Giacomo Bonanno, Modeling the intensity of competition
Abstract.
Within the context of a symmetric duopoly with linear demand and costs,
we construct a parameterized family of price-setting games, where the
parameter $\gamma\in[0,2]$ measures the degree or intensity of
competition; $\gamma = 0$ corresponds to collusion, a particular value
of $\gamma$ between 0 and 1 corresponds to the Cournot outcome,
$\gamma=1$ corresponds to the Bertrand outcome and, in general, as
$\gamma$ increases the intensity of competition increases. All the
games within the parameterized family share the same strategic
properties. We also construct a parameterized family of
quantity-setting games, where the parameter $\beta\in[0,2]$ measures
the intensity of competition; $\beta = 0$ corresponds to collusion,
$\beta=1$ corresponds to the Cournot outcome and a particular value of
$\beta$ between 1 and 2 corresponds to the Bertrand outcome. As $\beta$
increases, the intensity of competition increases. As an example of the
potential usefulness of this approach, we show that, contrary to the
view first put forward by Schumpeter (but later challenged by Arrow),
the incentive to introduce a cost-reducing innovation is an increasing
function of the intensity of competition (that is, an increasing
function of $\gamma$ in the price-setting case and of $\beta$ in the
quantity-setting case).
Giacomo Bonanno, Supposing and learning: a unified framework for belief revision
Abstract.
Consider two possible scenarios for belief revision. Initially the
agent either believes that A is not the case (that is, believes not-A)
or suspends belief about A. In one scenario she receives reliable
information that, as a matter of fact, A is the case; call this
scenario "learning that A". In the other scenario she reasons about
what she believes would be the case if A were the case; call this
scenario "supposing that A". We argue that there are important
differences between the two scenarios. It was shown in
Bonanno G. Artificial Intelligence 339 (2025)
that it is possible to view the AGM theory of belief revision as a
theory of hypothetical, or suppositional, reasoning, rather than a
theory of actual belief change in response to new information. By
making an addition to the Kripke-Lewis semantics considered
in
Bonanno G. Artificial Intelligence 339 (2025),
we (1) provide a unified framework for the analysis of both
suppositional beliefs and information-driven belief change, (2) argue
that some of the AGM axioms are not appropriate for the latter and (3)
provide a list of axioms that seem appropriate for belief change in
response to new information.
