Related papers: The mathematics of Spinpossible
Combinatorial Game Theory is a branch of mathematics and theoretical computer science that studies sequential 2-player games with perfect information. Normal play is the convention where a player who cannot move loses. Here, we generalize…
For 24 years, it has been an open problem to obtain improved bounds, for the maximal function over a sparse sequence of discrete spherical averages, going beyond the range for the full discrete spherical maximal function. I formulate a…
In combinatorial game theory, the lower and upper bounds of the number of games born by day $4$ have been recognized as $3.0 \cdot 10^{12}$ and $10^{434}$, respectively. In this study, we improve the lower bound to $10^{28.2}$ and the upper…
We continue the investigation of finite-duration variants of infinite-duration games by extending known results for games played on finite graphs to those played on infinite ones. In particular, we establish an equivalence between pushdown…
Recent successes of game-theoretic formulations in ML have caused a resurgence of research interest in differentiable games. Overwhelmingly, that research focuses on methods and upper bounds on their speed of convergence. In this work, we…
We study a robust optimal stopping problem with respect to a set $\cP$ of mutually singular probabilities. This can be interpreted as a zero-sum controller-stopper game in which the stopper is trying to maximize its pay-off while an adverse…
We consider the computational complexity of the question whether a certain strategy can be removed from a game by means of iterated elimination of dominated strategies. In particular, we study the influence of different definitions of…
The allowed patterns of a map are those permutations in the same relative order as the initial segments of orbits realized by the map. In this paper, we characterize and provide enumerative bounds for the allowed patterns of signed shifts,…
This paper investigates some necessary and sufficient conditions for a game to be a potential game. At first, we extend the classical results of Slade and Monderer and Shapley from games with one-dimensional action spaces to games with…
The theory behind the Lights Out game has been developed by several authors. The aim of this work is to present some results related to this game using Linear Algebra. We establish a criterion for the solubility of this game in the case of…
In this paper we investigate a game of optimal stopping with incomplete information. There are two players of which only one is informed about the precise structure of the game. Observing the informed player the uninformed player is given…
In this paper, we study the conjunction of possibility measures when they are interpreted as coherent upper probabilities, that is, as upper bounds for some set of probability measures. We identify conditions under which the minimum of two…
We prove an n-EXPTIME lower bound for the problem of deciding the winner in a reachability game on Higher Order Pushdown Automata (HPDA) of level n. This bound matches the known upper bound for parity games on HPDA. As a consequence the…
We show that the Brier game of prediction is mixable and find the optimal learning rate and substitution function for it. The resulting prediction algorithm is applied to predict results of football and tennis matches. The theoretical…
A comply/constrain game or a game with a Muller twist is a game where the next player is allowed to place constraints on opponent's next move. We develop a closed form formula for the Grundy value of the single-pile subtraction game where…
In this expository article, we give an overview of the concept of potential mean field games of first order. We give a new proof that minimizers of the potential are equilibria by using a Lagrangian formulation. We also provide criteria to…
Three notions of random stopping times exist in the literature. We introduce two concepts of equivalence of random stopping times, motivated by optimal stopping problems and stopping games respectively. We prove that these two concepts…
We study a new modification of the Arrival problem, which allows for nodes that exhibit random as well as controlled behaviour, in addition to switching nodes. We study the computational complexity of these extensions, building on existing…
We modify Wythoff's game by allowing an additional move, which we call a "split", and show how the $P$-positions are coded by the Tribonacci word. We analyze the table of letter positions of arbitrary $k$-bonacci words and find a…
We study infinite two-player games where one of the players is unsure about the set of moves available to the other player. In particular, the set of moves of the other player is a strict superset of what she assumes it to be. We explore…