[2] Rationality: The assumption that each player acts in a way that is designed to bring about what he or she most prefers given probabilities of various outcomes; von Neumann and Morgenstern showed that if these preferences satisfy certain conditions, this is mathematically equivalent to maximizing a payoff.
A straightforward example of maximizing payoff is that of monetary gain, but for the purpose of a game theory analysis, this payoff can take any desired outcome—cash reward, minimization of exertion or discomfort, or promoting justice can all be modeled as amassing an overall “utility” for the player.
The assumption of rationality states that players will always act in the way that best satisfies their ordering from best to worst of various possible outcomes.
However, that Nash equilibrium is not necessarily "efficient", meaning that there may be non-equilibrium outcomes of the game that would be better for both players.
Strictly dominated strategies cannot be a part of a Nash equilibrium, and as such, it is irrational for any player to play them.
On the other hand, weakly dominated strategies may be part of Nash equilibria.
The iterated elimination (or deletion, or removal) of dominated strategies (also denominated as IESDS, or IDSDS, or IRSDS) is one common technique for solving games that involves iteratively removing dominated strategies.