Related papers: Impartial achievement and avoidance games for gene…

Two-player quantitative zero-sum games provide a natural framework to synthesize controllers with performance guarantees for reactive systems within an uncontrollable environment. Classical settings include mean-payoff games, where the…

We start with the well-known game below: Two players hold a sheet of paper to their forehead on which a positive integer is written. The numbers are consecutive and each player can only see the number of the other one. In each time step,…

For normal play, impartial games, we define penults as those positions in which every option results in an immediate win for the other player. We explore the number of tokens in penults of two positional games, Impartial Tic and Impartial…

We consider a biased version of Maker-Breaker domination games, which were recently introduced by Gledel, Ir{\v{s}}i{\v{c}}, and Klav{\v{z}}ar. Two players, Dominator and Staller, alternatingly claim vertices of a graph $G$ where Dominator…

Estimating discrete games of complete information is often computationally difficult due to partial identification and the absence of closed-form moment characterizations. This paper proposes computationally tractable approaches to…

We study the computational complexity of finding stable outcomes in hedonic games, which are a class of coalition formation games. We restrict our attention to symmetric additively-separable hedonic games, which are a nontrivial subclass of…

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…

This paper studies a large class of two-player perfect-information turn-based parity games on infinite graphs, namely those generated by collapsible pushdown automata. The main motivation for studying these games comes from the connections…

In an impartial combinatorial game, both players have the same options in the game and all its subpositions. The classical Sprague-Grundy Theory was developed for short impartial games, where players have a finite number of options, there…

In this paper we will discuss scoring play games. We will give the basic definitions for scoring play games, and show that they form a well defined set, with clear and distinct outcome classes under these definitions. We will also show that…

In many situations, both in human and artificial societies, cooperating agents have different status with respect to the activity and it is not uncommon that certain actions are only allowed to coalitions that satisfy certain criteria,…

We consider the degrees of non-computability (Weihrauch degrees) of finding winning strategies (or more generally, Nash equilibria) in infinite sequential games with certain winning sets (or more generally, outcome sets). In particular, we…

We study the abstract Banach-Mazur game played with finitely generated structures instead of open sets. We characterize the existence of winning strategies aiming at a single countably generated structure. We also introduce the concept of…

We study biased Maker-Breaker positional games between two players, one of whom is playing randomly against an opponent with an optimal strategy. In this paper we consider the scenario when Maker plays randomly and Breaker is "clever", and…

Let $\Lambda$ be an infinite connected graph, and let $v_0$ be a vertex of $\Lambda$. We consider the following positional game. Two players, Maker and Breaker, play in alternating turns. Initially all edges of $\Lambda$ are marked as…

We study two positional games played on hypergraphs, whose edges may be interpreted as winning sets. Two players take turns picking a previously unpicked vertex of the hypergraph. We say a player fills an edge if that player has picked all…

We revisit games in partition function form, i.e. cooperative games where the payoff of a coalition depends on the partition of the entire set of players. We assume that each coalition computes its worth having probabilistic beliefs over…

We study a random game in which two players in turn play a fixed number of moves. For each move, there are two possible choices. To each possible outcome of the game we assign a winner in an i.i.d. fashion with a fixed parameter p. In the…

The classical, complete-information two-player games assume that the problem data (in particular the payoff matrix) is known exactly by both players. In a now famous result, Nash has shown that any such game has an equilibrium in mixed…

We study impartial take away games on 2 unordered piles of finite nonnegative numbers of tokens $(x,y)$. Two players alternate in removing at least one and at most all tokens from the respective piles, according to certain rules, and the…