Related papers: Battle Sheep is PSPACE-complete
In this paper we will be introducing a type of game which as far as this author is aware has never been studied before. These are games where there are two players, one who is trying to get one of his pieces, called a King to a predefined…
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…
Matching tile games are an extremely popular game genre. Arguably the most popular iteration, Match-3 games, are simple to understand puzzle games, making them great benchmarks for research. In this paper, we propose developing different…
Many problems in compositional synthesis and verification of multi-agent systems -- such as rational verification and assume-guarantee verification in probabilistic systems -- reduce to reasoning about two-player multi-objective stochastic…
This paper studies the optimization of strategies in the context of possibly randomized two players zero-sum games with incomplete information. We compare 5 algorithms for tuning the parameters of strategies over a benchmark of 12 games. A…
The Colonel Blotto game, formulated by Emile Borel, involves players allocating limited resources to multiple battlefields simultaneously, with the winner being the one who allocates more resources to each battlefield. Computation of the…
This paper presents an empirical exploration of non-transitivity in perfect-information games, specifically focusing on Xiangqi, a traditional Chinese board game comparable in game-tree complexity to chess and shogi. By analyzing over…
Tic Tac Toe is amongst the most well-known games. It has already been shown that it is a biased game, giving more chances to win for the first player leaving only a draw or a loss as possibilities for the opponent, assuming both the players…
We study the Maker-Maker version of the domination game introduced in 2018 by Duch\^ene et al. Given a graph, two players alternately claim vertices. The first player to claim a dominating set of the graph wins. As the Maker-Breaker…
In this paper we present TDLeaf(lambda), a variation on the TD(lambda) algorithm that enables it to be used in conjunction with game-tree search. We present some experiments in which our chess program ``KnightCap'' used TDLeaf(lambda) to…
Numerous popular abstract strategy games ranging from Hex and Havannah to Lines of Action belong to the class of connection games. Still, very few complexity results on such games have been obtained since Hex was proved PSPACE-complete in…
We introduce a new class of totally balanced cooperative TU games, namely p -additive games. It is inspired by the class of inventory games that arises from inventory situations with temporary discounts (Toledo, 2002) and contains the class…
We show that the classical game LaserTank is $\mathrm{NP}$-complete, even when the tank movement is restricted to a single column and the only blocks appearing on the board are mirrors and solid blocks. We show this by reducing $3$-SAT…
This paper presents a technique for approximating, up to any precision, the set of subgame-perfect equilibria (SPE) in discounted repeated games. The process starts with a single hypercube approximation of the set of SPE. Then the initial…
The centipede game is a two-player non-zero-sum game. Each turn, a player can choose whether they want to take or pass a growing reward. The classical, rational solution of this game shows defection in the first round, when in reality,…
Weighted voting games are a popular class of coalitional games that are widely used to model real-life situations of decision-making. They can be applied, for instance, to analyze legislative processes in parliaments or voting in corporate…
We analyze the computational complexity of several new variants of edge-matching puzzles. First we analyze inequality (instead of equality) constraints between adjacent tiles, proving the problem NP-complete for strict inequalities but…
We present the Battlesnake Challenge, a framework for multi-agent reinforcement learning with Human-In-the-Loop Learning (HILL). It is developed upon Battlesnake, a multiplayer extension of the traditional Snake game in which 2 or more…
We examine a two-person game we call Will-Testing in which the strategy space for both players is a real number. It has no equilibrium. When an infinitely large set of players plays this in all possible pairings, there is an equilibrium for…
We introduce a new two-player game on graphs, in which players alternate choosing vertices until the set of chosen vertices forms a dominating set. The last player to choose a vertex is the winner. The game fits into the scheme of several…