Related papers: How to correctly prune tropical trees
While discounted payoff games and classic games that reduce to them, like parity and mean-payoff games, are symmetric, their solutions are not. We have taken a fresh view on the constraints that optimal solutions need to satisfy, and…
Matrix games constitute a fundamental problem of game theory and describe a situation of two players with completely conflicting interests. We show how methods from statistical mechanics can be used to investigate the statistical properties…
This paper addresses the optimization problem to maximize the total costs that can be shared among a group of agents, while maintaining stability in the sense of the core constraints of a cooperative transferable utility game, or TU game.…
Adaptive momentum methods have recently attracted a lot of attention for training of deep neural networks. They use an exponential moving average of past gradients of the objective function to update both search directions and learning…
Algorithms for model checking and satisfiability of the modal $\mu$-calculus start by converting formulas to alternating parity tree automata. Thus, model checking is reduced to checking acceptance by tree automata and satisfiability to…
For an arbitrary tree we investigate the problems of constructing a maximum matching which minimizes or maximizes the cardinality of a maximum matching of the graph obtained from original one by its removal and present corresponding…
$\mu$-Calculus and automata on infinite trees are complementary ways of describing infinite tree languages. The correspondence between $\mu$-Calculus and alternating tree automaton is used to solve the satisfiability and model checking…
We study the applicability of quantum algorithms in computational game theory and generalize some results related to Subtraction games, which are sometimes referred to as one-heap Nim games. In quantum game theory, a subset of Subtraction…
The restricted max-min fair allocation problem seeks an allocation of resources to players that maximizes the minimum total value obtained by any player. It is NP-hard to approximate the problem to a ratio less than 2. Comparing the current…
This paper introduces a new structure of commutative semiring, generalizing the tropical semiring, and having an arithmetic that modifies the standard tropical operations, i.e. summation and maximum. Although our framework is combinatorial,…
Parity games have important practical applications in formal verification and synthesis, especially to solve the model-checking problem of the modal mu-calculus. They are also interesting from the theory perspective, because they are widely…
We study a fair division problem with indivisible items, namely the computation of maximin share allocations. Given a set of $n$ players, the maximin share of a single player is the best she can guarantee to herself, if she would partition…
We propose an algorithm for computing approximate Nash equilibria of partially observable games using Monte-Carlo tree search based on recent bandit methods. We obtain experimental results for the game of phantom tic-tac-toe, showing that…
Deterministic game-solving algorithms are conventionally analyzed in the light of their average-case complexity against a distribution of random game-trees, where leaf values are independently sampled from a fixed distribution. This…
We consider multidimensional optimization problems in the framework of tropical mathematics. The problems are formulated to minimize a nonlinear objective function that is defined on vectors over an idempotent semifield and calculated by…
We study nondeterministic strategies in parity games with the aim of computing a most permissive winning strategy. Following earlier work, we measure permissiveness in terms of the average number/weight of transitions blocked by the…
We propose an alternating minimization heuristic for regression over the space of tropical rational functions with fixed exponents. The method alternates between fitting the numerator and denominator terms via tropical polynomial…
Tropical algebra is an emerging field with a number of applications in various areas of mathematics. In many of these applications appeal to tropical polynomials allows to study properties of mathematical objects such as algebraic varieties…
Leadership games provide a powerful paradigm to model many real-world settings. Most literature focuses on games with a single follower who acts optimistically, breaking ties in favour of the leader. Unfortunately, for real-world…
Tropical circuits are circuits with Min and Plus, or Max and Plus operations as gates. Their importance stems from their intimate relation to dynamic programming algorithms. The power of tropical circuits lies somewhere between that of…