Related papers: The Linking-Unlinking Game
A setup is proposed to play a quantum version of the famous bimatrix game of Prisoners' Dilemma. Multi-slit electron diffraction with each player's pure strategy consisting of opening one of the two slits at his/her disposal are essential…
The notions of captured/lost vertices and dead edges in the Shannon game (Shannon switching game on nodes) are examined using graph theory. Simple methods are presented for identifying some dead edges and some captured sets of vertices,…
The main focus of this paper is on enhancement of two types of game-theoretic learning algorithms: log-linear learning and reinforcement learning. The standard analysis of log-linear learning needs a highly structured environment, i.e.…
Stochastic games combine controllable and adversarial non-determinism with stochastic behavior and are a common tool in control, verification and synthesis of reactive systems facing uncertainty. Multi-objective stochastic games are natural…
In this paper we study the (a : b) Maker-Breaker Connectivity game, played on the edge-set of the complete graph on n vertices. We determine the winner for almost all values of a and b.
We present a novel formulation of quantum game theory based on the Schmidt decomposition, which has the merit that the entanglement of quantum strategies is manifestly quantified. We apply this formulation to 2-player, 2-strategy symmetric…
Nonlocal games yield an unusual perspective on entangled quantum states. The defining property of such games is that a set of players in joint possession of an entangled state can win the game with higher probability than is allowed by…
In this paper, we present an online learning approach for two-player zero-sum linear quadratic games with unknown dynamics. We develop a framework combining regularized least squares model estimation, high probability confidence sets, and…
Strategic interactions between a group of individuals or organisations can be modelled as games played on networks, where a player's payoff depends not only on their actions but also on those of their neighbours. Inferring the network…
Game theoretical techniques have recently become prevalent in many engineering applications, notably in communications. With the emergence of cooperation as a new communication paradigm, and the need for self-organizing, decentralized, and…
We consider a scenario in which two reinforcement learning agents repeatedly play a matrix game against each other and update their parameters after each round. The agents' decision-making is transparent to each other, which allows each…
We consider three variants of a partisan combinatorial game between two players, Left and Right, played on an undirected simple graph. Left is able to delete vertices (and incident edges) while Right is able to delete edges. This natural…
We analyze the two-player game of Knock 'em Down, asymptotically as the number of tokens to be knocked down becomes large. Optimal play requires mixed strategies with deviations of order sqrt(n) from the naive law-of-large numbers…
We consider a two-player game in which the first player (the Guesser) tries to guess, edge-by-edge, the path that second player (the Chooser) takes through a directed graph. At each step, the Guesser makes a wager as to the correctness of…
Traditional coding theory guarantees valid decoding only if a minority of symbols are adversarially manipulated. In contrast, the game of coding framework ensures reliable decoding, even in the presence of an adversarial majority. This…
Lights Out! is a game played on a $5 \times 5$ grid of lights, or more generally on a graph. Pressing lights on the grid allows the player to turn off neighboring lights. The goal of the game is to start with a given initial configuration…
These notes present two normal surface theory algorithms to detect the unknot and use the split-link algorithm to prove that the figure-eight knot is knotted.
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…
Synchronous linear constraint system games are nonlocal games that verify whether or not two players share a solution to a given system of equations. Two algebraic objects associated to these games encode information about the existence of…
A combinatorial game is a two-player game without hidden information or chance elements. One of the major approaches to analyzing games in combinatorial game theory is to break down a given game position into a disjunctive sum of multiple…