  In the context of multi-agent systems, the rational verification problem is
concerned with checking which temporal logic properties will hold in a system
when its constituent agents are assumed to behave rationally and strategically
in pursuit of individual objectives. Typically, those objectives are expressed
as temporal logic formulae which the relevant agent desires to see satisfied.
Unfortunately, rational verification is computationally complex, and requires
specialised techniques in order to obtain practically useable implementations.
In this paper, we present such a technique. This technique relies on a
reduction of the rational verification problem to the solution of a collection
of parity games. Our approach has been implemented in the Equilibrium
Verification Environment (EVE) system. The EVE system takes as input a model of
a concurrent/multi-agent system represented using the Simple Reactive Modules
Language (SRML), where agent goals are represented as Linear Temporal Logic
(LTL) formulae, together with a claim about the equilibrium behaviour of the
system, also expressed as an LTL formula. EVE can then check whether the LTL
claim holds on some (or every) computation of the system that could arise
through agents choosing Nash equilibrium strategies; it can also check whether
a system has a Nash equilibrium, and synthesise individual strategies for
players in the multi-player game. After presenting our basic framework, we
describe our new technique and prove its correctness. We then describe our
implementation in the EVE system, and present experimental results which show
that EVE performs favourably in comparison to other existing tools that support
rational verification.
