The paper by Kohlberg and Mertens examines the strategic stability of equilibria in noncooperative games. It addresses the question of which Nash equilibria are strategically stable and whether every game has such an equilibrium. The authors identify three necessary conditions for strategic stability: backwards induction, iterated dominance, and invariance. They define a set-valued equilibrium concept that satisfies all three and prove that every game has at least one such equilibrium. They also show that the departure from the usual notion of single-valued equilibrium is minor, as the sets reduce to points in all generic games. The paper discusses various equilibrium concepts, including perfect, sequential, and proper equilibria, and highlights their limitations. It argues that these concepts fail to capture strategic stability because they may change when the game tree is altered in irrelevant ways. The authors propose a unified concept of strategic stability that satisfies both the backwards induction rationality of the extensive form and the iterated dominance rationality of the normal form, while being independent of irrelevant details in the game description. The authors define a set-valued equilibrium concept that satisfies existence, connectedness, backwards induction, invariance, and iterated dominance. They show that this concept is necessary for strategic stability and that it satisfies all the required properties. The paper also discusses the relationship between strategic stability and other equilibrium concepts, such as hyperstable and fully stable equilibria, and highlights the limitations of these concepts. The authors conclude that strategic stability is a fundamental concept in game theory and that the proposed set-valued equilibrium concept provides a robust framework for analyzing it.The paper by Kohlberg and Mertens examines the strategic stability of equilibria in noncooperative games. It addresses the question of which Nash equilibria are strategically stable and whether every game has such an equilibrium. The authors identify three necessary conditions for strategic stability: backwards induction, iterated dominance, and invariance. They define a set-valued equilibrium concept that satisfies all three and prove that every game has at least one such equilibrium. They also show that the departure from the usual notion of single-valued equilibrium is minor, as the sets reduce to points in all generic games. The paper discusses various equilibrium concepts, including perfect, sequential, and proper equilibria, and highlights their limitations. It argues that these concepts fail to capture strategic stability because they may change when the game tree is altered in irrelevant ways. The authors propose a unified concept of strategic stability that satisfies both the backwards induction rationality of the extensive form and the iterated dominance rationality of the normal form, while being independent of irrelevant details in the game description. The authors define a set-valued equilibrium concept that satisfies existence, connectedness, backwards induction, invariance, and iterated dominance. They show that this concept is necessary for strategic stability and that it satisfies all the required properties. The paper also discusses the relationship between strategic stability and other equilibrium concepts, such as hyperstable and fully stable equilibria, and highlights the limitations of these concepts. The authors conclude that strategic stability is a fundamental concept in game theory and that the proposed set-valued equilibrium concept provides a robust framework for analyzing it.