A ubiquitous learning problem in today's digital market is, during repeated interactions between a seller and a buyer, how a seller can gradually learn optimal pricing decisions based on the buyer's past purchase responses. A fundamental challenge of learning in such a strategic setup is that the buyer will naturally have incentives to manipulate his responses in order to induce more favorable learning outcomes for him. To understand the limits of the seller's learning when facing such a strategic and possibly manipulative buyer, we study a natural yet powerful buyer manipulation strategy. That is, before the pricing game starts, the buyer simply commits to "imitate" a different value function by pretending to always react optimally according to this imitative value function. We fully characterize the optimal imitative value function that the buyer should imitate as well as the resultant seller revenue and buyer surplus under this optimal buyer manipulation. Our characterizations reveal many useful insights about what happens at equilibrium. For example, a seller with concave production cost will obtain essentially 0 revenue at equilibrium whereas the revenue for a seller with convex production cost is the Bregman divergence of her cost function between no production and certain production. Finally, and importantly, we show that a more powerful class of pricing schemes does not necessarily increase, in fact, may be harmful to, the seller's revenue. Our results not only lead to an effective prescriptive way for buyers to manipulate learning algorithms but also shed lights on the limits of what a seller can really achieve when pricing in the dark.

A ubiquitous learning problem in today's digital market is, during repeated interactions between a seller and a buyer, how a seller can gradually learn optimal pricing decisions based on the buyer's past purchase responses. A fundamental challenge of learning in such a strategic setup is that the buyer will naturally have incentives to manipulate his responses in order to induce more favorable learning outcomes for him. To understand the limits of the seller's learning when facing such a strategic and possibly manipulative buyer, we study a natural yet powerful buyer manipulation strategy. That is, before the pricing game starts, the buyer simply commits to "imitate" a different value function by pretending to always react optimally according to this imitative value function. We fully characterize the optimal imitative value function that the buyer should imitate as well as the resultant seller revenue and buyer surplus under this optimal buyer manipulation.

"Make everything as simple as possible, but not simpler." This quote often attributed to Albert Einstein surmises a conflict that business leaders are facing with the adoption of artificial intelligence (AI) and machine learning (ML). When it comes to automated forecasting and decision-making, many are now embracing the idea of these advanced predictive solutions--but only until they begin to delve beyond the norms and already-familiar data. In this respect, just like the scientific community, business leaders crave "simplicity." However, they often have different definitions of the word, focusing more on how data can affirm their own gut feelings, rather than how deeper insight and newly proved theories can override that personal experience.

The Fourth Industrial Revolution, an age of automation, advanced AI, and human-machine collaboration is by most measures, well underway. In recent years, we have seen rapid advancements in machine intelligence, so much so that AI is matching or outperforming humans in many different areas. This is not to say that humans are obsolete. We still have our strengths and by recognizing what they are, can we take advantage of machines and get the best of both worlds. In imagine identification, Google's Neural Image Assessment (NIA) has been trained to accurately predict how we're likely to respond to a particular image based on how aesthetically pleasing it is.