相关论文: Further Hopping with Toads and Frogs
The paper [Ras15a] introduced distribution-valued games. This game-theoretic model uses probability distributions as payoffs for games in order to express uncertainty about the payoffs. The player's preferences for different payoffs are…
This paper provides effective methods for the polyhedral formulation of impartial finite combinatorial games as lattice games. Given a rational strategy for a lattice game, a polynomial time algorithm is presented to decide (i) whether a…
Flip a coin repeatedly, and stop whenever you want. Your payoff is the proportion of heads, and you wish to maximize this payoff in expectation. This so-called Chow-Robbins game is amenable to computer analysis, but while simple-minded…
In Newcomb's paradox you choose to receive either the contents of a particular closed box, or the contents of both that closed box and another one. Before you choose, a prediction algorithm deduces your choice, and fills the two boxes based…
The work we present in this paper initiated the formal study of fractional hedonic games, coalition formation games in which the utility of a player is the average value he ascribes to the members of his coalition. Among other settings,…
A positional game is a game where two players sequentially label vertices of a hypergraph, consisting of a board and a collection of winning sets, with colors assigned to each player until all vertices of the board are claimed. The first…
We introduce a new family of Parrondo's games of alternating losing strategies in order to get a winning result. In our version of the games we consider an ensemble of players and use "social" rules in which the probabilities of the games…
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…
We investigate combinatorial issues relating to the use of random orbit approximations to the attractor of an iterated function system with the aim of clarifying the role of the stochastic process during generation the orbit. A Baire…
We study a game in which one keeps flipping a coin until a given finite string of heads and tails occurs. We find the expected number of coin flips to end the game when the ending string consists of at most four maximal runs of heads or…
Planning safe robot motions in the presence of humans requires reliable forecasts of future human motion. However, simply predicting the most likely motion from prior interactions does not guarantee safety. Such forecasts fail to model the…
Inspired by the theory of poset games, we introduce a new compound of impartial combinatorial games and provide a complete analysis in the spirit of the Sprague-Grundy theory. Furthermore, we establish several substitution and reduction…
This work stages Foosball as a versatile platform for advancing scientific research, particularly in the realm of robot learning. We present an automated Foosball table along with its corresponding simulated counterpart, showcasing a…
We identify a choiceless variation of the box game paradox, in which players predict unknown real numbers with near-perfect accuracy despite lacking any useful information. We also verify that choice is necessary in the solution of the…
We investigate conditions under which positions in combinatorial games admit simple values. We introduce a unified diamond framework, the $\Diamond_A$-property ($A\in\{\mathbb{Z},\mathbb{D}$), for sets of positions closed under options.…
Combinatorial Game Theory has also been called `additive game theory', whenever the analysis involves sums of independent game components. Such {\em disjunctive sums} invoke comparison between games, which allows abstract values to be…
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…
We research a combinatorial game based on the Cookie Monster problem called the Cookie Monster game that generalizes the games of Nim and Wythoff. We also propose several combinatorial games that are in between the Cookie Monster game and…
We provide elementary proofs of several results concerning the possible outcomes arising from a fixed profile within the class of positional voting systems. Our arguments enable a simple and explicit construction of paradoxical profiles,…
We prove many new results about interacting Fock spaces. We pose many open problems; for most of them we prove that their solutions have no choice but being nontrivial. We ask the kind reader to consult the extended abstract in the paper.