  It is frequently suggested that predictions made by game theory could be
improved by considering computational restrictions when modeling agents. Under
the supposition that players in a game may desire to balance maximization of
payoff with minimization of strategy complexity, Rubinstein and co-authors
studied forms of Nash equilibrium where strategies are maximally simplified in
that no strategy can be further simplified without sacrificing payoff. Inspired
by this line of work, we introduce a notion of equilibrium whereby strategies
are also maximally simplified, but with respect to a simplification procedure
that is more careful in that a player will not simplify if the simplification
incents other players to deviate. We study such equilibria in two-player
machine games in which players choose finite automata that succinctly represent
strategies for repeated games; in this context, we present techniques for
establishing that an outcome is at equilibrium and present results on the
structure of equilibria.
