scholarly journals Expressiveness and Nash Equilibrium in Iterated Boolean Games

2021 ◽  
Vol 22 (2) ◽  
pp. 1-38
Author(s):  
Julian Gutierrez ◽  
Paul Harrenstein ◽  
Giuseppe Perelli ◽  
Michael Wooldridge
Keyword(s):  
Nash Equilibrium ◽  
Nash Equilibria ◽  
Infinite Sequence ◽  
Multi Agent Systems ◽  
Temporal Logics ◽  
Agent Systems ◽  
Temporal Properties ◽  
Multi Agent ◽  
Game Theoretic ◽  
Boolean Games

We define and investigate a novel notion of expressiveness for temporal logics that is based on game theoretic equilibria of multi-agent systems. We use iterated Boolean games as our abstract model of multi-agent systems [Gutierrez et al. 2013, 2015a]. In such a game, each agent  has a goal  , represented using (a fragment of) Linear Temporal Logic ( ) . The goal  captures agent  ’s preferences, in the sense that the models of  represent system behaviours that would satisfy  . Each player controls a subset of Boolean variables , and at each round in the game, player is at liberty to choose values for variables in any way that she sees fit. Play continues for an infinite sequence of rounds, and so as players act they collectively trace out a model for , which for every player will either satisfy or fail to satisfy their goal. Players are assumed to act strategically, taking into account the goals of other players, in an attempt to bring about computations satisfying their goal. In this setting, we apply the standard game-theoretic concept of (pure) Nash equilibria. The (possibly empty) set of Nash equilibria of an iterated Boolean game can be understood as inducing a set of computations, each computation representing one way the system could evolve if players chose strategies that together constitute a Nash equilibrium. Such a set of equilibrium computations expresses a temporal property—which may or may not be expressible within a particular fragment. The new notion of expressiveness that we formally define and investigate is then as follows: What temporal properties are characterised by the Nash equilibria of games in which agent goals are expressed in specific fragments of  ? We formally define and investigate this notion of expressiveness for a range of fragments. For example, a very natural question is the following: Suppose we have an iterated Boolean game in which every goal is represented using a particular fragment of : is it then always the case that the equilibria of the game can be characterised within ? We show that this is not true in general.

scholarly journals Characterising the Manipulability of Boolean Games

2017 ◽  
Author(s):  
Paul Harrenstein ◽  
Paolo Turrini ◽  
Michael Wooldridge
Keyword(s):  
Game Theory ◽  
Nash Equilibria ◽  
Multi Agent Systems ◽  
Agent Systems ◽  
Lexicographic Preferences ◽  
Incentive Engineering ◽  
Multi Agent ◽  
Boolean Games ◽  
The Cost ◽  
Complete Characterisation

The existence of (Nash) equilibria with undesirable properties is a well-known problem in game theory, which has motivated much research directed at the possibility of mechanisms for modifying games in order to eliminate undesirable equilibria, or induce desirable ones. Taxation schemes are a well-known mechanism for modifying games in this way. In the multi-agent systems community, taxation mechanisms for incentive engineering have been studied in the context of Boolean games with costs. These are games in which each player assigns truth-values to a set of propositional variables she uniquely controls in pursuit of satisfying an individual propositional goal formula; different choices for the player are also associated with different costs. In such a game, each player prefers primarily to see the satisfaction of their goal, and secondarily, to minimise the cost of their choice, thereby giving rise to lexicographic preferences over goal-satisfaction and costs. Within this setting, where taxes operate on costs only, however, it may well happen that the elimination or introduction of equilibria can only be achieved at the cost of simultaneously introducing less desirable equilibria or eliminating more attractive ones. Although this framework has been studied extensively, the problem of precisely characterising the equilibria that may be induced or eliminated has remained open. In this paper we close this problem, giving a complete characterisation of those mechanisms that can induce a set of outcomes of the game to be exactly the set of Nash Equilibrium outcomes.

An Evolutionary Game Theoretic Perspective on Learning in Multi-Agent Systems

Synthese ◽  
2004 ◽  
Vol 139 (2) ◽  
pp. 297-330 ◽  
Author(s):  
Karl Tuyls ◽  
Ann Nowe ◽  
Tom Lenaerts ◽  
Bernard Manderick
Keyword(s):  
Evolutionary Game ◽  
Multi Agent Systems ◽  
Agent Systems ◽  
Multi Agent ◽  
Game Theoretic

scholarly journals On Partially Controlled Multi-Agent Systems

1996 ◽  
Vol 4 ◽  
pp. 477-507 ◽  
Author(s):  
R. I. Brafman ◽  
M. Tennenholtz
Keyword(s):  
Expected Utility ◽  
The Other ◽  
Multi Agent System ◽  
Multi Agent Systems ◽  
Direct Control ◽  
Agent System ◽  
Agent Systems ◽  
Multi Agent ◽  
Game Theoretic

Motivated by the control theoretic distinction between controllable and uncontrollable events, we distinguish between two types of agents within a multi-agent system: controllable agents, which are directly controlled by the system's designer, and uncontrollable agents, which are not under the designer's direct control. We refer to such systems as partially controlled multi-agent systems, and we investigate how one might influence the behavior of the uncontrolled agents through appropriate design of the controlled agents. In particular, we wish to understand which problems are naturally described in these terms, what methods can be applied to influence the uncontrollable agents, the effectiveness of such methods, and whether similar methods work across different domains. Using a game-theoretic framework, this paper studies the design of partially controlled multi-agent systems in two contexts: in one context, the uncontrollable agents are expected utility maximizers, while in the other they are reinforcement learners. We suggest different techniques for controlling agents' behavior in each domain, assess their success, and examine their relationship.

scholarly journals Rational verification: game-theoretic verification of multi-agent systems

2021 ◽  
Author(s):  
Alessandro Abate ◽  
Julian Gutierrez ◽  
Lewis Hammond ◽  
Paul Harrenstein ◽  
Marta Kwiatkowska ◽  
...  
Keyword(s):  
Computer Science ◽  
Temporal Logic ◽  
State Of The Art ◽  
Multi Agent System ◽  
Multi Agent Systems ◽  
Agent Systems ◽  
The Past ◽  
Multi Agent ◽  
Game Theoretic ◽  
Temporal Logic Formula

AbstractWe provide a survey of the state of the art of rational verification: the problem of checking whether a given temporal logic formula ϕ is satisfied in some or all game-theoretic equilibria of a multi-agent system – that is, whether the system will exhibit the behavior ϕ represents under the assumption that agents within the system act rationally in pursuit of their preferences. After motivating and introducing the overall framework of rational verification, we discuss key results obtained in the past few years as well as relevant related work in logic, AI, and computer science.

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