Decentralized tracking-type games for multi-agent systems with coupled ARX models: Asymptotic Nash equilibria

Automatica ◽  
2008 ◽  
Vol 44 (3) ◽  
pp. 713-725 ◽  
Author(s):  
Tao Li ◽  
Ji-Feng Zhang
Keyword(s):  
Nash Equilibria ◽  
Multi Agent Systems ◽  
Agent Systems ◽  
Multi Agent

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.

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