Related papers: The Use of Symmetry for Models with Variable-size …
A bidimensional representation of the space of 2x2 Symmetric Games in the strategic representation is proposed. This representation provides a tool for the classification of 2x2 symmetric games, quantification of the fraction of them having…
We propose a general class of symmetric games called position-optimization games. Given a probability distribution $Q$ over a set of targets $\mathcal{Y}$, the $n$ players each choose a position in a space $\mathcal{X}$. A player's utility…
In another paper with the same name\cite{frame}, we proposed a new representation of Game Theory, but most results are given by specific examples and argument. In this paper, we try to prove the conclusions as far as we can, including a…
We propose an alternative to the tree representation of extensive form games. Games in product form represent information with $\sigma$-fields over a product set, and do not require an explicit description of the play temporality, as…
Symmetry arguments are frequently used -- often implicitly -- in mathematical modeling of natural selection. Symmetry simplifies the analysis of models and reduces the number of distinct population states to be considered. Here, I introduce…
Designing socially optimal policies in multi-agent environments is a fundamental challenge in both economics and artificial intelligence. This paper studies a general framework for learning Stackelberg equilibria in dynamic and uncertain…
By resorting to the vector space structure of finite games, skew-symmetric games (SSGs) are proposed and investigated as a natural subspace of finite games. First of all, for two player games, it is shown that the skew-symmetric games form…
This work is an extension of our earlier article, where a well-known integral representation of the logarithmic function was explored, and was accompanied with demonstrations of its usefulness in obtaining compact, easily-calculable, exact…
Normal-form games (NFGs) are the fundamental model of strategic interaction. We study their representation using neural networks. We describe the inherent equivariance of NFGs -- any permutation of strategies describes an equivalent game --…
Multi-agent reinforcement learning, despite its popularity and empirical success, faces significant scalability challenges in large-population dynamic games. Graphon mean field games (GMFGs) offer a principled framework for approximating…
We study a generic family of two-player continuous-time nonzero-sum stopping games modeling a war of attrition with symmetric information and stochastic payoffs that depend on an homogeneous linear diffusion. We first show that any…
Autonomous agents should coordinate effectively without prior knowledge of others' intents. While prior work has focused on intent inference, we address the inverse problem: how agents can strategically demonstrate their intents within…
In this paper we introduce a game whose value functions converge (as a parameter that measures the size of the steps goes to zero) uniformly to solutions to the second order Pucci maximal operators.
In this paper, we consider continuous-time semi-decentralized dynamics for the equilibrium computation in a class of aggregative games. Specifically, we propose a scheme where decentralized projected-gradient dynamics are driven by an…
The class of totally balanced games is a class of transferable-utility coalitional games providing important models of cooperative behavior used in mathematical economics. They coincide with market games of Shapley and Shubik and every…
Policy gradient methods enjoy strong practical performance in numerous tasks in reinforcement learning. Their theoretical understanding in multiagent settings, however, remains limited, especially beyond two-player competitive and potential…
The theory of mean field games aims at studying deterministic or stochastic differential games (Nash equilibria) as the number of agents tends to infinity. Since very few mean field games have explicit or semi-explicit solutions, numerical…
In this book, we present a curated collection of existing results on inverse problems for Mean Field Games (MFGs), a cutting-edge and rapidly evolving field of research. Our aim is to provide fresh insights, novel perspectives, and a…
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…
We introduce a contractive abstract dynamic programming framework and related policy iteration algorithms, specifically designed for sequential zero-sum games and minimax problems with a general structure. Aside from greater generality, the…