arXiv subjects

Julian Gutierrez

Publications and source records attributed to Julian Gutierrez.

24 records · Page 2Linked to original sources

arXiv2020

Equilibria for Games with Combined Qualitative and Quantitative Objectives

The overall aim of our research is to develop techniques to reason about the equilibrium properties of multi-agent systems. We model multi-agent systems as concurrent games, in which each player is a process that is assumed to act independently and strategically in pursuit of personal preferences. In this article, we study these games in the context of finite-memory strategies, and we assume players' preferences are defined by a qualitative and a quantitative objective, which are related by a lexicographic order: a player first prefers to satisfy its qualitative objective (given as a formula of Linear Temporal Logic) and then prefers to minimise costs (given by a mean-payoff function). Our main result is that deciding the existence of a strict epsilon Nash equilibrium in such games is 2ExpTime-complete (and hence decidable), even if players' deviations are implemented as infinite-memory strategies.

cs.LO↗

arXiv2020

Multi-Player Games with LDL Goals over Finite Traces

Linear Dynamic Logic on finite traces LDLf is a powerful logic for reasoning about the behaviour of concurrent and multi-agent systems. In this paper, we investigate techniques for both the characterisation and verification of equilibria in multi-player games with goals/objectives expressed using logics based on LDLf. This study builds upon a generalisation of Boolean games, a logic-based game model of multi-agent systems where players have goals succinctly represented in a logical way. Because LDLf goals are considered, in the settings we study -- Reactive Modules games and iterated Boolean games with goals over finite traces -- players' goals can be defined to be regular properties while achieved in a finite, but arbitrarily large, trace. In particular, using alternating automata, the paper investigates automata-theoretic approaches to the characterisation and verification of (pure strategy Nash) equilibria, shows that the set of Nash equilibria in multi-player games with LDLf objectives is regular, and provides complexity results for the associated automata constructions.

cs.LO↗

arXiv2020

A mean-field game price model with noise

In this paper, we propose a mean-field game model for the price formation of a commodity whose production is subjected to random fluctuations. The model generalizes existing deterministic price formation models. Agents seek to minimize their average cost by choosing their trading rates with a price that is characterized by a balance between supply and demand. The supply and the price processes are assumed to follow stochastic differential equations. Here, we show that, for linear dynamics and quadratic costs, the optimal trading rates are determined in feedback form. Hence, the price arises as the solution to a stochastic differential equation, whose coefficients depend on the solution of a system of ordinary differential equations.

math.AP↗

arXiv2019

Nash Equilibrium and Bisimulation Invariance

Game theory provides a well-established framework for the analysis of concurrent and multi-agent systems. The basic idea is that concurrent processes (agents) can be understood as corresponding to players in a game; plays represent the possible computation runs of the system; and strategies define the behaviour of agents. Typically, strategies are modelled as functions from sequences of system states to player actions. Analysing a system in such a setting involves computing the set of (Nash) equilibria in the concurrent game. However, we show that, with respect to the above model of strategies (arguably, the "standard" model in the computer science literature), bisimilarity does not preserve the existence of Nash equilibria. Thus, two concurrent games which are behaviourally equivalent from a semantic perspective, and which from a logical perspective satisfy the same temporal logic formulae, may nevertheless have fundamentally different properties (solutions) from a game theoretic perspective. Our aim in this paper is to explore the issues raised by this discovery. After illustrating the issue by way of a motivating example, we present three models of strategies with respect to which the existence of Nash equilibria is preserved under bisimilarity. We use some of these models of strategies to provide new semantic foundations for logics for strategic reasoning, and investigate restricted scenarios where bisimilarity can be shown to preserve the existence of Nash equilibria with respect to the conventional model of strategies in the computer science literature.

cs.LO↗

arXiv2012

The μ-Calculus Alternation Hierarchy Collapses over Structures with Restricted Connectivity

It is known that the alternation hierarchy of least and greatest fixpoint operators in the mu-calculus is strict. However, the strictness of the alternation hierarchy does not necessarily carry over when considering restricted classes of structures. A prominent instance is the class of infinite words over which the alternation-free fragment is already as expressive as the full mu-calculus. Our current understanding of when and why the mu-calculus alternation hierarchy is not strict is limited. This paper makes progress in answering these questions by showing that the alternation hierarchy of the mu-calculus collapses to the alternation-free fragment over some classes of structures, including infinite nested words and finite graphs with feedback vertex sets of a bounded size. Common to these classes is that the connectivity between the components in a structure from such a class is restricted in the sense that the removal of certain vertices from the structure's graph decomposes it into graphs in which all paths are of finite length. Our collapse results are obtained in an automata-theoretic setting. They subsume, generalize, and strengthen several prior results on the expressivity of the mu-calculus over restricted classes of structures.

cs.LO↗

arXiv2010

Logics and Games for True Concurrency

We study the underlying mathematical properties of various partial order models of concurrency based on transition systems, Petri nets, and event structures, and show that the concurrent behaviour of these systems can be captured in a uniform way by two simple and general dualities of local behaviour. Such dualities are used to define new mu-calculi and logic games for the analysis of concurrent systems with partial order semantics. Some results of this work are: the definition of a number of mu-calculi which, in some classes of systems, induce the same identifications as some of the best known bisimulation equivalences for concurrency; and the definition of (infinite) higher-order logic games for bisimulation and model-checking, where the players of the games are given (local) monadic second-order power on the sets of elements they are allowed to play. More specifically, we show that our games are sound and complete, and therefore, determined; moreover, they are decidable in the finite case and underpin novel decision procedures for bisimulation and model-checking. Since these mu-calculi and logic games generalise well-known fixpoint logics and game-theoretic decision procedures for concurrent systems with interleaving semantics, the results herein give some of the groundwork for the design of a logic-based, game-theoretic framework for studying, in a uniform way, several concurrent systems regardless of whether they have an interleaving or a partial order semantics.

cs.LO↗