A Class of Consistent Share Functions For Games in Coalition Structure

A cooperative game with transferable utility -or simply a TU-game- describes a situation in which players can obtain certain payoffs by cooperation.A value function for these games is a function which assigns to every such a game a distribution of the payoffs over the players in the game.An alternative type of solutions are share functions which assign to every player in a TU-game its share in the payoffs to be distributed.In this paper we consider cooperative games in which the players are organized into an a priori coalition structure being a finite partition of the set of players.We introduce a general method for defining a class of share functions for such games in coalition structure using a multiplication property that states that the share of player i in the total payoff is equal to the share of player i in some internal game within i 's a priori coalition, multiplied by the share of this coalition in an external game between the a priori given coalitions.We show that these coalition structure share functions satisfy certain consistency properties.We provide axiomatizations of this class of coalition structure share functions using these consistency and multiplication properties.game theory

Analyzing Catastrophic Backtracking Behavior in Practical Regular Expression Matching

We develop a formal perspective on how regular expression matching works in Java, a popular representative of the category of regex-directed matching engines. In particular, we define an automata model which captures all the aspects needed to study such matching engines in a formal way. Based on this, we propose two types of static analysis, which take a regular expression and tell whether there exists a family of strings which makes Java-style matching run in exponential time.Comment: In Proceedings AFL 2014, arXiv:1405.527

An Owen-type value for games with two-level communication structures

We introduce an Owen-type value for games with two-level communication structures, being structures where the players are partitioned into a coalition structure such that there exists restricted communication between as well as within the a priori unions of the coalition structure. Both types of communication restrictions are modeled by an undirected communication graph, so there is a communication graph between the unions of the coalition structure as well as a communication graph on the players in every union. We also show that, for particular two-level communication structures, the Owen value and the Aumann-Drèze value for games with coalition structures, the Myerson value for communication graph games and the equal surplus division solution appear as special cases of this new value

Ordered Context-Free Grammars Revisited

We continue our study of ordered context-free grammars, a grammar formalism that places an order on the parse trees produced by the corresponding context-free grammar. In particular, we simplify our previous definition of a derivation of a string for a given ordered context-free grammar, and present a parsing algorithm, using shared packed parse forests, with time complexity O(n^4), where n is the length of the input string being parsed.Comment: In Proceedings NCMA 2023, arXiv:2309.0733

An efficient and fair solution for communication graph games\ud

We introduce an efficient solution for games with communication graph structures and show that it is characterized by efficiency, fairness and a new axiom called component balancedness. This latter axiom compares for every component in the communication graph the total payo to the players of this component in the game itself to the total payoff of these players when applying the solution to the subgame induced by this component

When using voter advice applications, citizens should be aware that they reflect the political assumptions of their developers

Voter Advice Applications (VAA’s) have grown in popularity over recent election cycles, with users matched to a party on the basis of their agreement or disagreement with certain statements or policies. Here, Thomas Fossen and Bert Van Der Brink argue that though VAA’s present themselves as objective sources of political information, they in fact reflect the presuppositions of their developers, and their users should be aware of this when using them

Formalizing BPE Tokenization

In this paper, we formalize practical byte pair encoding tokenization as it is used in large language models and other NLP systems, in particular we formally define and investigate the semantics of the SentencePiece and HuggingFace tokenizers, in particular how they relate to each other, depending on how the tokenization rules are constructed. Beyond this we consider how tokenization can be performed in an incremental fashion, as well as doing it left-to-right using an amount of memory constant in the length of the string, enabling e.g. using a finite state string-to-string transducer.Comment: In Proceedings NCMA 2023, arXiv:2309.0733