Related papers: The Minority Game: a statistical physics perspecti…
Adaptive populations such as those in financial markets and distributed control can be modeled by the Minority Game. We consider how their dynamics depends on the agents' initial preferences of strategies, when the agents use linear or…
We show analytically how the fluctuations (i.e. standard deviation) in the Minority Game (MG) can be made to decrease below the random coin-toss limit if the agents use more general behavioral strategies. This suppression of the standard…
The paper introduces a new approach to theory of differential games in which entangled players try to predict and influence actions of their adversaries. The entanglement is generated be a joint probability density known by the players.…
Behavioral experiments on the Ultimatum Game have shown that we human beings have remarkable preference in fair play, contradicting the predictions by the game theory. Most of the existing models seeking for explanations, however, strictly…
Strategic-form min-max game theory examines the existence, multiplicity, selection of equilibria, and the worst-case computational complexity under perfect rationality. However, in many applications, games are drawn from an ensemble, and…
Economies and societal structures in general are complex stochastic systems which may not lend themselves well to algebraic analysis. An addition of subjective value criteria to the mechanics of interacting agents will further complicate…
This note explains why a large class of fair, or reversible "money games", i.e., stochastic models of wealth redistribution among agents, lead to steady states described by canonical and microcanonical distributions. The games considered…
We study the market impact of a meta-order in the framework of the Minority Game. This amounts to studying the response of the market when introducing a trader who buys or sells a fixed amount h for a finite time T. This perturbation…
In the evolutionary minority game, agents are allowed to evolve their strategies (``mutate'') based on past experience. We explore the dependence of the system's global behavior on the response time and the mutation threshold of the agents.…
The \((n,k)\) game models a group of \(n\) individuals with binary opinions, say 1 and 0, where a decision is made if at least \(k\) individuals hold opinion 1. This paper explores the dynamics of the game with heterogeneous agents under…
Given entropy's central role in multiple areas of physics and science, one important task is to develop a systematic and unifying approach to defining entropy. Games of chance become a natural candidate for characterising the uncertainty of…
We briefly introduce a new promising field of applications of statistical physics, opinion dynamics, where the systems at study are social groups or communities and the atoms/spins are the individuals (or agents) belonging to such groups.…
Players (people, firms, states, etc.) have privacy concerns that may affect their choice of actions in strategic settings. We use a variant of signaling games to model this effect and study its relation to pooling behavior,…
This essay gives a self-contained introduction to quantum game theory, and is primarily oriented to economists with little or no acquaintance with quantum mechanics. It assumes little more than a basic knowledge of vector algebra. Quantum…
This paper has two central aims: first, to provide simple conditions under which the generalized games in choice form and, consequently, the abstract economies, admit equilibrium; second, to study the solvability of several types of systems…
We propose an analytically tractable variation of the minority game in which rational agents use probabilistic strategies. In our model, $N$ agents choose between two alternatives repeatedly, and those who are in the minority get a pay-off…
We continue the analysis of quantum-like description of markets and economics. The approach has roots in the recently developed quantum game theory and quantum computing. The present paper is devoted to quantum English auction which are a…
Game theory has been one of the most successful quantitative concepts to describe social interactions, their strategical aspects, and outcomes. Among the payoff matrix quantifying the result of a social interaction, the interaction…
By considering diffusion on De Bruijn graphs, we study in details the dynamics of the histories in the Minority Game, a model of competition between adaptative agents. Such graphs describe the structure of temporal evolution of $M$ bits…
We introduce a simple stochastic dynamics for game theory. It assumes ``local'' rationality in the sense that any player climbs the gradient of his utility function in the presence of a stochastic force which represents deviation from…