Related papers: A randomized strategy in the mirror game
In each round of a Swiss-system tournament, players of similar score are paired against each other. An intentional early loss therefore might lead to weaker opponents in later rounds and thus to a better final tournament result - a…
Behavioural equivalences can be characterized via bisimulation, modal logics, and spoiler-duplicator games. In this paper we work in the general setting of coalgebra and focus on generic algorithms for computing the winning strategies of…
Pre-trained neural networks are commonly used and reused in the machine learning community. Alice trains a model for a particular task, and a part of her neural network is reused by Bob for a different task, often to great effect. To what…
We seek a route to the equilibrium where all the agents cooperate in the iterated prisoner's dilemma game on a two-dimensional plane, focusing on the role of tit-for-tat strategy. When a time horizon, within which a strategy can recall the…
In a recent work Conger and Howald derived asymptotic formulas for the randomness, after shuffling, of decks with repeating cards or all-distinct decks dealt into hands. In the latter case the deck does not need to be fully randomized: the…
Given a skew-symmetric matrix, the corresponding two-player symmetric zero-sum game is defined as follows: one player, the row player, chooses a row and the other player, the column player, chooses a column. The payoff of the row player is…
We consider the following game. A deck with $m$ copies of each of $n$ distinct cards is shuffled in a perfectly random way. The Guesser sequentially guesses the card from top to bottom. After each guess, the Guesser is informed whether the…
We study two-player games of infinite duration that are played on finite or infinite game graphs. A winning strategy for such a game is positional if it only depends on the current position, and not on the history of the play. A game is…
A sequence S is nonrepetitive if no two adjacent blocks of S are the same. In 1906 Thue proved that there exist arbitrarily long nonrepetitive sequences over 3 symbols. We consider the online variant of this result in which a nonrepetitive…
While many theoretical studies have revealed the strategies that could lead to and maintain cooperation in the Iterated Prisoner's Dilemma, less is known about what human participants actually do in this game and how strategies change when…
Consider the following probability puzzle: A fair coin is flipped n times. For each HT in the resulting sequence, Bob gets a point, and for each HH Alice gets a point. Who is more likely to win? We provide a proof that Bob wins more often…
We study two-player games of infinite duration that are played on finite or infinite game graphs. A winning strategy for such a game is positional if it only depends on the current position, and not on the history of the play. A game is…
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…
Two-player (antagonistic) games on (possibly stochastic) graphs are a prevalent model in theoretical computer science, notably as a framework for reactive synthesis. Optimal strategies may require randomisation when dealing with inherently…
We study two-player games with alternating moves played on infinite trees. Our main focus is on the case where the trees are full (regular) and the winning set is open (with respect to the product topology on the tree). Gale and Stewart…
We investigate the problem of secure source coding with a two-sided helper in a game-theoretic framework. Alice (A) and Helen (H) view iid correlated information sequences $X^n$ and $Y^n$ respectively. Alice communicates to Bob (B) at rate…
We study \emph{partial-information} two-player turn-based games on graphs with omega-regular objectives, when the partial-information player has \emph{limited memory}. Such games are a natural formalization for reactive synthesis when the…
We study a sequential resource allocation problem between a fixed number of arms. On each iteration the algorithm distributes a resource among the arms in order to maximize the expected success rate. Allocating more of the resource to a…
We study how to learn $\epsilon$-optimal strategies in zero-sum imperfect information games (IIG) with trajectory feedback. In this setting, players update their policies sequentially based on their observations over a fixed number of…
In 1982, Harary introduced the concept of Ramsey achievement game on graphs. Given a graph $F$ with no isolated vertices. Consider the following game played on the complete graph $K_n$ by two players Alice and Bob. First, Alice colors one…