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We introduce two-level discounted games played by two players on a perfect-information stochastic game graph. The upper level game is a discounted game and the lower level game is an undiscounted reachability game. Two-level games model…

We consider graph games of infinite duration with winning conditions in parameterized linear temporal logic, where the temporal operators are equipped with variables for time bounds. In model checking such specifications were introduced as…

We present polynomial-time algorithms as well as hardness results for equilibrium computation in atomic splittable routing games, for the case of general convex cost functions. These games model traffic in freight transportation, market…

In common-interest stochastic games all players receive an identical payoff. Players participating in such games must learn to coordinate with each other in order to receive the highest-possible value. A number of reinforcement learning…

This paper studies two-player zero-sum repeated Bayesian games in which every player has a private type that is unknown to the other player, and the initial probability of the type of every player is publicly known. The types of players are…

Based on the existing pivot rules, the simplex method for linear programming is not polynomial in the worst case. Therefore the optimal pivot of the simplex method is crucial. This study proposes the optimal rule to find all shortest pivot…

We study the problem of characterizing optimal learning algorithms for playing repeated games against an adversary with unknown payoffs. In this problem, the first player (called the learner) commits to a learning algorithm against a second…

Iterated coopetitive games capture the situation when one must efficiently balance between cooperation and competition with the other agents over time in order to win the game (e.g., to become the player with highest total utility).…

We study the problem of computing Stackelberg equilibria Stackelberg games whose underlying structure is in congestion games, focusing on the case where each player can choose a single resource (a.k.a. singleton congestion games) and one of…

This study presents a rigorous mathematical approach to the optimization of round and betting policies in Blackjack, using Markov Decision Processes (MDP) and Expected Utility Theory. The analysis considers a direct confrontation between a…

We describe the probability theory behind a casino game, blackjack, and the procedure to compute the optimal strategy for a deck of arbitrary cards and player's expected win given that he follows the optimal strategy. The exact blackjack…

Let $V$ be a multiset of $n$ points in $\mathbb{R}^d$, which we call voters, and let $k\geq 1$ and $\ell\geq 1$ be two given constants. We consider the following game, where two players $\mathcal{P}$ and $\mathcal{Q}$ compete over the…

Balanced knockout tournaments are ubiquitous in sports competitions and are also used in decision-making and elections. The traditional computational question, that asks to compute a draw (optimal draw) that maximizes the winning…

We consider infinite duration alternating move games. These games were previously studied by Roth, Balcan, Kalai and Mansour. They presented an FPTAS for computing an approximated equilibrium, and conjectured that there is a polynomial…

We study the problem of computing an approximate Nash equilibrium of continuous-action game without access to gradients. Such game access is common in reinforcement learning settings, where the environment is typically treated as a black…

We study a two-player discounted zero-sum stochastic game model for dynamic operational planning in military campaigns. At each stage, the players manage multiple commanders who order military actions on objectives that have an open line of…

Yahtzee is a classic dice game with a stochastic, combinatorial structure and delayed rewards, making it an interesting mid-scale RL benchmark. While an optimal policy for solitaire Yahtzee can be computed using dynamic programming methods,…

Despite the many recent practical and theoretical breakthroughs in computational game theory, equilibrium finding in extensive-form team games remains a significant challenge. While NP-hard in the worst case, there are provably efficient…

Many poker systems, whether created with heuristics or machine learning, rely on the probability of winning as a key input. However calculating the precise probability using combinatorics is an intractable problem, so instead we approximate…

Stackelberg games have been widely used to model interactive decision-making problems in a variety of domains such as energy systems, transportation, cybersecurity, and human-robot interaction. However, existing algorithms for solving…