Related papers: A probabilistic look at the infinite hat-guessing …
We propose a logical framework combining a game-theoretic study of abilities of agents to achieve quantitative objectives in multi-player games by optimizing payoffs or preferences on outcomes with a logical analysis of the abilities of…
Guessing games for directed graphs were introduced by Riis for studying multiple unicast network coding problems. In a guessing game, the players toss generalised dice and can see some of the other outcomes depending on the structure of an…
We study variants of regular infinite games where the strict alternation of moves between the two players is subject to modifications. The second player may postpone a move for a finite number of steps, or, in other words, exploit in his…
Can a probabilistic gambler get arbitrarily rich when all deterministic gamblers fail? We study this problem in the context of algorithmic randomness, introducing a new notion -- almost everywhere computable randomness. A binary sequence…
We examine a two-person game we call Will-Testing in which the strategy space for both players is a real number. It has no equilibrium. When an infinitely large set of players plays this in all possible pairings, there is an equilibrium for…
We study a model of games that combines concurrency, imperfect information and stochastic aspects. Those are finite states games in which, at each round, the two players choose, simultaneously and independently, an action. Then a successor…
The "War of Attrition" is a classical game theoretic model that was first introduced to mathematically describe certain non-violent animal behavior. The original setup considers two participating players in a one-shot game competing for a…
Reachability games are two-player games played on a graph, where the objective of $\texttt{REACH}$ player is to reach the target set whereas the objective of $\texttt{SAFE}$ player is to stay away from the target set. Reachability games…
We consider games with two antagonistic players --- \'Elo\"ise (modelling a program) and Ab\'elard (modelling a byzantine environment) --- and a third, unpredictable and uncontrollable player, that we call Nature. Motivated by the fact that…
Quantum entanglement is known to provide a strong advantage in many two-party distributed tasks. We investigate the question of how much entanglement is needed to reach optimal performance. For the first time we show that there exists a…
Machine learning relies on the assumption that unseen test instances of a classification problem follow the same distribution as observed training data. However, this principle can break down when machine learning is used to make important…
In this paper we study the Three Hat Problem which appeared in Puzzle Corner of the Technology Review magazine. This puzzle gives a scenario in which three players wearing hats are sitting together and each hat can be seen by everyone…
In this paper, we study a game with positive or plus infinite expectation and determine the optimal proportion of investment for maximizing the limit expectation of growth rate per attempt. With this objective, we introduce a new pricing…
We introduce an evolutionary game with feedback between perception and reality, which we call the reality game. It is a game of chance in which the probabilities for different objective outcomes (e.g., heads or tails in a coin toss) depend…
This paper is on developing some computer-assisted proof methods involving non-classical inequalities for Shannon entropy. Two areas of the applications of information inequalities are studied: Secret sharing schemes and hat guessing games.…
It is shown that an equiprobability hypothesis leads to a scenario in which it is possible to predict the outcome of a single toss of a fair coin with a success probability greater than 50%. We discuss whether this hypothesis might be…
To predict the behavior of a population game when time becomes very long, the process that characterizes the evolution of our game dynamics must be reversible. Known games satisfying this are 2 strategy games as well as potential games with…
We introduce games with probabilistic uncertainty, a natural model for controller synthesis in which the controller observes the state of the system through imprecise sensors that provide correct information about the current state with a…
In simple card games, cards are dealt one at a time and the player guesses each card sequentially. We study problems where feedback (e.g. correct/incorrect) is given after each guess. For decks with repeated values (as in blackjack where…
What happen in the brain when human beings play games with computers? Here a simple zero-sum game was conducted to investigate how people make decision via their brain even they know that their opponent is a computer. There are two choices…