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The preference graph is a combinatorial representation of the structure of a normal-form game. Its nodes are the strategy profiles, with an arc between profiles if they differ in the strategy of a single player, where the orientation…
Robots deployed to the real world must be able to interact with other agents in their environment. Dynamic game theory provides a powerful mathematical framework for modeling scenarios in which agents have individual objectives and…
We consider multi-player games played on graphs, in which the players aim at fulfilling their own (not necessarily antagonistic) objectives. In the spirit of evolutionary game theory, we suppose that the players have the right to repeatedly…
Many emerging applications - such as adversarial training, AI alignment, and robust optimization - can be framed as zero-sum games between neural nets, with von Neumann-Nash equilibria (NE) capturing the desirable system behavior. While…
Prediction is a well-studied machine learning task, and prediction algorithms are core ingredients in online products and services. Despite their centrality in the competition between online companies who offer prediction-based products,…
Artificial intelligence and robotic competitions are accompanied by a class of game paradigms in which each player privately commits a strategy to a game system which simulates the game using the collected joint strategy and then returns…
This work addresses the classic machine learning problem of online prediction with expert advice. We consider the finite-horizon version of this zero-sum, two-person game. Using verification arguments from optimal control theory, we view…
We develop a flexible stochastic approximation framework for analyzing the long-run behavior of learning in games (both continuous and finite). The proposed analysis template incorporates a wide array of popular learning algorithms,…
This manuscript portrays optimization as a process. In many practical applications the environment is so complex that it is infeasible to lay out a comprehensive theoretical model and use classical algorithmic theory and mathematical…
In multi-agent settings, game theory is a natural framework for describing the strategic interactions of agents whose objectives depend upon one another's behavior. Trajectory games capture these complex effects by design. In competitive…
Game Theory concepts have been successfully applied in a wide variety of domains over the past decade. Sports and games are one of the popular areas of game theory application owing to its merits and benefits in solving complex scenarios.…
We provide several applications of Optimistic Mirror Descent, an online learning algorithm based on the idea of predictable sequences. First, we recover the Mirror Prox algorithm for offline optimization, prove an extension to Holder-smooth…
Generative adversarial networks (GANs) are a novel approach to generative modelling, a task whose goal it is to learn a distribution of real data points. They have often proved difficult to train: GANs are unlike many techniques in machine…
We study the problem of learning Markov decision processes with finite state and action spaces when the transition probability distributions and loss functions are chosen adversarially and are allowed to change with time. We introduce an…
Incomplete cooperative games generalise the classical model of cooperative games by omitting the values of some of the coalitions. This allows to incorporate uncertainty into the model and study the underlying games as well as possible…
It is now well known that decentralised optimisation can be formulated as a potential game, and game-theoretical learning algorithms can be used to find an optimum. One of the most common learning techniques in game theory is fictitious…
Conventional noncooperative game theory hypothesizes that the joint strategy of a set of players in a game must satisfy an "equilibrium concept". All other joint strategies are considered impossible; the only issue is what equilibrium…
The General Video Game Artificial Intelligence (GVGAI) competition has been running for several years with various tracks. This paper focuses on the challenge of the GVGAI learning track in which 3 games are selected and 2 levels are given…
In classical game theory, optimal strategies are determined for games with complete information; this requires knowledge of the opponent's goals. We analyze games when a player is mistaken about their opponents goals. For definitiveness, we…
Simple stochastic games are turn-based 2.5-player zero-sum graph games with a reachability objective. The problem is to compute the winning probability as well as the optimal strategies of both players. In this paper, we compare the three…