  We study a game between two firms in which each provide a service based on
machine learning. The firms are presented with the opportunity to purchase a
new corpus of data, which will allow them to potentially improve the quality of
their products. The firms can decide whether or not they want to buy the data,
as well as which learning model to build with that data. We demonstrate a
reduction from this potentially complicated action space to a one-shot,
two-action game in which each firm only decides whether or not to buy the data.
The game admits several regimes which depend on the relative strength of the
two firms at the outset and the price at which the data is being offered. We
analyze the game's Nash equilibria in all parameter regimes and demonstrate
that, in expectation, the outcome of the game is that the initially stronger
firm's market position weakens whereas the initially weaker firm's market
position becomes stronger. Finally, we consider the perspective of the users of
the service and demonstrate that the expected outcome at equilibrium is not the
one which maximizes the welfare of the consumers.

Computer Science and Game Theory;Machine Learning