Related papers: Undecidability of Two-dimensional Robot Games
A two-person zero-sum infinite dimensional differential game of infinite duration with discounted payoff involving hybrid controls is studied. The minimizing player is allowed to take continuous, switching and impulse controls whereas the…
We introduce a guessing game involving a quantum channel, three parties - the sender, the receiver and an eavesdropper, Eve - and a quantum public side channel. We prove that a necessary and sufficient condition for the quantum channel to…
The game in which acts of participants don't have an adequate description in terms of Boolean logic and classical theory of probabilities is considered. The model of the game interaction is constructed on the basis of a non-distributive…
Several variations of hat guessing games have been popularly discussed in recreational mathematics. In a typical hat guessing game, after initially coordinating a strategy, each of $n$ players is assigned a hat from a given color set.…
Each vertex of the infinite $2$-dimensional square lattice graph is assigned, independently, a label that reads trap with probability $p$, target with probability $q$, and open with probability $(1-p-q)$, and each edge is assigned,…
The Z-domination game is a variant of the domination game in which each newly selected vertex $u$ in the game must have a not yet dominated neighbor, but after the move all vertices from the closed neighborhood of $u$ are declared to be…
We investigate determinacy of delay games with Borel winning conditions, infinite-duration two-player games in which one player may delay her moves to obtain a lookahead on her opponent's moves. First, we prove determinacy of such games…
The Maker-Breaker domination game (MBD game) is a two-player game played on a graph $G$ by Dominator and Staller. They alternately select unplayed vertices of $G$. The goal of Dominator is to form a dominating set with the set of vertices…
We extend the formalism of Conjectural Variations games to Stackelberg games involving multiple leaders and a single follower. To solve these nonconvex games, a common assumption is that the leaders compute their strategies having perfect…
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…
Determining an individual's strategic reasoning capability based solely on choice data is a complex task. This complexity arises because sophisticated players might have non-equilibrium beliefs about others, leading to non-equilibrium…
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…
Consider a situation with $n$ agents or players where some of the players form a coalition with a certain collective objective. Simple games are used to model systems that can decide whether coalitions are successful (winning) or not…
J. Beck has shown that if two players alternately select previously unchosen points from the plane, Player 1 can always build a congruent copy of any given finite goal set G, in spite of Player 2's efforts to stop him. We give a finite goal…
This paper provides effective methods for the polyhedral formulation of impartial finite combinatorial games as lattice games. Given a rational strategy for a lattice game, a polynomial time algorithm is presented to decide (i) whether a…
We consider two-player games over finite graphs in which both players are restricted by fairness constraints on their moves. Given a two player game graph $G=(V,E)$ and a set of fair moves $E_f\subseteq E$ a player is said to play "fair" in…
We study a modified prisoner's dilemma game taking place on two-dimensional disordered square lattices. The players are pure strategists and can either cooperate or defect with their immediate neighbors. In the generations each player…
We consider three related problems of robot movement in arbitrary dimensions: coverage, search, and navigation. For each problem, a spherical robot is asked to accomplish a motion-related task in an unknown environment whose geometry is…
We study algorithmic complexity of solving subtraction games in a~fixed dimension with a finite difference set. We prove that there exists a game in this class such that any algorithm solving the game runs in exponential time. Also we prove…
We introduce a new method, involving infinite games and Borel determinacy, which we use to answer several well-known questions in Borel combinatorics.