Related papers: Game-theoretic Investigation of Intensional Equali…
Strategic interactions between competitive entities are generally considered from the perspective of complete revelation of benefits achieved from those interactions, in the form of public payoff functions and/or beliefs, in the announced…
In this paper we introduce polytopal stochastic games, an extension of two-player, zero-sum, turn-based stochastic games, in which we may have uncertainty over the transition probabilities. In these games the uncertainty over the…
Underlying relationships among Multi-Agent Systems (MAS) in hazardous scenarios can be represented as Game-theoretic models. This paper proposes a new hierarchical network-based model called Game-theoretic Utility Tree (GUT), which…
A generalized model of games is proposed, in which cooperative games and non-cooperative games are special cases. Some games that are neither cooperative nor non-cooperative can be expressed and analyzed. The model is based on relationships…
Large language models (LLMs) have demonstrated strong reasoning, planning, and communication abilities, enabling them to operate as autonomous agents in open environments. While single-agent systems remain limited in adaptability and…
We present two novel symbolic algorithms for model checking the Alternating-time Temporal Logic ATL*, over both the infinite-trace and the finite-trace semantics. In particular, for infinite traces we design a novel symbolic reduction to…
We present an extensive mechanization of the meta-theory of Martin-L\"of Type Theory (MLTT) in the Coq proof assistant. Our development builds on pre-existing work in Agda to show not only the decidability of conversion, but also the…
The Unique Games Conjecture (UGC) constitutes a highly dynamic subarea within computational complexity theory, intricately linked to the outstanding P versus NP problem. Despite multiple insightful results in the past few years, a proof for…
The objective of this paper is to assess the quality of explanation heatmaps for image classification tasks. To assess the quality of explainability methods, we approach the task through the lens of accuracy and stability. In this work, we…
This paper improves the treatment of equality in guarded dependent type theory (GDTT), by combining it with cubical type theory (CTT). GDTT is an extensional type theory with guarded recursive types, which are useful for building models of…
We propose enhancing the use of propositions for denoting decisions and strategies as established in temporal languages such as CTL*, if interpreted on concurrent game models. The enhancement enables specifying varying coalition structure.…
Conventional noncooperative game theory hypothesizes that the joint strategy of a set of players in a game must satisfy an "equilibrium concept". All other joint strategies are considered impossible; the only issue is what equilibrium…
Alan Turing proposed in 1950 a framework called an imitation game to decide if a machine could think. Using mathematics developed largely after Turing -- category theory -- we analyze a broader class of universal imitation games (UIGs),…
Two intimately related new classes of games are introduced and studied: entropy games (EGs) and matrix multiplication games (MMGs). An EG is played on a finite arena by two-and-a-half players: Despot, Tribune and the non-deterministic…
This paper reviews the fully complete hypergames model of system $F$, presented a decade ago in the author's thesis. Instantiating type variables is modelled by allowing ``games as moves''. The uniformity of a quantified type variable…
The rapid advancements in large language models (LLMs) have presented challenges in evaluating those models. Existing evaluation methods are either reference-based or preference based, which inevitably need human intervention or introduce…
We contribute XTT, a cubical reconstruction of Observational Type Theory which extends Martin-L\"of's intensional type theory with a dependent equality type that enjoys function extensionality and a judgmental version of the unicity of…
Large language models (LLMs) have achieved notable progress. Despite their success, next-token prediction (NTP), the dominant method for LLM training and inference, is constrained in both contextual coverage and inference efficiency due to…
In this paper we describe an approach to resolve strategic games in which players can assume different types along the game. Our goal is to infer which type the opponent is adopting at each moment so that we can increase the player's odds.…
Algebraic theories with dependency between sorts form the structural core of Martin-L\"of type theory and similar systems. Their denotational semantics are typically studied using categorical techniques; many different categorical…