Related papers: Qunatifying Complexity in the Minority Game
We introduce a measure of complexity in terms of the average number of bits per time unit necessary to specify the sequence generated by the system. In random dynamical system, this indicator coincides with the rate K of divergence of…
Systemic risk measures are crucial for the stability of financial markets, yet classical formulations fail to capture the complexity of market volatility. We propose a new framework for systemic risk measurement on the variable-exponent…
This paper studies complexity theoretic aspects of quantum refereed games, which are abstract games between two competing players that send quantum states to a referee, who performs an efficiently implementable joint measurement on the two…
Inspired by socio-political scenarios, like dictatorships, in which a minority of people exercise control over a majority of weakly interconnected individuals, we propose vulnerability and power measures defined on groups of actors of…
We study a modification of the Evolutionary Minority Game (EMG) in which agents are placed in the nodes of a regular or a random graph. A neighborhood for each agent can thus be defined and a modification of the usual relaxation dynamics…
We present a complexity measure for any finite time series. This measure has invariance under any monotonic transformation of the time series, has a degree of robustness against noise, and has the adaptability of satisfying almost all the…
In this paper we propose a method that learns to play Pac-Man. We define a set of high-level observation and action modules. Actions are temporally extended, and multiple action modules may be in effect concurrently. A decision of the agent…
We introduce the minority game theory for two kinds of the Korean treasury bond (KTB) in Korean futures exchange markets. Since we discuss numerically the standard deviation and the global efficiency for an arbitrary strategy, our case is…
Feature-based SPL analysis and family-based model checking have seen rapid development. Many model checking problems can be reduced to two-player games on finite graphs. A prominent example is mu-calculus model checking, which is generally…
In this paper we consider a network of boolean agents that compete for a limited resource. The agents play the so called Generalized Minority Game where the capacity level is allowed to vary externally. We study the properties of such a…
The term {\em complexity} is used informally both as a quality and as a quantity. As a quality, complexity has something to do with our ability to understand a system or object -- we understand simple systems, but not complex ones. On…
In the classical context, the cooperative game theory concept of the Shapley value has been adapted for post hoc explanations of machine learning models. However, this approach does not easily translate to eXplainable Quantum ML (XQML).…
Since the introduction of the Kolmogorov complexity of binary sequences in the 1960s, there have been significant advancements in the topic of complexity measures for randomness assessment, which are of fundamental importance in theoretical…
In the real world, agents or entities are in a continuous state of interactions. These inter- actions lead to various types of complexity dynamics. One key difficulty in the study of complex agent interactions is the difficulty of modeling…
We investigate mean field game systems under invariance conditions for the state space, otherwise called {\it viability conditions} for the controlled dynamics. First we analyze separately the Hamilton-Jacobi and the Fokker-Planck…
We study a variation of the minority game. There are N agents. Each has to choose between one of two alternatives everyday, and there is reward to each member of the smaller group. The agents cannot communicate with each other, but try to…
Modern chess engines significantly outperform human players and are essential for evaluating positions and move quality. These engines assign a numerical evaluation $E$ to positions, indicating an advantage for either white or black, but…
We discuss a simple model based on the Minority Game which reproduces the main stylized facts of anomalous fluctuations in finance. We present the analytic solution of the model in the thermodynamic limit and show that stylized facts arise…
The formulation of Mean Field Games (MFG) typically requires continuous differentiability of the Hamiltonian in order to determine the advective term in the Kolmogorov--Fokker--Planck equation for the density of players. However, in many…
In this paper, we introduce an agent-based representation of games, in order to propose a compact representation for multi-party games in game theory. Our method is inspired by concepts in process theory and process algebra. In addition, we…