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This paper introduces a new solution concept for non-cooperative games in normal form with no ties and pure strategies: the Perfectly Transparent Equilibrium. The players are rational in all possible worlds and know each other's strategies…

Federated learning is a setting where agents, each with access to their own data source, combine models from local data to create a global model. If agents are drawing their data from different distributions, though, federated learning…

Quantum game theory offers a lot of interesting questions, and it is relevant to use the quantum information theory to resolve or improve games with lack of information : how to use the power of quantum entanglement to show the superiority…

Probabilistic concurrent/distributed strategies have so far not been investigated thoroughly in the context of imperfect information, where the Player has only partial knowledge of the moves made by the Opponent. In a situation where the…

The game of best choice (or "secretary problem") is a model for making an irrevocable decision among a fixed number of candidate choices that are presented sequentially in random order, one at a time. Because the classically optimal…

We study the problem of computing an $\epsilon$-Nash equilibrium in repeated games. Earlier work by Borgs et al. [2010] suggests that this problem is intractable. We show that if we make a slight change to their model---modeling the players…

Suppose one desires to randomly sample a pair of objects such as socks, hoping to get a matching pair. Even in the simplest situation for sampling, which is sampling with replacement, the innocent phrase "the distribution of the color of a…

Infinite games where several players seek to coordinate under imperfect information are known to be intractable, unless the information flow is severely restricted. Examples of undecidable cases typically feature a situation where players…

We show that in any $n$-player $m$-action normal-form game, we can obtain an approximate equilibrium by sampling any mixed-action equilibrium a small number of times. We study three types of equilibria: Nash, correlated and coarse…

We study the classic divide-and-choose method for equitably allocating divisible goods between two players who are rational, self-interested Bayesian agents. The players have additive values for the goods. The prior distributions on those…

A proper edge $t$-coloring of a graph $G$ is a coloring of edges of $G$ with colors $1,2,...,t$ such that all colors are used, and no two adjacent edges receive the same color. The set of colors of edges incident with a vertex $x$ is called…

Game Theory concepts have been successfully applied in a wide variety of domains over the past decade. Sports and games are one of the popular areas of game theory application owing to its merits and benefits in solving complex scenarios.…

We construct a statistical ensemble of games, where in each independent subensemble we have two players playing the same game. We derive the mean payoffs per move of the representative players of the game, and we evaluate all the…

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…

A poset game is a two-player game played over a partially ordered set (poset) in which the players alternate choosing an element of the poset, removing it and all elements greater than it. The first player unable to select an element of the…

Conformal prediction is a statistically rigorous method for quantifying uncertainty in models by having them output sets of predictions, with larger sets indicating more uncertainty. However, prediction sets are not inherently actionable;…

We consider how an agent should update her uncertainty when it is represented by a set P of probability distributions and the agent observes that a random variable X takes on value x, given that the agent makes decisions using the minimax…

Many variations of the classical graph coloring model have been intensively studied due to their multiple applications; scheduling problems and aircraft assignments, for instance, motivate the robust coloring problem. This model gets to…

We consider a state discrimination problem which deals with settings of minimum-error and unambiguous discrimination systematically by introducing a margin for the probability of an incorrect guess. We analyze discrimination of three…

Models in which the number of goals scored by a team in a soccer match follow a Poisson distribution, or a closely related one, have been widely discussed. We here consider a soccer match as an experiment to assess which of two teams is…