Related papers: Local obstructions in sequences revisited

With increasing game size, a problem of computational complexity arises. This is especially true in real world problems such as in social systems, where there is a significant population of players involved in the game, and the complexity…

In combinatorics, the probabilistic method is a very powerful tool to prove the existence of combinatorial objects with interesting and useful properties. Explicit constructions of objects with such properties are often very difficult, or…

We consider search problems with nonobligatory inspection and single-item or combinatorial selection. A decision maker is presented with a number of items, each of which contains an unknown price, and can pay an inspection cost to observe…

We introduce the sequence-set betting game, a generalization of An. A. Muchnik's non-monotonic betting game. Instead of successively partitioning the infinite binary strings by their value of a bit at a chosen position, as in the…

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…

We announce misere-play solutions to several previously-unsolved combinatorial games. The solutions are described in terms of misere quotients--commutative monoids that encode the additive structure of specific misere-play games. We also…

We consider the problem of learning to perform a task from demonstrations given by teachers or experts, when some of the experts' demonstrations might be adversarial and demonstrate an incorrect way to perform the task. We propose a novel…

The iterated prisoner's dilemma is a game that produces many counter-intuitive and complex behaviors in a social environment, based on very simple basic rules. It illustrates that cooperation can be a good thing even in a competitive world,…

In repeated games, players choose actions concurrently at each step. We consider a parameterized setting of repeated games in which the players form a population of an arbitrary size. Their utility functions encode a reachability objective.…

As we go along with a bioinformatic analysis we stumbled over a new combinatorial question. Although the problem is a very special one, there are maybe more applications than only this one we have. This text is mainly about the general…

This paper concerns two-player alternating play combinatorial games (Conway 1976) in the normal-play convention, i.e. last move wins. Specifically, we study impartial vector subtraction games on tuples of nonnegative integers (Golomb 1966),…

We introduce the notion of invariant vectors of a game and develop the Invariance Reduction Process, which first uses reduction of positions via invariance and then zero and merge reductions of games to arrive at smaller, solved sub-games…

We illustrate how one can use basic combinatorial theory and computer programming technique (Python) to analyze the combinatorial game: Mahjong. The results confirm some folklore concerning the game, and expose some unexpected results.…

This work studies Stackelberg network interdiction games -- an important class of games in which a defender first allocates (randomized) defense resources to a set of critical nodes on a graph while an adversary chooses its path to attack…

Strict linear feasibility or linear separation is usually tackled using efficient approximation/stochastic algorithms (that may even run in sub-linear times in expectation). However, today state of the art for solving…

Kolmogorov complexity is often used as a convenient language for counting and/or probabilistic existence proofs. However, there are some applications where Kolmogorov complexity is used in a more subtle way. We provide one (somehow)…

We revisit the game in which each of several players chooses a pattern and then a coin is flipped repeatedly until one of these patterns is generated. In particular, we demonstrate how to compute the probability of any one player winning…

A combinatorial game is a two-player game without hidden information or chance elements. The main object of combinatorial game theory is to obtain the outcome, which player has a winning strategy, of a given combinatorial game. Positions of…

In repeated-game applications where both the collusive and non-collusive outcomes can be supported as equilibria, researchers must resolve underlying selection questions if theory will be used to understand counterfactual policies. One…

A class of discrete Bidding Combinatorial Games that generalize alternating normal play was introduced by Kant, Larsson, Rai, and Upasany (2022). The major questions concerning optimal outcomes were resolved. By generalizing standard game…