Related papers: Optimal play in 'Guess Who?'

In this paper, we study a theoretical math problem of game theory and calculus of variations in which we minimize a functional involving two players. A general relationship between the optimal strategies for both players is presented,…

We study the optimal use of information in Markov games with incomplete information on one side and two states. We provide a finite-stage algorithm for calculating the limit value as the gap between stages goes to 0, and an optimal strategy…

In a variant of communication tasks, players cooperate in choosing their local strategies to compute a given task later, working separately. Utilizing quantum bits for communication and sharing entanglement between parties is a recognized…

Quantum entanglement has been recently demonstrated as a useful resource in conflicting interest games of incomplete information between two players, Alice and Bob [Pappa et al., Phys. Rev. Lett. 114, 020401 (2015)]. General setting for…

In this paper, we study the notion of admissibility for randomised strategies in concurrent games. Intuitively, an admissible strategy is one where the player plays `as well as possible', because there is no other strategy that dominates…

Consider concurrent, infinite duration, two-player win/lose games played on graphs. If the winning condition satisfies some simple requirement, the existence of Player 1 winning (finite-memory) strategies is equivalent to the existence of…

The 20 Questions (Q20) game is a well known game which encourages deductive reasoning and creativity. In the game, the answerer first thinks of an object such as a famous person or a kind of animal. Then the questioner tries to guess the…

In this paper we study the complexity of strategic argumentation for dialogue games. A dialogue game is a 2-player game where the parties play arguments. We show how to model dialogue games in a skeptical, non-monotonic formalism, and we…

The standard game-theoretic solution concept, Nash equilibrium, assumes that all players behave rationally. If we follow a Nash equilibrium and opponents are irrational (or follow strategies from a different Nash equilibrium), then we may…

Matrix games constitute a fundamental problem of game theory and describe a situation of two players with completely conflicting interests. We show how methods from statistical mechanics can be used to investigate the statistical properties…

Consider the following one player game. A deck containing $m$ copies of $n$ different card types is shuffled uniformly at random. Each round the player tries to guess the next card in the deck, and then the card is revealed and discarded.…

Acquiring your first language is an incredible feat and not easily duplicated. Learning to communicate using nothing but a few pictureless books, a corpus, would likely be impossible even for humans. Nevertheless, this is the dominating…

Best-response mechanisms (Nisan, Schapira, Valiant, Zohar, 2011) provide a unifying framework for studying various distributed protocols in which the participants are instructed to repeatedly best respond to each others' strategies. Two…

We revisit the classic 'guess my number' game and extend it from its familiar binary form to representations in any integer base. For each base we derive formulas for the number of cards needed to identify a given integer and, conversely,…

In recent years, agents have become capable of communicating seamlessly via natural language and navigating in environments that involve cooperation and competition, a fact that can introduce social dilemmas. Due to the interleaving of…

We characterize the optimal reward functions (scoring rules) that incentivize an agent to acquire information and report it truthfully to the principal. The optimal scoring rules let the agent make a simple binary bet in single-dimensional…

We generalize Ebert's Hat Problem for three persons and three colors. All players guess simultaneously the color of their own hat observing only the hat colors of the other players. It is also allowed for each player to pass: no color is…

We present two efficient algorithms that compute the optimal strategy for cop in the game of Cop v.s. Gambler where the gambler's strategy is not optimal but known to the cop. The first algorithm is analogous to Bellman-Ford algorithm for…

Consider the following hat guessing game: $n$ players are placed on $n$ vertices of a graph, each wearing a hat whose color is arbitrarily chosen from a set of $q$ possible colors. Each player can see the hat colors of his neighbors, but…

Winning probabilities of The Hat Game (Ebert's Hat Problem) with three players and three colors are only known in the symmetric case: all probabilities of the colors are equal. This paper solves the asymmetric case: probabilities may be…