This chapter compares the standard of strategic equilibrium with the two most commonly proposed standards for solutions: the standard of Nash equilibrium and the standard of nondomination. It also compares the standard of strategic equilibrium with other revisions of the standard of Nash equilibrium. All standards are taken to advance necessary conditions for solutions and to apply to ideal normal-form games, as the standard of strategic equilibrium does. This chapter's goal, in contrast with the preceding chapter's goal, is general comparison of the standard of strategic equilibrium with other standards for solutions, and not comparison of the standard's consequences with intuitions about solutions in particular cases. The chapter looks especially for conflict between the standard of strategic equilibrium and other standards. Are there cases in which it is possible to satisfy the standard of strategic equilibrium and possible to satisfy another standard, but impossible to satisfy both standards, so that the other standard argues against the standard of strategic equilibrium?

STRATEGIC AND NASH EQUILIBRIUM

Let us compare the standard of Nash equilibrium with the standard of strategic equilibrium, taking the two standards as potential rivals. We will see that the two standards do not conflict in ideal normal-form games. Where it is possible to satisfy each, it is possible to satisfy both, since every Nash equilibrium is a strategic equilibrium.

Not every strategic equilibrium is a Nash equilibrium. For example, some games have Nash equilibria and strategic equilibria but have more strategic equilibria than Nash equilibria. The game with an unattractive Nash equilibrium presented by Figure 7.3 is an illustration. It has a unique Nash equilibrium, but two strategic equilibria.