Related papers: Strongly Solving 2048 4x3
Yahtzee is a classic dice game with a stochastic, combinatorial structure and delayed rewards, making it an interesting mid-scale RL benchmark. While an optimal policy for solitaire Yahtzee can be computed using dynamic programming methods,…
The input to the Multiway Cut problem is a weighted undirected graph, with nonnegative edge weights, and $k$ designated terminals. The goal is to partition the vertices of the graph into $k$ parts, each containing exactly one of the…
Considering uncertainties and disturbances is an important, yet challenging, step in successful decision making. The problem becomes more challenging in safety-constrained environments. In this paper, we propose a robust and safe trajectory…
This paper presents a new solution concept for multiplayer stochastic games, namely, acceptable strategy profiles. For each player $i$ and state $s$ in a stochastic game, let $w_i(s)$ be a real number. A strategy profile is…
Consider the following probabilistic one-player game: The board is a graph with $n$ vertices, which initially contains no edges. In each step, a new edge is drawn uniformly at random from all non-edges and is presented to the player,…
A fundamental challenge in imperfect-information games is that states do not have well-defined values. As a result, depth-limited search algorithms used in single-agent settings and perfect-information games do not apply. This paper…
Reward allocation, also known as the credit assignment problem, has been an important topic in economics, engineering, and machine learning. An important concept in reward allocation is the core, which is the set of stable allocations where…
We study two-player zero-sum concurrent stochastic games with finite state and action space played for an infinite number of steps. In every step, the two players simultaneously and independently choose an action. Given the current state…
In this paper, we settle the sampling complexity of solving discounted two-player turn-based zero-sum stochastic games up to polylogarithmic factors. Given a stochastic game with discount factor $\gamma\in(0,1)$ we provide an algorithm that…
We consider imperfect information stochastic games where we require the players to use pure (i.e. non randomised) strategies. We consider reachability, safety, B\"uchi and co-B\"uchi objectives, and investigate the existence of…
Recent advances in deep reinforcement learning (RL) have led to considerable progress in many 2-player zero-sum games, such as Go, Poker and Starcraft. The purely adversarial nature of such games allows for conceptually simple and…
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…
State redistribution is an algorithm that stabilizes cut cells for embedded boundary grid methods. This work extends the earlier algorithm in several important ways. First, state redistribution is extended to three spatial dimensions.…
A two-player one-round binary game consists of two cooperative players who each replies by one bit to a message that he receives privately; they win the game if both questions and answers satisfy some predetermined property. A game is…
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…
We provide an algorithm to find the value and an optimal strategy of the solitaire variant of the Ten Thousand dice game in the framework of Markov Control Processes. Once an optimal critical threshold is found, the set of non-stopping…
A 5x5 board is the smallest board on which one can set up all kind of chess pieces as a start position. We consider Gardner's minichess variant in which all pieces are set as in a standard chessboard (from Rook to King). This game has…
We consider multiplayer stochastic games in which the payoff of each player is a bounded and Borel-measurable function of the infinite play. By using a generalization of the technique of Martin (1998) and Maitra and Sudderth (1998), we show…
We consider concurrent mean-payoff games, a very well-studied class of two-player (player 1 vs player 2) zero-sum games on finite-state graphs where every transition is assigned a reward between 0 and 1, and the payoff function is the…
We define a class of zero-sum games with combinatorial structure, where the best response problem of one player is to maximize a submodular function. For example, this class includes security games played on networks, as well as the problem…