This essay describes one economist's view of how Nash's work influenced the development of game theory as a tool for analyzing strategic behavior.

Most graduating medical students in the United States obtain hospital residencies through the National Resident Matching Program ("NRMP"). The NRMP, or "Match" as it is called, is a centralized procedure that begins each year with hospitals defining residency positions, including a fixed specification of the associated salaries. The Match has been criticized on the grounds that this salary inflexibility biases salaries downward and possibly interferes with efficient allocation of students to positions. This paper proposes a centralized procedure, called the "Flexible-Salary Match," which makes salaries fully flexible an may help to overcome those problems.

Starting from Hendricks and McAfee's (2000) example of the Allies' decision to feint at Calais and attack at Normandy on D-Day, this paper models misrepresentation of intentions to competitors or enemies. Allowing for the possibility of bounded strategic rationality and rational players' responses to it yields a sensible account of lying via costless, noiseless messages. In many cases the model has generically unique pure-strategy sequential equilibria, in which rational players exploit boundedly rational players, but are not themselves fooled. In others, the model has generically essentially unique mixed-strategy sequential equilibria, in which rational players' strategies protect all players from exploitation.

"Hide-and-Seek" games are zero-sum two-person games in which one player wins by matching the other's decision and the other wins by mismatching. Although such games are often played on cultural or geographic "landscapes" that frame decisions non-neutrally, equilibrium ignores such framing. This paper reconsiders the results of experiments by Rubinstein, Tversky, and others whose designs model non-neutral landscapes, in which subjects deviated systematically from equilibrium in response to them. Comparing alternative explanations theoretically and econometrically suggests that the deviations are best explained by a structural non-equilibrium model of initial responses based on "level-k" thinking, suitably adapted to non-neutral landscapes.