Related papers: A randomized strategy in the mirror game
In this paper, we consider zero-sum repeated games in which the maximizer is restricted to strategies requiring no more than a limited amount of randomness. Particularly, we analyze the maxmin payoff of the maximizer in two models: the…
In two-player finite-state stochastic games of partial observation on graphs, in every state of the graph, the players simultaneously choose an action, and their joint actions determine a probability distribution over the successor states.…
We unify and consolidate various results about non-signall-ing games, a subclass of non-local two-player one-round games, by introducing and studying several new families of games and establishing general theorems about them, which extend a…
We study two-player general sum repeated finite games where the rewards of each player are generated from an unknown distribution. Our aim is to find the egalitarian bargaining solution (EBS) for the repeated game, which can lead to much…
The winning condition of a parity game with costs requires an arbitrary, but fixed bound on the cost incurred between occurrences of odd colors and the next occurrence of a larger even one. Such games quantitatively extend parity games…
We study a variation of the minority game. There are N agents. Each has to choose between one of two alternatives everyday, and there is reward to each member of the smaller group. The agents cannot communicate with each other, but try to…
We consider a two-player search game on a tree $T$. One vertex (unknown to the players) is randomly selected as the target. The players alternately guess vertices. If a guess $v$ is not the target, then both players are informed in which…
Quantum resources may provide advantage over their classical counterparts. Theoretically, in certain tasks, this advantage can be very high. In this work, we construct such a task based on a game, mediated by Referee and played between…
We investigate symmetric equilibria of mutual reinforcement learning when both players alternately learn the optimal memory-two strategies against the opponent in the repeated prisoners' dilemma game. We provide a necessary condition for…
In the context of multiplayer games, the parallel repetition problem can be phrased as follows: given a game $G$ with optimal winning probability $1-\alpha$ and its repeated version $G^n$ (in which $n$ games are played together, in…
We study a combinatorial game derived from a problem in the German National Mathematics Competition. In this game, two players take turns removing numbers from a finite set of natural numbers, aiming to satisfy a certain divisibility…
We use a recently discovered constrained de Finetti reduction (aka "Post-Selection Lemma") to study the parallel repetition of multi-player non-local games under no-signalling strategies. Since the technique allows us to reduce general…
Infinitely repeated games can support cooperative outcomes that are not equilibria in the one-shot game. The idea is to make sure that any gains from deviating will be offset by retaliation in future rounds. However, this model of…
This paper studies the game of guessing riffle-shuffled cards with complete feedback. A deck of $n$ cards labelled 1 to $n$ is riffle-shuffled once and placed on a table. A player tries to guess the cards from top and is given complete…
We consider a card guessing game with complete feedback. An ordered deck of $n$ cards labeled $1$ up to $n$ is shelf-shuffled exactly one time. One after the other a single card is drawn from the shuffled deck. The guesser makes has guess…
We study the parallel Minority Game, where a group of agents, each having two choices, try to independently decide on a strategy such that they stay on minority between their own two choices. However, there are multiple such groups of…
We consider 2-player games played on a finite state space for infinite rounds. The games are concurrent: in each round, the two players choose their moves simultaneously; the current state and the moves determine the successor. We consider…
Repeated games have provided an explanation how mutual cooperation can be achieved even if defection is more favorable in a one-shot game in prisoner's dilemma situation. Recently found zero-determinant strategies have substantially been…
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.…
Given two finite ordered sets $A = \{a_1, \ldots, a_m\}$ and $B = \{b_1, \ldots, b_n\}$, introduce the set of $m n$ outcomes of the game $O = \{(a, b) \mid a \in A, b \in B\} = \{(a_i, b_j) \mid i \in I = \{1, \ldots, m\}, j \in J = \{1,…