Related papers: Higher-order Games with Dependent Types

We encode arbitrary finite impartial combinatorial games in terms of lattice points in rational convex polyhedra. Encodings provided by these \emph{lattice games} can be made particularly efficient for octal games, which we generalize to…

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…

We present a type theory combining both linearity and dependency by stratifying typing rules into a level for logics and a level for programs. The distinction between logics and programs decouples their semantics, allowing the type system…

This paper studies social interactions in a game theoretic model with players in a large social network. We consider observations from one single equilibrium of a large network game with asymmetric information, in which each player chooses…

We study multi-player turn-based games played on (potentially infinite) directed graphs. An outcome is assigned to every play of the game. Each player has a preference relation on the set of outcomes which allows him to compare plays. We…

Constructing effective algorithms to converge to Nash Equilibrium (NE) is an important problem in algorithmic game theory. Prior research generally posits that the upper bound on the convergence rate for games is $O\left(T^{-1/2}\right)$.…

A new class of projected dynamical systems of third order is investigated for quasi (parametric) variational inequalities in which the convex set in the classical variational inequality also depends upon the solution explicitly or…

In this work, we establish near-linear and strong convergence for a natural first-order iterative algorithm that simulates Von Neumann's Alternating Projections method in zero-sum games. First, we provide a precise analysis of Optimistic…

Using the duality techniques introduced by De Meyer (1996a, 1996b), De Meyer and Marino (2005) provided optimal strategies for both players in finitely repeated games with incomplete information on two sides, in the independent case. In…

Control of multi-agent systems via game theory is investigated. Assume a system level object is given, the utility functions for individual agents are designed to convert a multi-agent system into a potential game. First, for fixed…

This work investigates the problem of multi-agents trajectory prediction. Prior approaches lack of capability of capturing fine-grained dependencies among coordinated agents. In this paper, we propose a spatial-temporal trajectory…

Large Language Models (LLMs) reasoning abilities are increasingly being applied to classical board and card games, but the dominant approach -- involving prompting for direct move generation -- has significant drawbacks. It relies on the…

The object of this study are countably infinite games with perfect information that allow players to choose among arbitrarily many moves in a turn; in particular, we focus on the generalisations of the finite board games of Hex and…

Game comonads offer a categorical view of a number of model-comparison games central to model theory, such as pebble and Ehrenfeucht-Fra\"iss\'e games. Remarkably, the categories of coalgebras for these comonads capture preservation of…

Extensive-form games constitute the standard representation scheme for games with a temporal component. But do all extensive-form games correspond to protocols that we can implement in the real world? We often rule out games with imperfect…

We consider discrete-time uncertain processes with finite state space and study the properties of game-theoretic upper expectations developed by Shafer and Vovk. We start by proving some basic properties, e.g. monotonicity, law of iterated…

Hierarchies of conditional beliefs (Battigalli and Siniscalchi 1999) play a central role for the epistemic analysis of solution concepts in sequential games. They are practically modelled by type structures, which allow the analyst to…

We present two logical systems based on dependent types that are comparable to ZFC, both in terms of simplicity and having natural set theoretic interpretations. Our perspective is that of a mathematician trained in classical logic, but…

In this article, we present a new machine learning model by imitation based on the linguistic description of complex phenomena. The idea consists of, first, capturing the behaviour of human players by creating a computational perception…

Mean-field games (MFGs) have shown strong modeling capabilities for large systems in various fields, driving growth in computational methods for mean-field game problems. However, high order methods have not been thoroughly investigated. In…