Conservative vs optimistic rationality in games: A revisitation

Abstract

This paper revisits the problem of formalizing a conservative rationality concept in games. A rationality concept is said to be conservative if whenever it advises an agent to move from the status quo, that agent cannot be worse off at any of the possible equilibria that may be reached subsequent to this move, relative to the status quo. We formalize this notion for a wide class of games under complete information. Examining some leading concepts of rationality for such games, we find that the only concepts which are conservative are the stable set and the largest consistent set. An implication of our finding is that, along with the Nash equilibrium and the core, Harsanyi’s farsighted stable set and most of its descendants in actual fact lack farsightedness. Most of these rationality concepts are premised on a notion of optimism that we find to be “irrational” in that first movers in sequential games do not take into account the fact that subsequent moves are initiated by players who, even if they are optimistic, are utility maximizers.