Related papers: Semi-restricted Rock, Paper, Scissors
Simple stochastic games are turn-based 2.5-player zero-sum graph games with a reachability objective. The problem is to compute the winning probability as well as the optimal strategies of both players. In this paper, we compare the three…
The Rock-Scissors-Paper game has been studied to account for cyclic behaviour under various game dynamics. We use a two-person parametrised version of this game. The cyclic behaviour is observed near a heteroclinic cycle, in a heteroclinic…
The $(m,n)$-online Ramsey game is a combinatorial game between two players, Builder and Painter. Starting from an infinite set of isolated vertices, Builder draws an edge on each turn and Painter immediately paints it red or blue. Builder's…
We introduce and analyze the ordered Zeckendorf game, a novel combinatorial two-player game inspired by Zeckendorf's Theorem, which guarantees a unique decomposition of every positive integer as a sum of non-consecutive Fibonacci numbers.…
The central result of classical game theory states that every finite normal form game has a Nash equilibrium, provided that players are allowed to use randomized (mixed) strategies. However, in practice, humans are known to be bad at…
We introduce a generalization of "Solo Chess", a single-player variant of the game that can be played on chess.com. The standard version of the game is played on a regular 8 x 8 chessboard by a single player, with only white pieces, using…
We consider the following simple game: We are given a table with ten slots indexed one to ten. In each of the ten rounds of the game, three dice are rolled and the numbers are added. We then put this number into any free slot. For each…
Von Neumann's Min-Max Theorem guarantees that each player of a zero-sum matrix game has an optimal mixed strategy. This paper gives an elementary proof that each player has a near-optimal mixed strategy that chooses uniformly at random from…
Non-transitivity can arise in games with three or more strategies $A,B,C$, when $A$ beats $B$, $B$ beats $C$, and $C$ beats $A$, ($A>B>C>A$). An example is the children's game \textquotedblleft rock, scissors, paper" ($R,S,P$) where…
AlphaZero-style reinforcement learning (RL) algorithms have achieved superhuman performance in many complex board games such as Chess, Shogi, and Go. However, we showcase that these algorithms encounter significant and fundamental…
The game of Hex has two players who take turns placing stones of their respective colors on the hexagons of a rhombus-shaped hexagonal grid. Black wins by completing a crossing between two opposite edges, while White wins by completing a…
We consider a random knockout tournament among players $1, \ldots, n$, in which each match involves two players. The match format is specified by the number of matches played in each round, where the constitution of the matches in a round…
This paper examines multiplayer symmetric constant-sum games with more than two players in a competitive setting, including examples like Mahjong, Poker, and various board and video games. In contrast to two-player zero-sum games,…
A game is rigid if a near-optimal score guarantees, under the sole assumption of the validity of quantum mechanics, that the players are using an approximately unique quantum strategy. Rigidity has a vital role in quantum cryptography as it…
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…
This article discusses two contributions to decision-making in complex partially observable stochastic games. First, we apply two state-of-the-art search techniques that use Monte-Carlo sampling to the task of approximating a…
We study a type of generalized recursive game introduced by Castronova, Chen, and Zumbrun featuring increasing stakes, with an emphasis on continuous guts poker and $1$ v. $n$ coalitions. Our main results are to develop practical numerical…
We investigate a game played between two players, Maker and Breaker, on a countably infinite complete graph where the vertices are the rational numbers. The players alternately claim unclaimed edges. It is Maker's goal to have after…
In 1901, Bouton proved that a winning strategy of the game of Nim is given by the bitwise XOR, called the nim-sum. But, why does such a weird binary operation work? Led by this question, this paper introduces a categorical reinterpretation…
Policy space response oracles (PSRO) is a multi-agent reinforcement learning algorithm that has achieved state-of-the-art performance in very large two-player zero-sum games. PSRO is based on the tabular double oracle (DO) method, an…