Crowd effects and volatility in markets with competing agents

Dynamical spin-glass-like behavior in an evolutionary game

“…It was found, that the properties of the game depend on the memory length M and number of players N through the scaling variable α = 2 M /N [4,6,7]. The Minoriry game was thoroughly studied both numerically and analytically [8][9][10][11][12][13][14][15][16][17][18][19] along with the study of the original bar attendance problem [20,21] and various modifications of the Minority game [22][23][24][25][26][27][28][29] An important role is attributed to the observation that the dynamics of the memorized pattern and the strategies' scores are in certain regimes decoupled [30][31][32] and that the thermal noise can ge introduced in the players' decisions [33][34][35].…”

Competition-Driven Network Dynamics: Emergence of a Scale-Free Leadership Structure and Collective Efficiency

“…In the standard MG the variations in σ at the best performance point are low, and even an extended search (500 samples) in the strategy disorder space could not generate σ-s lower than 2.0, while in contrast, time series such as the red one in Fig.2b) are easily generated within 50 random samples in the optimal connectivity region. This emerging collective efficiency can be understood in terms of the crowdanticrowd description of the MG, as introduced by Johnson, Hart and Hui [5]. In the MG, low m means that only a small number of different strategies are possible, thus many agents are forced to use the same strategy and thus they behave as a crowd, or a group.…”

Continuous time dynamics of the thermal minority game

“…One of these systems is the minority game (MG) [4,5], a simple model based on Arthur's "El Farol" bar problem [6] which describes the behaviour of a group of competing heterogeneous agents subject to the economic law of supply and demand. Despite its simplicity, the MG is very non-trivial, and although much progress has been made in the qualitative [7][8][9] and quantitative [10,11] understanding of its features, a full analytic solution of the MG is still missing.The main hurdles in the way of an analytical study of the MG in its original formulation were its non-locality in time due to the dependence on the game history, its discrete kinematics and dynamics, and the "best-strategy" rule (see, however, [10]). The first of these obstacles was overcome in [12], where it was shown numerically that the macroscopic behaviour of the MG was unchanged if the real history was replaced by a random one.…”

“…One of these systems is the minority game (MG) [4,5], a simple model based on Arthur's "El Farol" bar problem [6] which describes the behaviour of a group of competing heterogeneous agents subject to the economic law of supply and demand. Despite its simplicity, the MG is very non-trivial, and although much progress has been made in the qualitative [7][8][9] and quantitative [10,11] understanding of its features, a full analytic solution of the MG is still missing.…”