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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…
We introduce a new approach for computing optimal equilibria via learning in games. It applies to extensive-form settings with any number of players, including mechanism design, information design, and solution concepts such as correlated,…
We show that for any $\varepsilon>0$ there is an XOR game $G=G(\varepsilon)$ with $\Theta(\varepsilon^{-1/5})$ inputs for one player and $\Theta(\varepsilon^{-2/5})$ inputs for the other player such that $\Omega(\varepsilon^{-1/5})$ ebits…
In this paper, we introduce a framework of new mathematical representation of Game Theory, including static classical game and static quantum game. The idea is to find a set of base vectors in every single-player strategy space and to…
Algorithmic game theory (AGT) focuses on the design and analysis of algorithms for interacting agents, with interactions rigorously formalized within the framework of games. Results from AGT find applications in domains such as online…
Two standard algorithms for approximately solving two-player zero-sum concurrent reachability games are value iteration and strategy iteration. We prove upper and lower bounds of 2^(m^(Theta(N))) on the worst case number of iterations…
We develop methods to formally describe and compare games, in order to probe questions of game structure and design, and as a stepping stone to predicting player behavior from design patterns. We define a grammar-like formalism to describe…
Reachability games are two-player games played on a graph, where the objective of $\texttt{REACH}$ player is to reach the target set whereas the objective of $\texttt{SAFE}$ player is to stay away from the target set. Reachability games…
Offline learning of strategies takes data efficiency to its extreme by restricting algorithms to a fixed dataset of state-action trajectories. We consider the problem in a mixed-motive multiagent setting, where the goal is to solve a game…
Blotto Games are a popular model of multi-dimensional strategic resource allocation. Two players allocate resources in different battlefields in an auction setting. While competition with equal budgets is well understood, little is known…
We present a model of pragmatic language understanding, where utterances are produced and understood by searching for regularized equilibria of signaling games. In this model (which we call ReCo, for Regularized Conventions), speakers and…
In strategic scenarios where decision-makers operate at different hierarchical levels, traditional optimization methods are often inadequate for handling uncertainties from incomplete information or unpredictable external factors. To fill…
A valuation for a player in a game in extensive form is an assignment of numeric values to the players moves. The valuation reflects the desirability moves. We assume a myopic player, who chooses a move with the highest valuation.…
Imagine we want to split a group of agents into teams in the most \emph{efficient} way, considering that each agent has their own preferences about their teammates. This scenario is modeled by the extensively studied \textsc{Coalition…
We propose a distributed algorithm to compute an equilibrium in aggregate games where players communicate over a fixed undirected network. Our algorithm exploits correlated perturbation to obfuscate information shared over the network. We…
Evaluating agent performance when outcomes are stochastic and agents use randomized strategies can be challenging when there is limited data available. The variance of sampled outcomes may make the simple approach of Monte Carlo sampling…
Simple stochastic games are turn-based 2.5-player games with a reachability objective. The basic question asks whether one player can ensure reaching a given target with at least a given probability. A natural extension is games with a…
Tic Tac Toe is amongst the most well-known games. It has already been shown that it is a biased game, giving more chances to win for the first player leaving only a draw or a loss as possibilities for the opponent, assuming both the players…
We seek a route to the equilibrium where all the agents cooperate in the iterated prisoner's dilemma game on a two-dimensional plane, focusing on the role of tit-for-tat strategy. When a time horizon, within which a strategy can recall the…
We propose a novel online learning method for minimizing regret in large extensive-form games. The approach learns a function approximator online to estimate the regret for choosing a particular action. A no-regret algorithm uses these…