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A minimum cost routing admits an arriving request on the minimum cost route if this minimum cost does not exceed the cost of the request, and rejects the request otherwise. Minimum cost routing strategies naturally arise as a result of optimization of the network performance or incorporating quality of service (QoS) requirements into the admission and routing processes. In the former case the implied cost of the resources represents the expected future revenue losses due to insufficient resources for servicing future requests. In the latter case the cost of a route represents the QoS provided to the request. In both cases due to the aggregation, delays in disseminating signaling information, statistical inferences, nonsteady or adversarial operational environment the cost of the resources may not be known exactly. Usually this uncertainty is modeled by assuming that the resource costs are random variables with some fixed probability distributions. We propose to explore a different approach intended to guard against the worst case scenario with respect to the resource costs. We solve the corresponding game in a symmetric case.