Related papers: Generalized Three and Four Person Hat Game

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…

We introduce a natural variant of weighted voting games, which we refer to as k-Prize Weighted Voting Games. Such games consist of n players with weights, and k prizes, of possibly differing values. The players form coalitions, and the i-th…

Penney's game is a two player zero-sum game in which each player chooses a three-flip pattern of heads and tails and the winner is the player whose pattern occurs first in repeated tosses of a fair coin. Because the players choose…

How many fair coin tosses to choose 1 of $n$ options with uniform probability? Although a probability problem, the solution is essentially number-theoretic, with special roles for Mersenne numbers, Fermat numbers, and the haupt exponent. We…

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…

We give operational meaning to wave-particle duality in terms of discrimination games. Duality arises as a constraint on the probability of winning these games. The games are played with the aid of an n-port interferometer, and involve 3…

Game coloring is a well-studied two-player game in which each player properly colors one vertex of a graph at a time until all the vertices are colored. An `eternal' version of game coloring is introduced in this paper in which the vertices…

We consider multi-player graph games with partial-observation and parity objective. While the decision problem for three-player games with a coalition of the first and second players against the third player is undecidable, we present a…

We consider the following game, played on a $k$-uniform hypergraph $H$. There are $q$ colors available and two players take it in turns to color vertices. A partial coloring is proper if no edge is mono-chromatic. One player, A, wishes to…

In Problem #1542 of Mathematics Magazine, Grossman and Turett define the Cantor game. In his 2007 Mathematics Magazine article about the Cantor game, Matt Baker proves several results and poses three challenging questions about it: Do there…

Two-player win/lose games of infinite duration are involved in several disciplines including computer science and logic. If such a game has deterministic winning strategies, one may ask how simple such strategies can get. The answer may…

In many settings where multiple agents interact, the optimal choices for each agent depend heavily on the choices of the others. These coupled interactions are well-described by a general-sum differential game, in which players have…

Inspired by a chessboard puzzle of Dudeney, the general position problem in graph theory asks for a largest set $S$ of vertices in a graph such that no three elements of $S$ lie on a common shortest path. The number of vertices in such a…

The problem of computing a common point that lies in the intersection of a finite number of closed convex sets, each known to one agent in a network, is studied. This issue, known as the distributed convex feasibility problem or the…

Minority game is a model of heterogeneous players who think inductively. In this game, each player chooses one out of two alternatives every turn and those who end up in the minority side wins. It is instructive to extend the minority game…

This paper studies two-player zero-sum games played on graphs and makes contributions toward the following question: given an objective, how much memory is required to play optimally for that objective? We study regular objectives, where…

Most work in game theory assumes that players are perfect reasoners and have common knowledge of all significant aspects of the game. In earlier work, we proposed a framework for representing and analyzing games with possibly unaware…

Consider a very simple class of (finite) games: after an initial move by nature, each player makes one move. Moreover, the players have common interests: at each node, all the players get the same payoff. We show that the problem of…

Resource allocation problems across multiple contests are ubiquitous in adversarial settings, from military operations to market competition. While Colonel Blotto and General Lotto games have provided valuable theoretical foundations for…

This paper has a twofold scope. The first one is to clarify and put in evidence the isomorphic character of two theories developed in quite different fields: on one side, threshold logic, on the other side, simple games. One of the main…