Surprise in contests

We consider a two-player asymmetric dynamic contest with a binary effort choice and a finite number of periods, in which one player wins if and only if he is able to surprise his rival by attacking first. The unique subgame perfect equilibrium in mixed strategies, in which the probability of a surprise increases over time, is examined. It is found that the chance of a surprise is highest at the “last minute.” Nonetheless, it remains small if the cost of effort is small. With an infinite horizon, the probability remains constant over time; however, it increases as players become more impatient. Applications are discussed.