Extended Graded Modalities in Strategy Logic

07/12/2016
by   Benjamin Aminof, et al.
0

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 union aleph_0, aleph_1, 2^aleph_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 GradedNSL, 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.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
03/07/2020

Module checking of pushdown multi-agent systems

In this paper, we investigate the module-checking problem of pushdown mu...
research
05/24/2018

On the Computational Complexity of Model Checking for Dynamic Epistemic Logic with S5 Models

Dynamic epistemic logic (DEL) is a logical framework for representing an...
research
01/24/2022

Reasoning about Human-Friendly Strategies in Repeated Keyword Auctions

In online advertising, search engines sell ad placements for keywords co...
research
05/24/2023

Discounting in Strategy Logic

Discounting is an important dimension in multi-agent systems as long as ...
research
03/14/2022

A Logic for Hyperproperties in Multi-Agent Systems

Hyperproperties are commonly used in computer security to define informa...
research
08/05/2023

Multi-Agent Verification and Control with Probabilistic Model Checking

Probabilistic model checking is a technique for formal automated reasoni...
research
02/23/2023

(Arbitrary) Partial Communication

Communication within groups of agents has been lately the focus of resea...

Please sign up or login with your details

Forgot password? Click here to reset