomenon of herding that can emerge spontaneously in the evolution of the system, in which most agents utilize only a few resources, leaving the vast majority of the remaining resources little exploited [11,16,17,32,34,35,[50][51][52][53][54][55]. The herding behavior can propagate through the system, as the few heavily used resources would be depleted quickly, directing most agents to another possibly small set of resources, which would be depleted as well, and so on.…”

“…In the traditional minority game, the dynamical rules stipulate that competition and learning among agents can lead to the detrimental herding behavior, to which game systems composed of less diversified agents are particularly susceptible [32][33][34][35]. In our minority game system of agents empowered with RL, herding is dramatically suppressed.…”

“…In the original minority game model, an individual's scheme for state updating (or decision making) is essentially a trial-anderror learning process based on the global historical winning information [4]. In other models, learning mechanisms based local information from neighbors were proposed [11,12,16,17,25,28,[31][32][33][34][35]. The issue of controlling and optimizing complex resource allocation systems was also investigated [32], e.g., utilizing pinning control to harness the herding behavior, where it was demonstrated that a small number of control points in the network can suppress or even eliminate herding.…”

Multiagent model and mean field theory of complex auction dynamics

“…The rational upper bound of bid price k is k V c < -, ensuring positive payoff for the winner. Our construction of a computational model for the LUBA auction process benefits from the fact that a host of social and economical behaviors can be described by the minority game model [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37], a multi-agent model characterizing a population of selfish individuals competing for limited common resources. The similarity between LUBA auction process and those described by the minority game model suggests strongly the suitability of using multi-agent models to understand the LUBA auction dynamics.…”

Controlling herding in minority game systems

“…Given resource-allocation system that exhibits complex dynamics, a defining virtue of optimal performance is that the available resources are exploited evenly or uniformly by all agents in the system. In contrast, an undesired or even catastrophic behavior is the emergence of herding, in which a vast majority of agents concentrate on a few resources, leaving many other resources idle or unused 1 2 3 4 5 6 7 8 9 10 11 12 . Herd behavior has also attracted much attention in traditional economics 13 14 15 16 .…”