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We present a systematic investigation of the quantum games, constructed using a novel repeated game protocol, when played repeatedly ad infinitum. We focus on establishing that such repeated games -- by virtue of inherent quantum-mechanical…
Iterated bipartite quantum games are implemented in terms of the discrete-time quantum walk on the line. Our proposal allows for conditional strategies, as two rational agents make a choice from a restricted set of two-qubit unitary…
Game theory, as an analytical tool, is frequently utilized to analyze human behavior in social science research. With the high alignment between the behavior of Large Language Models (LLMs) and humans, a promising research direction is to…
We develop the counterpart of weak KAM theory for potential mean field games. This allows to describe the long time behavior of time-dependent potential mean field game systems. Our main result is the existence of a limit, as time tends to…
Metric Temporal Logic (MTL) and Timed Propositional Temporal Logic (TPTL) are prominent extensions of Linear Temporal Logic to specify properties about data languages. In this paper, we consider the class of data languages of non-monotonic…
Among the various forms of reasoning studied in the context of artificial intelligence, qualitative reasoning makes it possible to infer new knowledge in the context of imprecise, incomplete information without numerical values. In this…
Large Language Models (LLMs) are increasingly applied to domains that require reasoning about other agents' behavior, such as negotiation, policy design, and market simulation, yet existing research has mostly evaluated their adherence to…
There is a long history in game theory on the topic of Bayesian or "rational" learning, in which each player maintains beliefs over a set of alternative behaviours, or types, for the other players. This idea has gained increasing interest…
The Value Problem for weighted timed games (WTGs) consists in determining, given a two-player weighted timed game with a reachability objective and a rational threshold, whether or not the value of the game exceeds the threshold. This…
The probabilistic modal {\mu}-calculus is a fixed-point logic designed for expressing properties of probabilistic labeled transition systems (PLTS's). Two equivalent semantics have been studied for this logic, both assigning to each state a…
Purpose: We propose a model to present a possible mechanism for obtaining sizeable behavioural structures by simulating an agent based on the evolutionary public good game with available social learning. Methods: The model considered a…
Real-time cybersecurity and privacy applications require reliable verification methods and system design tools to ensure their correctness. Many of these reactive real-time applications embedded in various infrastructures, such as airports,…
Examples of games between two partners with mixed strategies, calculated by the use of the probability amplitude as some vector in Hilbert space are given. The games are macroscopic, no microscopic quantum agent is supposed. The reason for…
This paper presents (permissive) \emph{Quantitative Strategy Templates} (QaSTels) to succinctly represent infinitely many winning strategies in two-player energy and mean-payoff games. This transfers the recently introduced concept of…
In this paper we address the decision problem for a fragment of set theory with restricted quantification which extends the language studied in [4] with pair related quantifiers and constructs, in view of possible applications in the field…
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 the empirical approach to game-theoretic analysis (EGTA), the model of the game comes not from declarative representation, but is derived by interrogation of a procedural description of the game environment. The motivation for developing…
A new logic for verification of security policies is proposed. The logic, HyperLTL, extends linear-time temporal logic (LTL) with connectives for explicit and simultaneous quantification over multiple execution paths, thereby enabling…
The paper introduces a new approach to theory of differential games in which entangled players try to predict and influence actions of their adversaries. The entanglement is generated be a joint probability density known by the players.…
A canonical formalism and constraint analysis for discrete systems subject to a variational action principle are devised. The formalism is equivalent to the covariant formulation, encompasses global and local discrete time evolution moves…