Related papers: Invertibility modulo dead-ending no-P-universes
We propose an interpretation of the infinite sum of combinatorial games. In such an interpretation, plays involve infinite runs, but without loops. The notion of a run is quite natural, but different possibilities arises for the notion of…
Quantum game theory lays a foundation for understanding the interaction of people using quantum computers with conflicting interests. Recently Zhang proposed a simple yet rich model to study quantum strategic games, and addressed some…
In many multiagent environments, a designer has some, but limited control over the game being played. In this paper, we formalize this by considering incompletely specified games, in which some entries of the payoff matrices can be chosen…
If $R$ and $M$ are Hilbert modules (in the sense of R. G. Douglas and V. I. Paulsen), we study the relationship between invertible module maps $X:R\to{M}$ and $X_{z}:R/R_{z}\to{M/M_{z}}$. In particular, for quasi-free Hilbert modules $R$…
We consider the problem of a particular kind of quantum correlation that arises in some two-party games. In these games, one player is presented with a question they must answer, yielding an outcome of either 'win' or 'lose'. Molina and…
We define a class of zero-sum games with combinatorial structure, where the best response problem of one player is to maximize a submodular function. For example, this class includes security games played on networks, as well as the problem…
We study variations of classical combinatorial games on two finite heaps of tokens, a.k.a. \emph{subtraction games}. Given non-negative integers $p_1,q_1, p_2,q_2$, where $p_1q_2 > q_1p_2$, $p_1>0$ and $q_2>0$, two players alternate in…
A two-player one-round binary game consists of two cooperative players who each replies by one bit to a message that he receives privately; they win the game if both questions and answers satisfy some predetermined property. A game is…
In this paper, we analyze the mis\`ere versions of two impartial combinatorial games: k-Bounded Greedy Nim and Greedy Nim. We present a complete solution to both games by showing necessary and sufficient conditions for a position to be…
Zero forcing is a combinatorial game played on a graph where the goal is to start with all vertices unfilled and to change them to filled at minimal cost. In the original variation of the game there were two options. Namely, to fill any one…
Games on recursive game graphs can be used to reason about the control flow of sequential programs with recursion. In games over recursive game graphs, the most natural notion of strategy is the modular strategy, i.e., a strategy that is…
This paper studies complexity theoretic aspects of quantum refereed games, which are abstract games between two competing players that send quantum states to a referee, who performs an efficiently implementable joint measurement on the two…
The physical world obeys the rules of quantum, as opposed to classical, physics. Since the playing of any particular game requires physical resources, the question arises as to how Game Theory itself would change if it were extended into…
The class of passable games was recently introduced by Selinger as a class of combinatorial games that are suitable for modelling monotone set coloring games such as Hex. In a monotone set coloring game, the players alternately color the…
Imitation is simple behavior which uses successful actions of others in order to deal with one's own problems. Because success of imitation generally depends on whether profit of an imitating agent coincides with those of other agents or…
Game-theoretic probability uses the structure of gambles to define a concept like probability, but which is more flexible and robust. We show that results in game-theoretic probability can be thought of as minimax theorems for specific…
We study the applicability of quantum algorithms in computational game theory and generalize some results related to Subtraction games, which are sometimes referred to as one-heap Nim games. In quantum game theory, a subset of Subtraction…
We survey recent developments in the theory of impartial combinatorial games in misere play, focusing on how the Sprague-Grundy theory of normal-play impartial games generalizes to misere play via the indistinguishability quotient…
Combinatorial Game Theory typically studies sequential rulesets with perfect information where two players alternate moves. There are rulesets with {\em entailing moves} that break the alternating play axiom and/or restrict the other…
Games with unawareness model strategic situations in which players' perceptions about the game are limited. They take into account the fact that the players may be unaware of some of the strategies available to them or their opponents as…