Related papers: Local obstructions in sequences revisited

In this paper, we introduce post-selection games, a generalization of nonlocal games where each round can be not only won or lost by the players, but also discarded by the referee. Such games naturally formalize possibilistic proofs of…

Subtraction games are a class of impartial combinatorial games whose positions correspond to nonnegative integers and whose moves correspond to subtracting one of a fixed set of numbers from the current position. Though they are easy to…

In this note, we investigate combinatorial games where both players move randomly (each turn, independently selecting a legal move uniformly at random). In this model, we provide closed-form expressions for the expected number of turns in a…

We propose and analyse a 2-parameter family of 2-player games on two heaps of tokens, and present a strategy based on a class of sequences. The strategy looks easy, but is actually hard. A class of exotic numeration systems is then used,…

We prove an infinite family of lacunary recurrences for the Lucas numbers using combinatorial means.

We characterize winning strategies in various infinite games involving filters on the natural numbers in terms of combinatorics or structural properties of the given filter. These generalize several ultrafilter games of Galvin.

We are often interested in decomposing complex, structured data into simple components that explain the data. The linear version of this problem is well-studied as dictionary learning and factor analysis. In this work, we propose a…

Game semantics and winning strategies offer a potential conceptual bridge between semantics and proof systems of logics. We illustrate this link for hybrid logic -- an extension of modal logic that allows for explicit reference to worlds…

In this paper, we introduce and study a first-order mean-field game obstacle problem. We examine the case of local dependence on the measure under assumptions that include both the logarithmic case and power-like nonlinearities. Since the…

In many combinatorial games, one can prove that the first player wins under best play using a simple but non-constructive argument called strategy-stealing. This work is about the complexity behind these proofs: how hard is it to actually…

Regular games form a well-established class of games for analysis and synthesis of reactive systems. They include coloured Muller games, McNaughton games, Muller games, Rabin games, and Streett games. These games are played on directed…

In this work the properties of multi choice minority games are studied by means of extensive computational simulations. We have considered several ways of rewarding the strategies of the players and compared the resulting behaviours of the…

In this note, we prove the existence of an equilibrium concept, dubbed conditional strategy equilibrium, for non-cooperative games in which a strategy of a player is a function from the other players' actions to her own actions. We study…

We examine a type of modified Monte Carlo Tree Search (MCTS) for strategising in combinatorial games. The modifications are derived by analysing simplified strategies and simplified versions of the underlying game and then using the results…

We use a recently discovered constrained de Finetti reduction (aka "Post-Selection Lemma") to study the parallel repetition of multi-player non-local games under no-signalling strategies. Since the technique allows us to reduce general…

Knockout tournaments, also known as single-elimination or cup tournaments, are a popular form of sports competitions. In the standard probabilistic setting, for each pairing of players, one of the players wins the game with a certain (a…

We present a robust framework with computational algorithms to support decision makers in sequential games. Our framework includes methods to solve games with complete information, assess the robustness of such solutions and, finally,…

This paper coins the notion of Joker games, a variant of concurrent games where the players are not strictly adversarial. Instead, Player 1 can get help from Player 2 by playing a Joker move. We formalize these games as cost games and…

Operating vehicles in adversarial environments require non-conventional planning techniques. A two-player, zero-sum non-cooperative game is introduced, which is solved via a linear program. An extension is proposed to construct networks…

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…