This paper analyses a model of strategic exploration in which competing players independently explore a set of alternatives. The model features a multiple-player multiple-armed bandit problem and captures a strategic trade-off between pre-emption—covert exploration of alternatives that the opponent will explore in the future—and prioritization—exploration of the most promising alternatives. Our results explain how the strategic trade-off shapes equilibrium behaviours and outcomes, for example, in technology races between superpowers and R&D competitions between firms. We show that players compete on the same set of alternatives, leading to duplicated exploration from start to finish, and they explore alternatives that are a priori less promising before more promising ones are exhausted. The model also predicts that competition induces players to implement unreliable technologies too early, even though they should wait for the technologies to mature. Coordinated exploration is impossible even if the alternatives are equally promising, but it can emerge in equilibrium following a phase of pre-emptive competition if there is a short deadline. With asymmetric capacities of exploration, the weak player conducts extensive instead of intensive exploration—exploring as many alternatives as the strong player does but never fully exploring any.

In markets for indivisible resources such as workers and objects, subsidy and taxation for an agent may depend on the set of acquired resources and prices. This paper investigates how such transfer policies interfere with the substitutes condition, which is critical for market equilibrium existence and auction mechanism performance among other important issues. For environments where the condition holds in the absence of policy intervention, we investigate which transfer policies preserve the substitutes condition in various economically meaningful settings, establishing a series of characterisation theorems. For environments where the condition may fail without policy intervention, we examine how to use transfer policies to re-establish it, finding exactly when transfer policies based on scales are effective for that purpose. These results serve to inform policymakers, market designers, and market participants of how transfer policies may impact markets, so more informed decisions can be made.