+/*
+ * diff(priorlogL, sigma) = w ( (x - mu)² - sigma² ) / sigma³
+ * maximizer for sigma is given by: sum_i[ (w_i/sigma)³ ((x - mu)² - sigma²) ] = 0
+ * sum_i[ w_i ( (x - mu)² - sigma² ) ] = 0 |: sigma != 0
+ * sum_i[ w_i (x - mu)² ] = sum[ w_i sigma² ]
+ * sigma = sqrt( sum_i[ w_i (x - mu)² ] / sum[w_i] )
+ */
+void update_prior_sigma(float *mu, float *sigma, int num_players)