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Mean field games (MFGs) offer a powerful framework for modeling large-scale multi-agent systems. This paper addresses MFGs formulated in continuous time with discrete state spaces, where agents' dynamics are governed by continuous-time…
Game theory provides an effective way to model strategic interactions among rational agents. In the context of formal verification, these ideas can be used to produce guarantees on the correctness of multi-agent systems, with a diverse…
We formulate a theory of agent-based models in which agents compete to be in a winning group. The agents may be part of a network or not, and the winning group may be a minority group or not. The novel feature of the present formalism is…
We investigate further several properties of the minority game we have recently introduced. We explain the origin of the phase transition and give an analytical expression of $\sigma^2/N$ in the $N\ll2^M$ region. The ability of the players…
This paper studies the finite-time horizon Markov games where the agents' dynamics are decoupled but the rewards can possibly be coupled across agents. The policy class is restricted to local policies where agents make decisions using their…
We use generating functional methods to solve the so-called inner product versions of the minority game (MG), with fake and/or real market histories, by generalizing the theory developed recently for look-up table MGs with real histories.…
We introduce a class of strategic games in which agents are assigned to nodes of a topology graph and the utility of an agent depends on both the agent's inherent utilities for other agents as well as her distance from these agents on the…
We introduce the concept of a \emph{cycle pattern} for directed graphs as functions from the set of cycles to the set $\{-,0,+\}$. The key example for such a pattern is derived from a weight function, giving rise to the sign of the total…
Hedonic games are fundamental models for investigating the formation of coalitions among a set of strategic agents, where every agent has a certain utility for every possible coalition of agents it can be part of. To avoid the…
Mean-payoff games (MPGs) are infinite duration two-player zero-sum games played on weighted graphs. Under the hypothesis of perfect information, they admit memoryless optimal strategies for both players and can be solved in…
We consider a simplified version of the Wealth Game, which is an agent-based financial market model with many interesting features resembling the real stock market. Market makers are not present in the game so that the majority traders are…
The general picture of game theoretic modeling dealt with here is characterized by a set of big players, also referred to as principals or major agents, acting on the background of large pools of small players, the impact of the behavior of…
With remarkable significance in migration prediction, global disease mitigation, urban planning and many others, an arresting challenge is to predict human mobility fluxes between any two locations. A number of methods have been proposed…
Economic ensembles can be modeled as networks of interacting agents whose be-haviors are described in terms of game theory. The evolutionary paradigm has been applied to two-person games to discover strategies in this context.…
The mean field games (MFG) paradigm was introduced to provide tractable approximations of games involving very large populations. The theory typically rests on two key assumptions: homogeneity, meaning that all players share the same…
We study distributionally robust Markov games (DR-MGs) with the average-reward criterion, a framework for multi-agent decision-making under uncertainty over extended horizons. In average reward DR-MGs, agents aim to maximize their…
Most machine learning approaches to scientific discovery frame hypotheses as end-to-end predictions, obscuring the incremental structure of scientific reasoning. We propose The Hypothesis Game, a symbolic formalism for hypothesis refinement…
We investigate mean-field games (MFG) in which agents can actively control their speed of access to information. Specifically, the agents can dynamically decide to obtain observations with reduced delay by accepting higher observation…
When controlling multi-agent systems, the trade-off between performance and scalability is a major challenge. Here, we address this difficulty by using mean field games (MFGs), which is a framework that deduces the macroscopic dynamics…
We present and study a Minority Game based model of a financial market where adaptive agents -- the speculators -- interact with deterministic agents -- called producers. Speculators trade only if they detect predictable patterns which…