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We consider the problem of prediction by a machine learning algorithm, called learner, within an adversarial learning setting. The learner's task is to correctly predict the class of data passed to it as a query. However, along with queries containing clean data, the learner could also receive malicious or adversarial queries from an adversary. The objective of the adversary is to evade the learner's prediction mechanism by sending adversarial queries that result in erroneous class prediction by the learner, while the learner's objective is to reduce the incorrect prediction of these adversarial queries without degrading the prediction quality of clean queries. We propose a game theory-based technique called a Repeated Bayesian Sequential Game where the learner interacts repeatedly with a model of the adversary using self play to determine the distribution of adversarial versus clean queries. It then strategically selects a classifier from a set of pre-trained classifiers that balances the likelihood of correct prediction for the query along with reducing the costs to use the classifier. We have evaluated our proposed technique using clean and adversarial text data with deep neural network-based classifiers and shown that the learner can select an appropriate classifier that is commensurate with the query type (clean or adversarial) while remaining aware of the cost to use the classifier.