This talk considers trial-offer markets where customers can try products before buying them and where market makers display social
signals such as market shares. Consumer preferences are modelled by a multinomial logit with social influence and position bias and the social signal for a product is given by its current market share raised to power r. The talk reviews optimal (and non-optimal) policies for a variety of settings which depends on the value of r. The results make interesting connections between discrete choice models, assortment optimization, and Robbins-Monroe algorithms in stochastic approximation. A number of open will also be presented. They also show that various policies are able to control effectively the social signals to benefits both consumers and the markets, addressing a critical issue identified in prior seminal work.