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An attempt is made to find a comprehensive mathematical framework in which to investigate the problems of well-posedness and asymptotic analysis for fully nonlinear evolutionary game theoretic models. The model should be rich enough to…
Physical theories grounded in mathematical symmetries are an essential component of our understanding of a wide range of properties of the universe. Similarly, in the domain of machine learning, an awareness of symmetries such as rotation…
We study the correlated equilibrium polytope $P_G$ of a game $G$ from a combinatorial point of view. We introduce the region of full-dimensionality for this class of polytopes and prove that it is a semialgebraic set for any game. Using a…
Meta-analysis aims to combine effect measures from several studies. For continuous outcomes, the most popular effect measures use simple or standardized differences in sample means. However, a number of applications focus on the absolute…
Adaptive machines have the potential to assist or interfere with human behavior in a range of contexts, from cognitive decision-making to physical device assistance. Therefore it is critical to understand how machine learning algorithms can…
Traditional solvable game theory and mean-field-type game theory (risk-aware games) predominantly focus on quadratic costs due to their analytical tractability. Nevertheless, they often fail to capture critical non-linearities inherent in…
We consider a class of two-player dynamic stochastic nonzero-sum games where the state transition and observation equations are linear, and the primitive random variables are Gaussian. Each controller acquires possibly different dynamic…
Imitation is simple behavior which uses successful actions of others in order to deal with one's own problems. Because success of imitation generally depends on whether profit of an imitating agent coincides with those of other agents or…
An iterative finite difference scheme for mean field games (MFGs) is proposed. The target MFGs are derived from control problems for multidimensional systems with advection terms. For such MFGs, linearization using the Cole-Hopf…
Multi-agent influence diagrams (MAIDs) are a popular form of graphical model that, for certain classes of games, have been shown to offer key complexity and explainability advantages over traditional extensive form game (EFG)…
We study turn-based quantitative games of infinite duration opposing two antagonistic players and played over graphs. This model is widely accepted as providing the adequate framework for formalizing the synthesis question for reactive…
In this paper, we consider a distributed Bayesian Nash equilibrium (BNE) seeking problem in incomplete-information aggregative games, which is a generalization of Bayesian games and deterministic aggregative games. We handle the aggregation…
Conformal symmetry is taken as an attribute of theories of massless fields in manifolds with specific dimensionalities. This paper shows that this is not an absolute truth; it is a consequence of the mathematical representation used for the…
We present a Mean Field Game approach to obtain the rate function for the empirical measure of interacting particles under McKean-Vlasov dynamics. Although the result is well known, our approach relies on PDE methods and provides another…
Traditionally, mechanism design focuses on simultaneous-move games (e.g., Myerson (1981)). In this paper, we study mechanism design with sequential-move games, and provide two results on revelation principles for general solution concepts…
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…
Groups of humans are often able to find ways to cooperate with one another in complex, temporally extended social dilemmas. Models based on behavioral economics are only able to explain this phenomenon for unrealistic stateless matrix…
We examine global non-asymptotic convergence properties of policy gradient methods for multi-agent reinforcement learning (RL) problems in Markov potential games (MPG). To learn a Nash equilibrium of an MPG in which the size of state space…
We consider N-player and mean field games in continuous time over a finite horizon, where the position of each agent belongs to {-1,1}. If there is uniqueness of mean field game solutions, e.g. under monotonicity assumptions, then the…
We present several new characterizations of correlated equilibria in games with continuous utility functions. These have the advantage of being more computationally and analytically tractable than the standard definition in terms of…