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We consider a stochastic game of control and stopping specified in terms of a process X-t = -theta Lambda(t)+W-t, representing the holdings of Player 1, where W is a Brownian motion, theta is a Bernoulli random variable indicating whether Player 2 is active or not, and Lambda is a nondecreasing continuous process representing the accumulated "theft" or "fraud" performed by Player 2 (if active) against Player 1. Player 1 cannot observe theta or Lambda directly but can merely observe the path of the process X and may choose a stopping rule tau to deactivate Player 2 at a cost M. Player 1 thus does not know if she is the victim of fraud or not and operates in this sense under unknown competition. Player 2 can observe both theta and W and seeks to choose a fraud strategy Lambda that maximizes the expected discounted amount E [integral(tau)(0) e(-rs)d Lambda(s)vertical bar theta = 1], whereas Player 1 seeks to choose the stopping strategy tau so as to minimize the expected discounted cost E[theta integral(tau)(0) e(-rs)d Lambda(s) + e(-rr)MI({tau, infinity})]. This non-zero-sum game belongs to a class of stochastic dynamic games with unknown competition and continuous controls and is motivated by applications in fraud detection; it combines filtering (detection), stochastic control, optimal stopping, strategic features (games), and asymmetric information. We derive Nash equilibria for this game; for some parameter values we find an equilibrium in pure strategies, and for other parameter values we find an equilibrium by allowing for randomized stopping strategies.