Abstract. A modification of the classical secretary problem is considered that is obtained by adding the second player called a censor who tries to preclude the other player’s optimal choice by imposing some restrictions on the search. Nash equilibrium is found in explicit form of mixed strategies for two different types of censorship. The asymptotic behavior of diverse numerical quantities associated with optimal strategies for both players are studied in the case when the number of objects tends to infinity.

Keywords: optimal choice problem, Markov chain stopping, matrix game, Nash equilibrium, mixed strategy, threshold strategy.