arXiv subjects

Stanisław Kaźmierowski

Publications and source records attributed to Stanisław Kaźmierowski.

5 recordsLinked to original sources

arXiv2026

Nearly Group-Separable Elections

We study the problem of computing how close a given election is to being group-separable, measuring proximity by swaps of adjacent candidates in the votes. We also consider several other domains, including caterpillar group-separable, balanced group-separable, single-peaked, and single-crossing ones. Our problem is generally intractable, but we find practical FPT algorithms parameterized by the number of candidates or swaps. For the latter case, our algorithm applies to all domains characterized by finite forbidden subelections, resolving a well-established open problem. We supplement our theoretical findings with experimental analysis.

cs.GT↗

arXiv2024

Equilibria of the Colonel Blotto Games with Costs

This paper studies a generalized variant of the Colonel Blotto game, referred to as the Colonel Blotto game with costs. Unlike the classic Colonel Blotto game, which imposes the use-it-or-lose-it budget assumption, the Colonel Blotto game with costs captures the strategic importance of costs related both to obtaining resources and assigning them across battlefields. We show that every instance of the Colonel Blotto game with costs is strategically equivalent to an instance of the zero-sum Colonel Blotto game with one additional battlefield. This enables the computation of Nash equilibria of the Colonel Blotto game with costs in polynomial time with respect to the game parameters: the number of battlefields and the number of resources available to the players.

cs.GT↗

arXiv2024

An Equilibrium Analysis of the Arad-Rubinstein Game

Colonel Blotto games with discrete strategy spaces effectively illustrate the intricate nature of multidimensional strategic reasoning. This paper studies the equilibrium set of such games where, in line with prior experimental work, the tie-breaking rule is allowed to be flexible. We begin by pointing out that equilibrium constructions known from the literature extend to our class of games. However, we also note that irrespective of the tie-breaking rule, the equilibrium set is excessively large. Specifically, any pure strategy that allocates at most twice the fair share to each battlefield is used with positive probability in some equilibrium. Furthermore, refinements based on the elimination of weakly dominated strategies prove ineffective. To derive specific predictions amid this multiplicity, we compute strategies resulting from long-run adaptive learning.

cs.GT↗

arXiv2024

Efficient Method for Finding Optimal Strategies in Chopstick Auctions with Uniform Objects Values

We propose an algorithm for computing Nash equilibria (NE) in a class of conflicts with multiple battlefields with uniform battlefield values and a non-linear aggregation function. By expanding the symmetrization idea of Hart [9], proposed for the Colonel Blotto game, to the wider class of symmetric conflicts with multiple battlefields, we reduce the number of strategies of the players by an exponential factor. We propose a clash matrix algorithm which allows for computing the payoffs in the symmetrized model in polynomial time. Combining symmetrization and clash matrix algorithm with the double oracle algorithm we obtain an algorithm for computing NE in the models in question that achieves a significant speed-up as compared to the standard, LP-based, approach. We also introduce a heuristic to further speed up the process. Overall, our approach offers an efficient and novel method for computing NE in a specific class of conflicts, with potential practical applications in various fields.

cs.GT↗

arXiv2023

Computation of Nash Equilibria of Attack and Defense Games on Networks

We consider the computation of a Nash equilibrium in attack and defense games on networks (Bloch et al. [1]). We prove that a Nash Equilibrium of the game can be computed in polynomial time with respect to the number of nodes in the network. We propose an algorithm that runs in O(n4) time with respect to the number of nodes of the network, n.

cs.GT↗