Whales and Sonar: Environmental Exemptions for the Navy’s Mid-Frequency Active Sonar Training

Mid-frequency active (MFA) sonar emits pulses of sound from an underwater transmitter to help determine the size, distance, and speed of objects. The sound waves bounce off objects and reflect back to underwater acoustic receivers as an echo. MFA sonar has been used since World War II, and the Navy indicates it is the only reliable way to track submarines, especially more recently designed submarines that operate more quietly, making them more difficult to detect. Scientists have asserted that sonar may harm certain marine mammals under certain conditions, especially beaked whales. Depending on the exposure, they believe that sonar may damage the ears of the mammals, causing hemorrhaging and/or disorientation. The Navy agrees that the sonar may harm some marine mammals, but says it has taken protective measures so that animals are not harmed. MFA training must comply with a variety of environmental laws, unless an exemption is granted by the appropriate authority. Marine mammals are protected under the Marine Mammal Protection Act (MMPA) and some under the Endangered Species Act (ESA). The training program must also comply with the National Environmental Policy Act (NEPA), and in some cases the Coastal Zone Management Act (CZMA). Each of these laws provides some exemption for certain federal actions. The Navy has invoked all of the exemptions to continue its sonar training exercises. Litigation challenging the MFA training off the coast of Southern California ended with a November 2008 U.S. Supreme Court decision. The Supreme Court said that the lower court had improperly favored the possibility of injuring marine animals over the importance of military readiness. The Supreme Court’s ruling allowed the training to continue without the limitations imposed on it by other courts. (pdf contains 20pp.)

The von Neumann-Morgenstern stable sets for 2x2 games

We analyze the von Neumann and Morgenstern stable sets for the mixed extension of 2 2 games when only single profitable deviations are allowed. We show that the games without a strict Nash equilibrium have a unique vN&M stable set and otherwise they have infinite sets.