Abstract:
This work is about analysing reasoning about games - specially the social network
games, polymatrix games, priority separable games and large games. Towards the
reasoning we employ di↵erent logics - namely the least fixed point logic and a multi
modal logic with the reachability operator. We highlight expressibility of game
theoretic properties of interest like - Nash Equilibrium, Finite Improvement Paths,
Weak Acyclity. We have results where we initially fix the number of players for the
game and also, where we try to have the same hold for an arbitrary set of players.
We use the monadic variant of least fixed point logic (MLFP) to express the
Nash Equilibrium for separable games like priority separable and polymatrix games.
We also show how the framework of Improvement Graphs with the logic of MLFP is
interesting enough to be able to similarly express notions in the connected literature
of Fair Division and Voting. Our hope is to fully flesh out this framework so that
we have transfer results from one domain to the other.
We use variants of multi modal logics with added capabilities required to have
access to games. We show a complete axiomatisation of the logic for our respective
games of threshold reasoning in social network games and large games. We also
show bisimulation for the both the modal logics respectively. We also come up
with a Monadic Second Order Logic of Strategization for Large Games. The logic
turns out to be undecidable that is we have a proof for its finite satisfiability being
undecidable.
