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When testing a statistical hypothesis, is it legitimate to deliberate on the basis of initial data about whether and how to collect further data? Game-theoretic probability's fundamental principle for testing by betting says yes, provided…
Competitive online games use rating systems to match players with similar skills to ensure a satisfying experience for players. In this paper, we focus on the importance of addressing different aspects of playing behavior when modeling…
This paper gives game-theoretic versions of several results on "merging of opinions" obtained in measure-theoretic probability and algorithmic randomness theory. An advantage of the game-theoretic versions over the measure-theoretic results…
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…
Partially-ordered set games, also called poset games, are a class of two-player combinatorial games. The playing field consists of a set of elements, some of which are greater than other elements. Two players take turns removing an element…
Poset games are a class of combinatorial game that remain unsolved. Soltys and Wilson proved that computing wining strategies is in \textbf{PSPACE} and aside from special cases such as Nim and N-Free games, \textbf{P} time algorithms for…
In this work, we design the game semantics for timed equivalences and preorders of timed processes. The timed games corresponding to the various timed relations form a hierarchy. These games are similar to Stirling's bisimulation games. If…
In a distributed game we imagine a team Player engaging a team Opponent in a distributed fashion. Such games and their strategies have been formalised in concurrent games based on event structures. However there are limitations in founding…
In this work the properties of multi choice minority games are studied by means of extensive computational simulations. We have considered several ways of rewarding the strategies of the players and compared the resulting behaviours of the…
In this paper, we consider combinatorial game rulesets based on data structures normally covered in an undergraduate Computer Science Data Structures course: arrays, stacks, queues, priority queues, sets, linked lists, and binary trees. We…
Game semantics is a trace-like denotational semantics for programming languages where the notion of legal observable behaviour of a term is defined combinatorially, by means of rules of a game between the term (the "Proponent") and its…
We study so-called invariant games played with a fixed number $d$ of heaps of matches. A game is described by a finite list $\mathcal{M}$ of integer vectors of length $d$ specifying the legal moves. A move consists in changing the current…
We consider repeated games where the players behave according to cumulative prospect theory (CPT). We show that, when the players have calibrated strategies and behave according to CPT, the natural analog of the notion of correlated…
We present constructions regarding the general behaviour of biased positional games, and amongst others show that the outcome of such a game can differ in an arbitrary way depending on which player starts the game, and that fair biased…
The class of algorithmically computable simple games (i) includes the class of games that have finite carriers and (ii) is included in the class of games that have finite winning coalitions. This paper characterizes computable games,…
We investigate multi-round team competitions between two teams, where each team selects one of its players simultaneously in each round and each player can play at most once. The competition defines an extensive-form game with perfect…
We introduce a way to compare actions in decision problems. One action is safer than another if the set of beliefs at which the decision-maker prefers the safer action expands as the decision-maker becomes more risk averse. We provide a…
Game semantics is a rich and successful class of denotational models for programming languages. Most game models feature a rather intuitive setup, yet surprisingly difficult proofs of such basic results as associativity of composition of…
Impartial subtraction games on the nonnegative integers have been studied by many and discussed in detail in for example the remarkable work Winning Ways by Conway, Berlekamp and Guy. We describe how comply variations of these games,…
Combinatorial Levy processes evolve on general state spaces of countable combinatorial structures. In this setting, the usual Levy process properties of stationary, independent increments are defined in an unconventional way in terms of the…