To translate this idea into a precise computational variable, we use a recent precise measure from financial theory. The intuitive idea is that the presence of strategic agents in a market can be inferred by a statistical change in the order arrival process, from a homogeneous Poisson process to a mixture process (where the arrival intensity switches randomly) Selleck HKI272 (Easley et al., 1997). The idea is that any increase in trader information, or even a perception of such an increase, will change order arrival. For example, orders may arrive more rapidly as traders try to trade quickly before information leaks out, or orders may thin out as traders place orders more cautiously, afraid of

being on the wrong end of a trade against a better-informed partner (Easley et al., 2002). We therefore constructed signaling pathway a statistic that measured the dynamic of breaks in Poisson homogeneity during trading. We called this

metric Poisson inhomogeneity detector (PID). PID is a statistic that increases as the evidence against a homogenous Poisson order arrival process increases over the recent past. Specifically, it tests whether the number of arrivals in the last interval of 9 s conforms to a Poisson distribution with fixed arrival intensity. This measure, first proposed and investigated by Brown and Zhao (2002), has good statistical power (in small samples) to reject the null hypothesis of homogenous arrival in favor of the alternative that the arrival rates obtain from Poisson distributions with different arrival rates across the M intervals. Letting xixi denote the number of arrivals in interval i(i=1,…,M), and equation(Equation 1) yi=(xi+38)1/2,then the PID is defined as equation(Equation 2) PID=4∑mi(y(i)−Y)2,where YY equals the average (across M intervals) of the values of yiyi. Under the null hypothesis, PID approximately follows a χ2 distribution with M − 1 degrees of

Farnesyltransferase freedom. Taking M = 24, this means that the critical value corresponding to p = 0.05 is PID = 36. As PID grows, the evidence against the null hypothesis of no change in arrival rate increases (Figure 6A; Figure S4). Using this model, we were then able to construct a parametric regressor for each subject, measuring inferred intention over time. The regressor averaged the value of PID over the period in which the subject observed the arrival of asks and bids in the market (see Experimental Procedures). Critically, this parametric regressor was uncorrelated with either CPV (r = 0.06 ± 0.02) or the deviation in prices from the fundamental values (r = 0.001 ± 0.09). Changes in PID were then input as a parametric regressor in a general linear model to test whether activity in vmPFC and dmPFC showed a greater modulation to this metric during a contrast between bubble markets versus nonbubble markets (analogously to the contrast using CPV as modulator).