相关论文: Calculating Ultra-Strong and Extended Solutions fo…
We analyze the computational complexity of the popular computer games Threes!, 1024!, 2048 and many of their variants. For most known versions expanded to an m x n board, we show that it is NP-hard to decide whether a given starting…
We study a robust Dynkin game over a set of mutually singular probabilities. We first prove that for the conservative player of the game, her lower and upper value processes coincide (i.e. She has a value process $V $ in the game). Such a…
We study variants of a stochastic game inspired by backgammon where players may propose to double the stake, with the game state dictated by a one-dimensional random walk. Our variants allow for different numbers of proposals and different…
Flip a coin repeatedly, and stop whenever you want. Your payoff is the proportion of heads, and you wish to maximize this payoff in expectation. This so-called Chow-Robbins game is amenable to computer analysis, but while simple-minded…
We introduce a class of extensive form games where players might not be able to foresee the possible consequences of their decisions and form a model of their opponents which they exploit to achieve a more profitable outcome. We improve…
The solution set of a system of polynomial equations typically contains ill-behaved, singular points. Resolution is a fundamental process in geometry in which we replace singular points with smooth points, while keeping the rest of the…
We present tournament results and several powerful strategies for the Iterated Prisoner's Dilemma created using reinforcement learning techniques (evolutionary and particle swarm algorithms). These strategies are trained to perform well…
We consider a deterministic game with alternate moves and complete information, of which the issue is always the victory of one of the two opponents. We assume that this game is the realization of a random model enjoying some independence…
Usually, to apply game-theoretic methods, we must specify utilities precisely, and we run the risk that the solutions we compute are not robust to errors in this specification. Ordinal games provide an attractive alternative: they require…
Strong solving of perfect-information games certifies optimal play from every reachable position, but the required state-space coverage is often prohibitive. Weak solving is far cheaper, yet it certifies correctness only at the initial…
We develop value iteration-based algorithms to solve in a unified manner different classes of combinatorial zero-sum games with mean-payoff type rewards. These algorithms rely on an oracle, evaluating the dynamic programming operator up to…
Stackelberg equilibria have become increasingly important as a solution concept in computational game theory, largely inspired by practical problems such as security settings. In practice, however, there is typically uncertainty regarding…
An heuristic approach to compute strong Nash (Aumann) equilibria is presented. The method is based on differential evolution and three variants of a generative relation for strong Nash equilibria characterization. Numerical experiments…
Recently, reinforcement learning has been successfully applied to the logical game of Go, various Atari games, and even a 3D game, Labyrinth, though it continues to have problems in sparse reward settings. It is difficult to explore, but…
Tournament solutions are frequently used to select winners from a set of alternatives based on pairwise comparisons between alternatives. Prior work has shown that several common tournament solutions tend to select large winner sets and…
Determining how close a winner of an election is to becoming a loser, or distinguishing between different possible winners of an election, are major problems in computational social choice. We tackle these problems for so-called weighted…
2048 is a stochastic single-player game involving 16 cells on a 4 by 4 grid, where a player chooses a direction among up, down, left, and right to obtain a score by merging two tiles with the same number located in neighboring cells along…
This paper addresses the problem of multi-agent inverse reinforcement learning (MIRL) in a two-player general-sum stochastic game framework. Five variants of MIRL are considered: uCS-MIRL, advE-MIRL, cooE-MIRL, uCE-MIRL, and uNE-MIRL, each…
We transform a Muller game with n vertices into a safety game with (n!)^3 vertices whose solution allows to determine the winning regions of the Muller game and to compute a finite-state winning strategy for one player. This yields a novel…
The Nakamura number of a simple game plays a critical role in preference aggregation (or multi-criterion ranking): the number of alternatives that the players can always deal with rationally is less than this number. We comprehensively…