Reasoning about equilibria in game-like concurrent systems

Gutiérrez, Julián; Harrenstein, Paul; Wooldridge, Michael

doi:10.1016/j.apal.2016.10.009

Cited by 17 publications

(29 citation statements)

References 25 publications

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“…Pure-strategy Nash equilibria in Boolean games have been studied previously (e.g., in [8,4,13,5]) but, to the best of our knowledge, apart from a very recent exception (see [15]), not in game models where the players are allowed to interact for an infinite number of rounds, which is the setting our main results pertain to. In particular, in [15], the present framework was extended in order to consider both linear-time and branching-time goals as well as explicit structures (arenas, boards) where the games are played.…”

Section: Related Workmentioning

confidence: 98%

“…In particular, in [15], the present framework was extended in order to consider both linear-time and branching-time goals as well as explicit structures (arenas, boards) where the games are played.…”

Section: Related Workmentioning

confidence: 99%

“…It then seems reasonable to consider linear-time temporal logics with such expressive power, e.g., a natural choice would be the linear-time μ-calculus [2] which elegantly extends LTL with extremal fixpoint operators. The study of a game model that extends iterated Boolean games, and which considers goals given by, e.g., the linear-time or the modal μ-calculus, is presented in [15], where, amongst others, some hardness results for the computational complexity of the synthesis of strategies are provided. Another important technical component of this work was the formalisation of conditions underpinning the Folk Theorems.…”

Section: Future Workmentioning

confidence: 99%

See 2 more Smart Citations

Iterated Boolean games

Gutiérrez

Harrenstein

Wooldridge

2015

Information and Computation

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Iterated games are well-known in the game theory literature. We study iterated Boolean games. These are games in which players repeatedly choose truth values for Boolean variables they have control over. Our model of iterated Boolean games assumes that players have goals given by formulae of Linear Temporal Logic (LTL), a formalism for expressing properties of state sequences. In order to represent the strategies of players in such games, we use a finite state machine model. After introducing and formally defining iterated Boolean games, we investigate the computational complexity of their associated game-theoretic decision problems, as well as semantic conditions characterising classes of LTL properties that are preserved by equilibrium points (pure-strategy Nash equilibria) whenever they exist.

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Section: Related Workmentioning

confidence: 98%

Section: Related Workmentioning

confidence: 99%

Section: Future Workmentioning

confidence: 99%

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Iterated Boolean games

Gutiérrez

Harrenstein

Wooldridge

2015

Information and Computation

Self Cite

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“…Therefore, the application of the exponential Vardi-Wolper construction for LTL can be avoided by replacing it with the equivalent linear alternating word automaton [Vardi 1996]. In this way, we can avoid the +1 in the tower of exponential of STL [KT] complexity, obtaining an optimal 2EXPTIME algorithm [Alur et al 2002;Gutierrez et al 2014].…”

Section: Complexity Of Reasoning About Games In Stlmentioning

confidence: 99%

Reasoning About Substructures and Games

Benerecetti

Mogavero

Murano

2015

ACM Trans. Comput. Logic

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Studi di Napoli Federico IIMany decision problems in formal verification and design can be suitably formulated in game-theoretic terms. This is the case for the model checking of open and closed systems and both controller and reactive synthesis. Interpreted in this context, these problems require one to find a strategy (i.e., a plan) to force the system to fulfill some desired goal, no matter what the opponent (e.g., the environment) does. A strategy essentially constrains the possible behaviors of the system to those that are compatible with the decisions dictated by the plan itself. Therefore, finding a strategy to meet some goal basically reduces to identifying a portion of the model of interest (i.e., one of its substructures) that satisfies that goal. In this view, the ability to reason about substructures becomes a crucial aspect for several fundamental problems.In this article, we present and study a new branching-time temporal logic, called Substructure Temporal Logic (STL for short), whose distinctive feature is to allow for quantifying over the possible substructure of a given structure. The logic is obtained by adding four new temporal-like operators to CTL , whose interpretation is given relative to the partial order induced by a suitable substructure relation. STL turns out to be very expressive and allows one to capture in a very natural way many well-known problems, such as module checking, reactive synthesis, and reasoning about games in a wide sense. A formal account of the model-theoretic properties of the new logic and results about (un)decidability and complexity of related decision problems are also provided.

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“…2 Since many natural formulas have a small number of quantifiers, and even smaller nesting depth of blocks of quantifiers, the complexity of the model-checking problem is not as bad as it seems. Several solution concepts can be expressed as SL formulas with a small number of quantifiers [9,18,26,29,30,37]. We illustrate this by expressing uniqueness of various solution concepts, including winning-strategies in two-player zero-sum games and equilibria in multi-player non zero-sum games.…”

Section: Introductionmentioning

confidence: 99%

Extended Graded Modalities in Strategy Logic

Aminof

Malvone

Murano

et al. 2016

Electron. Proc. Theor. Comput. Sci.

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Strategy Logic (SL) is a logical formalism for strategic reasoning in multi-agent systems. Its main feature is that it has variables for strategies that are associated to specific agents with a binding operator. We introduce Graded Strategy Logic (GRADEDSL), an extension of SL by graded quantifiers over tuples of strategy variables, i.e., "there exist at least g different tuples (x 1 , ..., x n ) of strategies" where g is a cardinal from the set N ∪ {ℵ 0 , ℵ 1 , 2 ℵ 0 }. We prove that the model-checking problem of GRADEDSL is decidable. We then turn to the complexity of fragments of GRADEDSL. When the g's are restricted to finite cardinals, written GRADED N SL, the complexity of model-checking is no harder than for SL, i.e., it is non-elementary in the quantifier rank. We illustrate our formalism by showing how to count the number of different strategy profiles that are Nash equilibria (NE), or subgame-perfect equilibria (SPE). By analyzing the structure of the specific formulas involved, we conclude that the important problems of checking for the existence of a unique NE or SPE can both be solved in 2EXPTIME, which is not harder than merely checking for the existence of such equilibria.

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Reasoning about equilibria in game-like concurrent systems

Cited by 17 publications

References 25 publications

Iterated Boolean games

Iterated Boolean games

Reasoning About Substructures and Games

Extended Graded Modalities in Strategy Logic

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