scholarly journals Nash Equilibria for Multi-agent Network Flow with Controllable Capacities

2015 ◽  
pp. 47-62 ◽  
Author(s):  
Nadia Chaabane Fakhfakh ◽  
Cyril Briand ◽  
Marie-José Huguet
Keyword(s):  
Network Flow ◽  
Nash Equilibria ◽  
Multi Agent

Cross-provincial Cross-region Power Trading Optimization Modeling

2020 ◽  
Vol 13 (8) ◽  
pp. 1183-1189
Author(s):  
Jing-wen Chen ◽  
Yan Xiao ◽  
Hong-she Dang ◽  
Rong Zhang
Keyword(s):  
Network Flow ◽  
Optimal Allocation ◽  
Route Optimization ◽  
Regional Power ◽  
Power Resources ◽  
Gray Theory ◽  
Power Trading ◽  
Study Results ◽  
Multi Agent ◽  
Regional Economic Disparities

Background: China's power resources are unevenly distributed in geography, and the supply-demand imbalance becomes worse due to regional economic disparities. It is essential to optimize the allocation of power resources through cross-provincial and cross-regional power trading. Methods: This paper uses load forecasting, transaction subject data declaration, and route optimization models to achieve optimal allocation of electricity and power resources cross-provincial and cross-regional and maximize social benefits. Gray theory is used to predict the medium and longterm loads, while multi-agent technology is used to report the power trading price. Results: Cross-provincial and cross-regional power trading become a network flow problem, through which we can find the optimized complete trading paths. Conclusion: Numerical case study results has verified the efficiency of the proposed method in optimizing power allocation across provinces and regions.

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.

scholarly journals General features of Nash equilibria in combinations of elementary interactions in symmetric two-person games

2021 ◽  
Vol 94 (5) ◽  
Author(s):  
György Szabó ◽  
Balázs Király
Keyword(s):  
Mathematical Models ◽  
Nash Equilibria ◽  
Matrix Decomposition ◽  
Payoff Matrix ◽  
Zero Eigenvalue ◽  
Macroscopic Behavior ◽  
Different Types ◽  
Multi Agent ◽  
Different Characteristics ◽  
Pair Interactions

AbstractTwo-person games are used in many multi-agent mathematical models to describe pair interactions. The type (pure or mixed) and the number of Nash equilibria affect fundamentally the macroscopic behavior of these systems. In this paper, the general features of Nash equilibria are investigated systematically within the framework of matrix decomposition for n strategies. This approach distinguishes four types of elementary interactions that each possess fundamentally different characteristics. The possible Nash equilibria are discussed separately for different types of interactions and also for their combinations. A relation is established between the existence of infinitely many mixed Nash equilibria and the zero-eigenvalue eigenvectors of the payoff matrix.

scholarly journals Nash Equilibria in Multi-Agent Motor Interactions

2009 ◽  
Vol 5 (8) ◽  
pp. e1000468 ◽  
Author(s):  
Daniel A. Braun ◽  
Pedro A. Ortega ◽  
Daniel M. Wolpert
Keyword(s):  
Nash Equilibria ◽  
Multi Agent

scholarly journals A posteriori probabilistic feasibility guarantees for Nash equilibria in uncertain multi-agent games

2020 ◽  
Vol 53 (2) ◽  
pp. 3403-3408
Author(s):  
George Pantazis ◽  
Filiberto Fele ◽  
Kostas Margellos
Keyword(s):  
Nash Equilibria ◽  
A Posteriori ◽  
Multi Agent

scholarly journals Rational Verification for Probabilistic Systems

2021 ◽  
Author(s):  
Julian Gutierrez ◽  
Lewis Hammond ◽  
Anthony W. Lin ◽  
Muhammad Najib ◽  
Michael Wooldridge
Keyword(s):  
Cooperative Games ◽  
Nash Equilibria ◽  
Deterministic Systems ◽  
Probabilistic Systems ◽  
Verification Problem ◽  
Markov Decision ◽  
Probabilistic Setting ◽  
Multi Agent ◽  
Game Theoretic ◽  
Non Cooperative Games

Rational verification is the problem of determining which temporal logic properties will hold in a multi-agent system, under the assumption that agents in the system act rationally, by choosing strategies that collectively form a game-theoretic equilibrium. Previous work in this area has largely focussed on deterministic systems. In this paper, we develop the theory and algorithms for rational verification in probabilistic systems. We focus on concurrent stochastic games (CSGs), which can be used to model uncertainty and randomness in complex multi-agent environments. We study the rational verification problem for both non-cooperative games and cooperative games in the qualitative probabilistic setting. In the former case, we consider LTL properties satisfied by the Nash equilibria of the game and in the latter case LTL properties satisfied by the core. In both cases, we show that the problem is 2EXPTIME-complete, thus not harder than the much simpler verification problem of model checking LTL properties of systems modelled as Markov decision processes (MDPs).

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