Budget-Constrained Reinforcement of Ranked Objects

TL;DR

This paper investigates how a principal can optimally allocate a limited budget to improve the ranking of entries by equalizing scores across disjoint ranges, using a game-theoretic approach and an efficient algorithm.

Contribution

It introduces a novel game-theoretic model for budget allocation in ranking systems and provides a unique optimal strategy with an efficient implementation.

Findings

Optimal strategy involves equalizing scores across disjoint ranges.

Unique reinforcement strategy is identified and characterized.

An efficient algorithm for implementing the optimal strategy is developed.

Abstract

Commercial entries, such as hotels, are ranked according to score by a search engine or recommendation system, and the score of each can be improved upon by making a targeted investment, e.g., advertising. We study the problem of how a principal, who owns or supports a set of entries, can optimally allocate a budget to maximize their ranking. Representing the set of ranked scores as a probability distribution over scores, we treat this question as a game between distributions. We show that, in the general case, the best ranking is achieved by equalizing the scores of several disjoint score ranges. We show that there is a unique optimal reinforcement strategy, and provide an efficient algorithm implementing it.