The purpose of this comment is to put Adversarial Risk Analysis into historical perspective. To what extent is it a 'new research area' adding 'anticipating the actions of one's opponents' to traditional risk analysis [1, p. 852]? To what extent is it the application of already published principles to a modern set of problems, such as terrorism, biological attack, etc.?
All of the literature to be reviewed centers around decision-making in the presence of more than one decision-maker. Classical game theory, which concentrates on simultaneous games, is generally conceded to have started with Von Neumann and Morgenstern , who advocate the minimax solution to constant-sum two-person games. This formulation assumes that each player knows the utilities of the other player, and that these are strictly opposed: what is better for one player is worse for the other. They apply a minimax principle, which proposes that each player protect against the worst that the opponent might do. Under these assumptions, they prove that there are mixed (i.e. probabilistic) strategies for both players such that neither can do better. Nash later generalized this result to show for arbitrary, non-necessarily constant sum simultaneousmove games, the existence of a pair of strategies such that neither player, knowing the (possibly mixed) strategy of the other, would have incentive to change.
This program faced several difficulties. The first was non-uniqueness of the solution. Suppose two people set a time to meet in New York City, but neglect to specify where. Then each location in the city is a Nash-equilibrium, and the structure of the game is unhelpful in guiding the players (see [4, p. 56]). Nonetheless, a majority of Schelling's informal sample met at the information booth at Grand Central Station. How they know this has to do with the context of the game, and not with its abstract structure, which is Schelling's point. Harsanyi and Selten [5] address this issue by imposing additional 'principles' increasingly divorced from application, but sufficient to prove uniqueness of Nash equilibrium.
The second difficulty revolved around the minimax principle. Such was the prestige of von Neumann and Morgenstern that there was interest in making the minimax principle a foundation for statistics. The books of Wald [6] and Blackwell and Girshick [7] aim in this direction. The purpose of Savage's 'Foundations of Statistics' (1954) was to justify the minimax approaches to statistics. In this he failed, and only gradually came to see that the Bayesian principle that his book did justify had strengths not shared by the minimax approach he had failed to justify (see [8, p. iv]).
A third difficulty is that there are few situations of simultaneous moves. The classical games, such as chess, checkers, bridge and poker, all have sequential moves, in which each player can make use of the knowledge of an opponent's previous moves in deciding what to do. Conceptually this difficulty can be overcome by considering a player's 'type' ([9]), which determines what move a player would make in each possible situation. Then players are imagined to choose types simultaneously at the beginning of the game. In practice, there are too many types for this to be helpful.
The critical application during this period had to do with nuclear weapons, and the threat that, even by accident, the United States and the Soviet Union would obliterate each other, and, quite possibly, all human life on the planet. The most useful bridge between the theoretical work mentioned above and the practical needs of managing the cold war was in Schelling's 'The Strategy of Conflict ' (1960). He explains (p. 3) 'The term 'strategy' is taken, here, from the theory of games, which distinguishes games of skill, games of chance, and games of strategy, the latter being those in which the best course of action for each player depends on what the other players do. The term is intended to focus on the interdependence of the adversaries' decisions and on their expectations about each other's behavior. ' (p. 3).
In Schelling's formulation, the international parties both share an interest in avoiding mutual destruction and have opposing political interests. To make threats and promises credible in such circumstances requires a demonstration of commitment to a course of action, which means persuasively to make one's actions more predictable. On the other hand, tactically it is useful to keep one's enemy/counterpart guessing. This tension is at the heart of his section on 'strategy with a random component' (pp. 175 and 203).