Related papers: Cycles, determinism and persistence in agent-based…
We consider a class of dynamic collective choice models with social interactions, whereby a large number of non-uniform agents have to individually settle on one of multiple discrete alternative choices, with the relevance of their would-be…
We study the dynamics of the batch minority game, with random external information, using generating functional techniques a la De Dominicis. The relevant control parameter in this model is the ratio $\alpha=p/N$ of the number $p$ of…
Commuters looking for the shortest path to their destinations, the security of networked computers, hedge funds trading on the same stocks, governments and populations acting to mitigate an epidemic, or employers and employees agreeing on a…
We consider deterministic Mean Field Games (MFG) in all Euclidean space with a cost functional continuous with respect to the distribution of the agents and attaining its minima in a compact set. We first show that the static MFG with such…
Price dynamics is analyzed in terms of a model which includes the possibility of effective forces due to trend followers or trend adverse strategies. The method is tested on the data of a minority-majority model and indeed it is capable of…
We study the continuous time dynamics of the Thermal Minority Game. We find that the dynamical equations of the model reduce to a set of stochastic differential equations for an interacting disordered system with non-trivial random…
Global games are a class of incomplete information games where the payoffs exhibit strategic complementarity leading to an incentive for the agents to coordinate their actions. Such games have been used to model scenarios in many…
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.…
Game-theoretic probability uses the structure of gambles to define a concept like probability, but which is more flexible and robust. We show that results in game-theoretic probability can be thought of as minimax theorems for specific…
A brief review is given of the minority game, an idealized model stimulated by a market of speculative agents, and its complex many-body behaviour. Particular consideration is given to analytic results for the model rather than discussions…
In this paper, we study the number of equilibria of the replicator-mutator dynamics for both deterministic and random multi-player two-strategy evolutionary games. For deterministic games, using Decartes' rule of signs, we provide a formula…
We introduce a quantitative framework for separating skill and chance in games by modeling them as complementary sources of control over stochastic decision trees. We define the Skill-Luck Index S(G) in [-1, 1] by decomposing game outcomes…
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…
We propose a general interpretation for long-range correlation effects in the activity and volatility of financial markets. This interpretation is based on the fact that the choice between `active' and `inactive' strategies is subordinated…
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…
Both the phenomenology and the theory of minority games (MG) with more than two strategies per agent are different from those of the conventional and extensively studied case S=2. MGs with $S>2$ exhibit nontrivial statistics of the…
We present a new tool for the study of multiplayer stochastic games, namely the modified game, which is a normal-form game that depends on the discount factor, the initial state, and for every player a partition of the set of states and a…
Matrix games constitute a fundamental problem of game theory and describe a situation of two players with completely conflicting interests. We show how methods from statistical mechanics can be used to investigate the statistical properties…
Mean Field Games (MFGs) can potentially scale multi-agent systems to extremely large populations of agents. Yet, most of the literature assumes a single initial distribution for the agents, which limits the practical applications of MFGs.…
Regular games form a well-established class of games for analysis and synthesis of reactive systems. They include coloured Muller games, McNaughton games, Muller games, Rabin games, and Streett games. These games are played on directed…