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While discounted payoff games and classic games that reduce to them, like parity and mean-payoff games, are symmetric, their solutions are not. We have taken a fresh view on the properties that optimal solutions need to have, and devised a…

We study variations of classical combinatorial games on two finite heaps of tokens, a.k.a. \emph{subtraction games}. Given non-negative integers $p_1,q_1, p_2,q_2$, where $p_1q_2 > q_1p_2$, $p_1>0$ and $q_2>0$, two players alternate in…

We consider two-player games played over finite state spaces for an infinite number of rounds. At each state, the players simultaneously choose moves; the moves determine a successor state. It is often advantageous for players to choose…

We study an impartial avoidance game introduced by Anderson and Harary. The game is played by two players who alternately select previously unselected elements of a finite group. The first player who cannot select an element without making…

We study an impartial game introduced by Anderson and Harary. The game is played by two players who alternately choose previously-unselected elements of a finite group. The first player who builds a generating set from the jointly-selected…

We study the complexity of solving two-player infinite duration games played on a fixed finite graph, where the control of a node is not predetermined but rather assigned randomly. In classic random-turn games, control of each node is…

Prisoner's Dilemma (PD) is a widely studied game that plays an important role in Game Theory. This paper aims at extending PD Tournaments to the case of infinite, finite or infinitesimal payoffs using Sergeyev's Infinity Computing (IC). By…

Toral introduced so-called cooperative Parrondo games, in which there are N players (3 or more) arranged in a circle. At each turn one player is randomly chosen to play. He plays either game A or game B. Game A results in a win or loss of…

We consider extensive form win-lose games over a complete binary-tree of depth $n$ where players act in an alternating manner. We study arguably the simplest random structure of payoffs over such games where 0/1 payoffs in the leafs are…

Social distance games have been extensively studied as a coalition formation model where the utilities of agents in each coalition were captured using a utility function u that took into account distances in a given social network. In this…

We apply the Sprague-Grundy Theorem to LCTR, a new impartial game on partitions in which players take turns removing either the Left Column or the Top Row of the corresponding Young diagram. We establish that the Sprague-Grundy value of any…

Parrondo games with spatial dependence were introduced by Toral (2001) and have been studied extensively. In Toral's model, $N$ players are arranged in a circle. The players play either game $A$ or game $B$. In game $A$, a randomly chosen…

In 1990, Mermin presented a n player game that is won with certainty using n spin-1/2 particles in a GHZ state whilst no classical strategy (or local theory) can win with probability higher than ${1/2} + \frac{1}{2^{\lceil n/2 \rceil}}$…

We examine two-player games over finite weighted graphs with quantitative (mean-payoff or energy) objective, where one of the players additionally needs to satisfy a fairness objective. The specific fairness we consider is called 'strong…

Considering linear-quadratic discrete-time games with unknown input/output/state (i/o/s) dynamics and state, we provide necessary and sufficient conditions for the existence and uniqueness of feedback Nash equilibria (FNE) in the…

We discuss a model of a two-person, non-cooperative stochastic game, inspired by the discrete version of the red-and-black gambling problem presented by Dubins and Savage. Assume that two players hold certain amounts of money. At each stage…

The influential work of Bravo et al. 2018 shows that derivative free play in strongly monotone games has complexity $O(d^2/\varepsilon^3)$, where $\varepsilon$ is the target accuracy on the expected squared distance to the solution. This…

The space of finite games can be decomposed into three orthogonal subspaces [5], which are the subspaces of pure potential games, nonstrategic games and pure harmonic games. The orthogonal projections onto these subspaces are represented as…

We consider multi-player graph games with partial-observation and parity objective. While the decision problem for three-player games with a coalition of the first and second players against the third player is undecidable, we present a…

A game theory inspired methodology is proposed for finding a function's saddle points. While explicit descent methods are known to have severe convergence issues, implicit methods are natural in an adversarial setting, as they take the…