Games and Logics for Informational Cascades
Andreea Achimescu

Abstract:
Informational cascades occur when it is optimal for decision-makers to
abandon their own private information in favour of inferences they
make about other individuals' information. The informational cascade
model, centred on the core notion of Bayesian update, has been able to
explain, at least partially, many observed conformism patterns in
social settings.
  The aim of this thesis is to put the informational cascade model in
game theoretic terms and analyse it using a new probabilistic
epistemic logic. The strength of game theory lies in its mathematical
apparatus that structures and identifies strategic choices. Regarding
informational cascades as games of imperfect information with chance
moves allows us to capture, in a natural way, the reasoning of agents
engaged in an informational cascade. The strength of a logical
treatment of games is, among others, the incorporation of all levels
of an agent's beliefs into an analysis of optimal behaviour. This
attribute is instrumental in analysing games with paradoxical
collective outcomes like informational cascades. False cascades, a
term that denotes people herding on the wrong decision, are
paradoxical outcomes because they are intuitively inconsistent with
the intentions of the individuals that generate them.
  We first formalize the Urn Model, the canonical example of
informational cascades, as a game of imperfect information. Next, we
prove that the unique perfect Bayesian equilibrium of this game
sometimes leads to false cascades. Then, we determine various changes
that need to be put in place in order to ensure more socially
desirable outcomes in informational cascade games. Finally, we propose
a new logic, Probabilistic Logic of Communication and Change, to treat
social dynamics of information games. We prove it is a sound and
complete logic with respect to Bayesian Kripke structures and proceed
to apply it to sequential social information flow games.