A stability theorem for symmetrically rational counterplanning

In the absence of contrary information, it would seem prudent for a competitor to attribute to his opponents the same level of rationality that he himself employs. In the context of a general, linear-quadratic, nonzero-sum, two-person game, it is shown that a counterplanning procedure consistent with this principle of symmetrical rationality always converges to the unique Nash equilibrium for the game.The work of R. Kalaba and L. Tesfatsion was partially supported by the National Science Foundation under Grant No. ENG-77-28432 and by the National Institutes of Health under Grant No. GM-23732-03.