Related papers: A Game of Nontransitive Dice

We show that under some general conditions the finite memory determinacy of a class of two-player win/lose games played on finite graphs implies the existence of a Nash equilibrium built from finite memory strategies for the corresponding…

We introduce a 2-player game played on an infinite grid, initially empty, where each player in turn chooses a vertex and colours it. The first player aims to create some pattern from a target set, while the second player aims to prevent it.…

In this paper, I prove the existence of a pure-strategy Nash equilibrium for a large class of games with nonconvex strategy spaces. Specifically, if each player's strategies form a compact, connected Euclidean neighborhood retract and if…

We prove that a deterministic n-person shortest path game has a Nash equlibrium in pure and stationary strategies if it is edge-symmetric (that is (u,v) is a move whenever (v,u) is, apart from moves entering terminal vertices) and the…

This paper considers a two-player game where each player chooses a resource from a finite collection of options. Each resource brings a random reward. Both players have statistical information regarding the rewards of each resource.…

Zeckendorf proved that every positive integer $n$ can be written uniquely as the sum of non-adjacent Fibonacci numbers; a similar result holds for other positive linear recurrence sequences. These legal decompositions can be used to…

We consider a multi-player non-zero-sum turn-based game (abbreviated as multi-player game) on a finite directed graph. A secure equilibrium (SE) is a strategy profile in which no player has the incentive to deviate from the strategy because…

Let A be a finite subset of $\nat$. Then NIM(A;n) is the following 2-player game: initially there are $n$ stones on the board and the players alternate removing $a\in A$ stones. The first player who cannot move loses. This game has been…

A group of players which contain n sellers and n buyers bargain over the partitions of n pies. A seller(/buyer) has to reach an agreement with a buyer (/seller) on the division of a pie. The players bargain in a system like the stock…

This paper studies a 2-players zero-sum Dynkin game arising from pricing an option on an asset whose rate of return is unknown to both players. Using filtering techniques we first reduce the problem to a zero-sum Dynkin game on a…

In an $\epsilon$-Nash equilibrium, a player can gain at most $\epsilon$ by unilaterally changing his behaviour. For two-player (bimatrix) games with payoffs in $[0,1]$, the best-known$\epsilon$ achievable in polynomial time is 0.3393. In…

We consider a partially asymmetric three-players zero-sum game with two strategic variables. Two players (A and B) have the same payoff functions, and Player C does not. Two strategic variables are $t_i$'s and $s_i$'s for $i=A, B, C$.…

In this paper we consider non zero-sum games where multiple players control the drift of a process, and their payoffs depend on its ergodic behaviour. We establish their connection with systems of Ergodic BSDEs, and prove the existence of a…

Wide machine learning tasks can be formulated as non-convex multi-player games, where Nash equilibrium (NE) is an acceptable solution to all players, since no one can benefit from changing its strategy unilaterally. Attributed to the…

We consider a general nonzero-sum impulse game with two players. The main mathematical contribution of the paper is a verification theorem which provides, under some regularity conditions, a suitable system of quasi-variational inequalities…

In this paper we study the nonzero-sum Dynkin game in continuous time which is a two player non-cooperative game on stopping times. We show that it has a Nash equilibrium point for general stochastic processes. As an application, we…

In the game "Super Six", after successfully getting rid of a stick by rolling with the die a number that is not occupied, the player has the choice to continue to roll the die or to stop and to hand over the die to their opponent. The…

We introduce a variant of the classic poker game blackjack -- the continuous blackjack. We study the Nash Equilibrium as well as the case where players deviate from it. We then pivot to the study of a large class of adaptive strategies and…

We examine short combinatorial games for three or more players under a new play convention in which a player who cannot move on their turn is the unique loser. We show that many theorems of impartial and partizan two-player games under…

Quantum games with incomplete information can be studied within a Bayesian framework. We consider a version of prisoner's dilemma (PD) in this framework with three players and characterize the Nash equilibria. A variation of the standard PD…