Related papers: How to correctly prune tropical trees

We introduce a new model involving TU-games and exogenous structures. Specifically, we consider that each player in a population can choose an element in a strategy set and that, for every possible strategy profile, a TU-game is associated…

This paper examines multiplayer symmetric constant-sum games with more than two players in a competitive setting, including examples like Mahjong, Poker, and various board and video games. In contrast to two-player zero-sum games,…

Projection games constitute an important class of nonlocal games where, for any answer from the first player, there is a unique correct answer for the second player. This class of games captures nonlocal games arising from constraint…

Subtraction games is a class of combinatorial games. It was solved since the Sprague-Grundy Theory was put forward. This paper described a new algorithm for subtraction games. The new algorithm can find win or lost positions in subtraction…

The article provides a solution algorithm for the linear programming problem (LPP) with the latter being presented as an antagonistic matrix game so the game's further solution is based on the iterative method. The algorithm is presented as…

We define a two-player combinatorial game in which players take alternate turns; each turn consists on deleting a vertex of a graph, together with all the edges containing such vertex. If any vertex became isolated by a player's move then…

We consider a discrete best approximation problem formulated in the framework of tropical algebra, which deals with the theory and applications of algebraic systems with idempotent operations. Given a set of samples of input and output of…

The alpha-beta pruning algorithms have been popular in game tree searching ever since they were discovered. Numerous enhancements are proposed in literature and it is often overwhelming as to which would be the best for implementation. A…

We reconcile the discrepancy between the complex and tropical counts of some enumerative problems reducing to positive characteristic. Each problem that we consider suggests a prime with special behaviour. Modulo this prime, the solutions…

Many packing, scheduling and covering problems that were previously considered by computer science literature in the context of various transportation and production problems, appear also suitable for describing and modeling various…

We address the online linear optimization problem when the actions of the forecaster are represented by binary vectors. Our goal is to understand the magnitude of the minimax regret for the worst possible set of actions. We study the…

Weighted timed games are played by two players on a timed automaton equipped with weights: one player wants to minimise the accumulated weight while reaching a target, while the other has an opposite objective. Used in a reactive synthesis…

The min-max optimization problem, also known as the saddle point problem, is a classical optimization problem which is also studied in the context of zero-sum games. Given a class of objective functions, the goal is to find a value for the…

The policy iteration method is a classical algorithm for solving optimal control problems. In this paper, we introduce a policy iteration method for Mean Field Games systems, and we study the convergence of this procedure to a solution of…

We consider an autonomous navigation problem, whereby a traveler aims at traversing an environment in which an adversary tries to set an ambush. A two players zero sum game is introduced. Players' strategies are computed as random path…

We apply Game Theory to a mathematical representation of two competing teams of agents connected within a complex network, where the ability of each side to manoeuvre their resource and degrade that of the other depends on their ability to…

We study parameterized versions of classical algorithms for computing shortest-path trees. This is most easily expressed in terms of tropical geometry. Applications include shortest paths in traffic networks with variable link travel times.

This paper extends the optimal-trading framework developed in arXiv:2409.03586v1 to compute optimal strategies with real-world constraints. The aim of the current paper, as with the previous, is to study trading in the context of…

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 properties that optimal solutions need to have, and devised a…

Parikh's game logic is a PDL-like fixpoint logic interpreted on monotone neighbourhood frames that represent the strategic power of players in determined two-player games. Game logic translates into a fragment of the monotone…