Optimizing Expected Utility in a Multinomial Logit Model with Position Bias and Social Influence

Motivated by applications in retail, online advertising, and cultural markets, this paper studies how to find the optimal assortment and positioning of products subject to a capacity constraint. We prove that the optimal assortment and positioning can be found in polynomial time for a multinomial logit model capturing utilities, position bias, and social influence. Moreover, in a dynamic market, we show that the policy that applies the optimal assortment and positioning and leverages social influence outperforms in expectation any policy not using social influence

Dynamic Learning of Sequential Choice Bandit Problem under Marketing Fatigue

Motivated by the observation that overexposure to unwanted marketing activities leads to customer dissatisfaction, we consider a setting where a platform offers a sequence of messages to its users and is penalized when users abandon the platform due to marketing fatigue. We propose a novel sequential choice model to capture multiple interactions taking place between the platform and its user: Upon receiving a message, a user decides on one of the three actions: accept the message, skip and receive the next message, or abandon the platform. Based on user feedback, the platform dynamically learns users' abandonment distribution and their valuations of messages to determine the length of the sequence and the order of the messages, while maximizing the cumulative payoff over a horizon of length T. We refer to this online learning task as the sequential choice bandit problem. For the offline combinatorial optimization problem, we show that an efficient polynomial-time algorithm exists. For the online problem, we propose an algorithm that balances exploration and exploitation, and characterize its regret bound. Lastly, we demonstrate how to extend the model with user contexts to incorporate personalization

Proving the performance of a new revenue management system

Revenue management (RM) is a complicated business process that can best be described as control of sales (using prices, restrictions, or capacity), usually using software as a tool to aid decisions. RM software can play a mere informative role, supplying analysts with formatted and summarized data who use it to make control decisions (setting a price or allocating capacity for a price point), or, play a deeper role, automating the decisions process completely, at the other extreme. The RM models and algorithms in the academic literature by and large concentrate on the latter, completely automated, level of functionality. A firm considering using a new RM model or RM system needs to evaluate its performance. Academic papers justify the performance of their models using simulations, where customer booking requests are simulated according to some process and model, and the revenue perfor- mance of the algorithm compared to an alternate set of algorithms. Such simulations, while an accepted part of the academic literature, and indeed providing research insight, often lack credibility with management. Even methodologically, they are usually awed, as the simula- tions only test \within-model" performance, and say nothing as to the appropriateness of the model in the first place. Even simulations that test against alternate models or competition are limited by their inherent necessity on fixing some model as the universe for their testing. These problems are exacerbated with RM models that attempt to model customer purchase behav- ior or competition, as the right models for competitive actions or customer purchases remain somewhat of a mystery, or at least with no consensus on their validity. How then to validate a model? Putting it another way, we want to show that a particular model or algorithm is the cause of a certain improvement to the RM process compared to the existing process. We take care to emphasize that we want to prove the said model as the cause of performance, and to compare against a (incumbent) process rather than against an alternate model. In this paper we describe a \live" testing experiment that we conducted at Iberia Airlines on a set of flights. A set of competing algorithms control a set of flights during adjacent weeks, and their behavior and results are observed over a relatively long period of time (9 months). In parallel, a group of control flights were managed using the traditional mix of manual and algorithmic control (incumbent system). Such \sandbox" testing, while common at many large internet search and e-commerce companies is relatively rare in the revenue management area. Sandbox testing has an undisputable model of customer behavior but the experimental design and analysis of results is less clear. In this paper we describe the philosophy behind the experiment, the organizational challenges, the design and setup of the experiment, and outline the analysis of the results. This paper is a complement to a (more technical) related paper that describes the econometrics and statistical analysis of the results.Revenue management, airlines, sandbox testing,econometric analysis.

Bayesian Inference of Arrival Rate and Substitution Behavior from Sales Transaction Data with Stockouts

When an item goes out of stock, sales transaction data no longer reflect the original customer demand, since some customers leave with no purchase while others substitute alternative products for the one that was out of stock. Here we develop a Bayesian hierarchical model for inferring the underlying customer arrival rate and choice model from sales transaction data and the corresponding stock levels. The model uses a nonhomogeneous Poisson process to allow the arrival rate to vary throughout the day, and allows for a variety of choice models. Model parameters are inferred using a stochastic gradient MCMC algorithm that can scale to large transaction databases. We fit the model to data from a local bakery and show that it is able to make accurate out-of-sample predictions, and to provide actionable insight into lost cookie sales

On equilibria in duopolies with finite strategy spaces

We will call a game a reachable (pure strategy) equilibria game if starting from any strategy by any player, by a sequence of best-response moves we are able to reach a (pure strategy) equilibrium. We give a characterization of all finite strategy space duopolies with reachable equilibria. We describe some applications of the sufficient conditions of the characterization.duopoly, equilibria, revenue management, discrete-choice theory