Abstract
We study a game between two firms in which each
provides 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