a study in suspense and surprise - part II
Finished reading the paper Suspense And Surprise finally. Honestly, the paper itself is already a masterclass of organizing contents so as to achieve high informational utility. Following what we left yesterday, here’s the rest, and some closing thoughts before the end. Illustrations of Suspense-Opt. Info Policies In the simplest setting where there are only two states $\Omega = {A, B}$ (i.e. whether AGT or FRA would win in the world cup final), suspense maximizing belief martingale give rise to the followig dynamics. Say, starting from initial prior$\mu_A = \mu_B = 0.5$, at period $t$ the optimal belief (say, WLOG let’s consider one side of the world, $\mu_t \equiv \text{Pr}(A)$), either takes a high value $\mu_t = H_t > 1/2$ or low value $\mu_t = L_t = 1 - H_t$. Stepping onto the next period, there are two possible changes to the new belief $\mu_{t + 1}$ - with high possibility the agent observes additional confirmation - that the higher(lower) belief gets “confirmed” a little bit further, like $H_t \to H_{t +1}$ where $H_{t + 1} > H_t$ and vice versa for $L_t$. Alternatively with small possibility, a plot twist happens, $H_t \to L_{t + 1}$ and vice versa for $L_t$. ...