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We solve the dynamics of large spherical Minority Games (MG) in the presence of non-negligible time dependent external contributions to the overall market bid. The latter represent the actions of market regulators, or other major natural or…
In this paper we introduce temporal action graph games (TAGGs), a novel graphical representation of imperfect-information extensive form games. We show that when a game involves anonymity or context-specific utility independencies, its…
Classical game theory addresses decision problems in multi-agent environment where one rational agent's decision affects other agents' payoffs. Game theory has widespread application in economic, social and biological sciences. In recent…
In the original two-choice minority game (MG), selfish players cooperate with each other even though direct communication is not allowed. Moreover, there is a periodic dynamics in the MG whenever the strategy space size is much smaller than…
The use of game theoretic methods for control in multiagent systems has been an important topic in recent research. Valid utility games in particular have been used to model real-world problems; such games have the convenient property that…
Complex systems can exhibit unexpected large changes, e.g. a crash in a financial market. We examine the large endogenous changes arising within a non-trivial generalization of the Minority Game: the Grand Canonical Minority Game (GCMG).…
This work lies in the fusion of experimental economics and data mining. It continues author's previous work on mining behaviour rules of human subjects from experimental data, where game-theoretic predictions partially fail to work.…
The Minority Game is a simple model for the collective behavior of agents in an idealized situation where they have to compete through adaptation for a finite resource. This review summarizes the statistical mechanics community efforts to…
A new representation of Game Theory is developed in this paper. State of players is represented by a density matrix, and payoff function is a set of hermitian operators, which when applied onto the density matrix give the payoff of players.…
We show that the Minority Game, a model of interacting heterogeneous agents, can be described as a spin systems and it displays a phase transition between a symmetric phase and a symmetry broken phase where the games outcome is predicable.…
We study analytically and numerically Minority Games in which agents may invest in different assets (or markets), considering both the canonical and the grand-canonical versions. We find that the likelihood of agents trading in a given…
The \$-Game was recently introduced as an extension of the Minority Game. In this paper we compare this model with the well know Minority Game and the Majority Game models. Due to the inter-temporal nature of the market payoff, we introduce…
Stochastic games are a convenient formalism for modelling systems that comprise rational agents competing or collaborating within uncertain environments. Probabilistic model checking techniques for this class of models allow us to formally…
This paper introduces algorithm instance games (AIGs) as a conceptual classification applying to games in which outcomes are resolved from joint strategies algorithmically. For such games, a fundamental question asks: How do the details of…
The dynamics of minority games with agents trading on different time scales is studied via dynamical mean-field theory. We analyze the case where the agents' decision-making process is deterministic and its stochastic generalization with…
Two intimately related new classes of games are introduced and studied: entropy games (EGs) and matrix multiplication games (MMGs). An EG is played on a finite arena by two-and-a-half players: Despot, Tribune and the non-deterministic…
Perfect synchronicity in $N$-player games is a useful theoretical dream, but communication delays are inevitable and may result in asynchronous interactions. Some systems such as financial markets are asynchronous by design, and yet most…
We consider the dynamics of player's strategies in repeated market games, where the selection of strategies is determined by a learning model. Prior theoretical analysis and experimental data show that after large number of plays the…
We consider a version of large population games whose agents compete for resources using strategies with adaptable preferences. Diversity among the agents reduces their maladpative behavior. We find interesting scaling relations with…
This paper studies Mean Field Games (MFGs) in which agent dynamics are given by jump processes of controlled intensity, with mean-field interaction via the controls and affecting the jump intensities. We establish the existence of MFG…