Related papers: Quantitative Reductions and Vertex-Ranked Infinite…
This paper provides effective methods for the polyhedral formulation of impartial finite combinatorial games as lattice games. Given a rational strategy for a lattice game, a polynomial time algorithm is presented to decide (i) whether a…
Recent developments surrounding resource theories have shown that any quantum state or measurement resource, with respect to a convex (and compact) set of resourceless objects, provides an advantage in a tailored subchannel or state…
Quantitative verification techniques have been developed for the formal analysis of a variety of probabilistic models, such as Markov chains, Markov decision process and their variants. They can be used to produce guarantees on quantitative…
In this thesis, we survey techniques and results from the study of Complexity Theory and Games. We then apply these techniques to obtain new results for previously unstudied games. Our contributions in the games Hexiom, Cut the Rope, and…
Bertrand et al. [1] (LMCS 2019) describe two-player zero-sum games in which one player tries to achieve a reachability objective in $n$ games (on the same finite arena) simultaneously by broadcasting actions, and where the opponent has full…
In this paper, we study two-player zero-sum turn-based games played on a finite multidimensional weighted graph. In recent papers all dimensions use the same measure, whereas here we allow to combine different measures. Such heterogeneous…
We introduce a new class of context dependent, incomplete information games to serve as structured prediction models for settings with significant strategic interactions. Our games map the input context to outcomes by first condensing the…
This paper investigates a class of games with large strategy spaces, motivated by challenges in AI alignment and language games. We introduce the hidden game problem, where for each player, an unknown subset of strategies consistently…
Repeated quantum game theory addresses long term relations among players who choose quantum strategies. In the conventional quantum game theory, single round quantum games or at most finitely repeated games have been widely studied, however…
Quantum Decision Theory, advanced earlier by the authors, and illustrated for lotteries with gains, is generalized to the games containing lotteries with gains as well as losses. The mathematical structure of the approach is based on the…
We introduce frame-equivalence games tailored for reasoning about the size, modal depth, number of occurrences of symbols and number of different propositional variables of modal formulae defining a given frame-property. Using these games,…
A new solution concept for two-player zero-sum matrix games with multi-dimensional payoff is introduced. It is based on extensions of vector orders in K-dimensional spaces to order relations in their power sets, so-called set relations, and…
In this paper, we propose the Quantile Option Architecture (QUOTA) for exploration based on recent advances in distributional reinforcement learning (RL). In QUOTA, decision making is based on quantiles of a value distribution, not only the…
We introduce quantum XOR games, a model of two-player one-round games that extends the model of XOR games by allowing the referee's questions to the players to be quantum states. We give examples showing that quantum XOR games exhibit a…
In complexity theory, gap-preserving reductions play a crucial role in studying hardness of approximation and in analyzing the relative complexity of multiprover interactive proof systems. In the quantum setting, multiprover interactive…
We demonstrate the usefulness of adding delay to infinite games with quantitative winning conditions. In a delay game, one of the players may delay her moves to obtain a lookahead on her opponent's moves. We show that determining the winner…
We introduce a new unified framework for modelling both decision problems and finite games based on quantifiers and selection functions. We show that the canonical utility maximisation is one special case of a quantifier and that our more…
Compiling Bell games under cryptographic assumptions replaces the need for physical separation, allowing nonlocality to be probed with a single untrusted device. While Kalai et al. (STOC'23) showed that this compilation preserves quantum…
Risk-aversion and bounded rationality are two key characteristics of human decision-making. Risk-averse quantal-response equilibrium (RQE) is a solution concept that incorporates these features, providing a more realistic depiction of human…
We introduce a constraint-based framework for studying infinite qualitative simulations concerned with contingencies such as time, space, shape, size, abstracted into a finite set of qualitative relations. To define the simulations, we…