arXiv subjects

Václav Kratochvíl

Publications and source records attributed to Václav Kratochvíl.

6 recordsLinked to original sources

arXiv2026

An Anonymized Urn-Based Experimental Dataset on Decision-Making under Risk and Ambiguity

This data paper describes an anonymized release derived from controlled behavioral experiments on decision-making under risk (known probabilities) and ambiguous uncertainty (partially specified or unknown probabilities) in Ellsberg-type urn tasks. The release contains 4,486 decision records from 246 adult participant records across two implementations (laboratory and online). In each task, participants reported their maximum stake to enter a subsequent lottery; these stake responses can be interpreted as proxies for willingness to pay within the implemented incentive mechanism. In a subset of tasks, participants also selected the color they wished to bet on. The online implementation additionally includes ex-post evaluations of perceived uncertainty across situations. The repository further provides detailed game definitions, realized lottery outcomes, participant instructions, and a data dictionary of variables. The source export contained 4,544 decision records; 58 records belonging to five participants younger than 18 were excluded from this release because documentation of guardian permission for unrestricted public data publication was not available. The dataset supports replication studies, comparisons of ambiguity-attitude models, and analyses of behavioral stability under repeated participation.

econ.GN↗

arXiv2026

Graphical view on linear extensions of finite posets

One of the possible cryptomorphic definitions of a partially ordered set (= a poset) $P$ on a non-empty finite ground set $N$ is in terms of the set ${\cal L}(P)$ of all its linear extensions, that is, in terms of the set of total orders on $N$ consistent with $P$. Any total order on $N$ can be interpreted as a node of a particular graph, called the permutohedral graph (over $N$), because it is indeed the graph of a certain polytope in $\mathbb{R}^{N}$, known as the permutohedron. It is shown in the paper that a non-empty set of total orders on $N$ equals to ${\cal L}(P)$ for some poset $P$ on $N$ if and only if it is a geodetically convex set in the permutohedral graph. This result means that a purely graphical concept of geodetical convexity in this graph is a cryptomorphic definition of a finite poset. In particular, the lattice of geodetically convex sets in this graph is graded and its height function is described in graphical terms. A counter-example, however, shows that the height function does not correspond to the usual graphical diameter, relating this matter to a combinatorial concept of the dimension of a poset. Two alternative cryptomorphic views on a poset $P$ on $N$ are also discussed. The geometric counterpart is its full-dimensional braid cone in $\mathbb{R}^{N}$, while a combinatorial alternative is a topology on $N$ distinguishing points, often referred as a (finite) distributive lattice.

math.CO↗

arXiv2021

Facets of the cone of exact games

The class of exact transferable utility coalitional games, introduced in 1972 by Schmeidler, has been studied both in the context of game theory and in the context of imprecise probabilities. We characterize the cone of exact games by describing the minimal set of linear inequalities defining this cone; these facet-defining inequalities for the exact cone appear to correspond to certain set systems (= systems of coalitions). We noticed that non-empty proper coalitions having non-zero coefficients in these facet-defining inequalities form set systems with particular properties. More specifically, we introduce the concept of a semi-balanced system of coalitions, which generalizes the classic concept of a balanced coalitional system in cooperative game theory. The semi-balanced coalitional systems provide valid inequalities for the exact cone and minimal semi-balanced systems (in the sense of inclusion of set systems) characterize this cone. We also introduce basic classification of minimal semi-balanced systems, their pictorial representatives and a substantial concept of an indecomposable (minimal) semi-balanced system of coalitions. The main result of the paper is that indecomposable semi-balanced systems are in one-to-one correspondence with facet-defining inequalities for the exact cone. The secondary relevant result is the rebuttal of a former conjecture claiming that a coalitional game is exact iff it is totally balanced and its anti-dual is also totally balanced. We additionally characterize those inequalities which are facet-defining both for the exact cone and the cone of totally balanced games.

math.CO↗

arXiv2017

Composition of Credal Sets via Polyhedral Geometry

Recently introduced composition operator for credal sets is an analogy of such operators in probability, possibility, evidence and valuation-based systems theories. It was designed to construct multidimensional models (in the framework of credal sets) from a system of low- dimensional credal sets. In this paper we study its potential from the computational point of view utilizing methods of polyhedral geometry.

cs.AI↗

arXiv2017

Solving the Goddard problem by an influence diagram

Influence diagrams are a decision-theoretic extension of probabilistic graphical models. In this paper we show how they can be used to solve the Goddard problem. We present results of numerical experiments with this problem and compare the solutions provided by influence diagrams with the optimal solution.

cs.AI↗

arXiv2015

Influence diagrams for the optimization of a vehicle speed profile

Influence diagrams are decision theoretic extensions of Bayesian networks. They are applied to diverse decision problems. In this paper we apply influence diagrams to the optimization of a vehicle speed profile. We present results of computational experiments in which an influence diagram was used to optimize the speed profile of a Formula 1 race car at the Silverstone F1 circuit. The computed lap time and speed profiles correspond well to those achieved by test pilots. An extended version of our model that considers a more complex optimization function and diverse traffic constraints is currently being tested onboard a testing car by a major car manufacturer. This paper opens doors for new applications of influence diagrams.

cs.AI↗