  We introduce a model of competing agents in a prophet setting, where rewards
arrive online, and decisions are made immediately and irrevocably. The rewards
are unknown from the outset, but they are drawn from a known probability
distribution. In the standard prophet setting, a single agent makes selection
decisions in an attempt to maximize her expected reward. The novelty of our
model is the introduction of a competition setting, where multiple agents
compete over the arriving rewards, and make online selection decisions
simultaneously, as rewards arrive. If a given reward is selected by more than a
single agent, ties are broken either randomly or by a fixed ranking of the
agents. The consideration of competition turns the prophet setting from an
online decision making scenario to a multi-agent game.
  For both random and ranked tie-breaking rules, we present simple threshold
strategies for the agents that give them high guarantees, independent of the
strategies taken by others. In particular, for random tie-breaking, every agent
can guarantee herself at least $\frac{1}{k+1}$ of the highest reward, and at
least $\frac{1}{2k}$ of the optimal social welfare. For ranked tie-breaking,
the $i$th ranked agent can guarantee herself at least a half of the $i$th
highest reward. We complement these results by matching upper bounds, even with
respect to equilibrium profiles. For ranked tie-breaking rule, we also show a
correspondence between the equilibrium of the $k$-agent game and the optimal
strategy of a single decision maker who can select up to $k$ rewards.
