Related papers: $2^3$ Quantified Boolean Formula Games and Their C…
We consider the problem of incrementally solving a sequence of quantified Boolean formulae (QBF). Incremental solving aims at using information learned from one formula in the process of solving the next formulae in the sequence. Based on a…
We use the example of playing a 2-player game with entangled quantum objects to investigate the effect of quantum correlation. We find that for simple game scenarios it is classical correlation that is the central feature and that these…
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…
Weighted voting games are ubiquitous mathematical models which are used in economics, political science, neuroscience, threshold logic, reliability theory and distributed systems. They model situations where agents with variable voting…
We analyze the computational complexity of two 2-player games involving packing objects into a box. In the first game, players alternate drawing polycubes from a shared pile and placing them into an initially empty box in any available…
This paper depicts algorithms for solving the decision Boolean Satisfiability Problem. An extreme problem is formulated to analyze the complexity of algorithms and the complexity for solving it. A novel and easy reformulation as a lottery…
We analyze the Gambler's problem, a simple reinforcement learning problem where the gambler has the chance to double or lose the bets until the target is reached. This is an early example introduced in the reinforcement learning textbook by…
We study computational aspects of three prominent voting rules that use approval ballots to elect multiple winners. These rules are satisfaction approval voting, proportional approval voting, and reweighted approval voting. We first show…
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…
Recent successes of game-theoretic formulations in ML have caused a resurgence of research interest in differentiable games. Overwhelmingly, that research focuses on methods and upper bounds on their speed of convergence. In this work, we…
A new approach to play games quantum mechanically is proposed. We consider two players who perform measurements in an EPR-type setting. The payoff relations are defined as functions of *correlations*, i.e. without reference to classical or…
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…
An extension of QPTL is considered where functional dependencies among the quantified variables can be restricted in such a way that their current values are independent of the future values of the other variables. This restriction is…
In this paper, the CHSH quantum game is extended to four players. This is achieved by exploring all possible 4-variable Boolean functions to identify those that yield a game scenario with a quantum advantage using a specific entangled…
We present a quantization scheme for a three-player Prisoner's Dilemma game. It is shown that entanglement plays a dominant role in the three-player quantum game. Four different types of payoffs are identified on the basis of different…
We exploit symmetries to give short proofs for two prominent formula families of QBF proof complexity. On the one hand, we employ symmetry breakers. On the other hand, we enrich the (relatively weak) QBF resolution calculus Q-Res with the…
We introduce the notion of linearly representable games. Broadly speaking, these are TU games that can be described by as many parameters as the number of players, like weighted voting games, airport games, or bankruptcy games. We show that…
We consider two aspects of quantum game theory: the extent to which the quantum solution solves the original classical game, and to what extent the new solution can be obtained in a classical model.
We study finite-memory (FM) determinacy in games on finite graphs, a central question for applications in controller synthesis, as FM strategies correspond to implementable controllers. We establish general conditions under which FM…
A poset game is a two-player game played over a partially ordered set (poset) in which the players alternate choosing an element of the poset, removing it and all elements greater than it. The first player unable to select an element of the…