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.

 
 Giacomo Bonanno,   The logic of KM belief update is contained in the logic of AGM belief revision

Abstract.

For each axiom of KM belief update we provide a corresponding axiom in a modal logic containing three modal operators: a unimodal belief operator $B$, a bimodal conditional operator $>$ and the unimodal necessity operator $\square$. We then compare the resulting logic to the similar logic obtained from converting the AGM axioms of belief revision into modal axioms and show that the latter contains the former. Denoting the latter by L_{AGM} and the former by L_{KM} we show that every axiom of L_{KM} is a theorem of L_{AGM} . Thus AGM belief revision can be seen as a special case of KM belief update. For the strong version of KM belief update we show that the difference between L_{KM} and L_{AGM} can be narrowed down to a single axiom, which deals exclusively with unsurprising information, that is, with formulas that were not initially disbelieved.