  We present a novel coalgebraic formulation of infinite extensive games. We
define both the game trees and the strategy profiles by possibly infinite
systems of corecursive equations. Certain strategy profiles are proved to be
subgame perfect equilibria using a novel proof principle of predicate
coinduction. We characterize all subgame perfect equilibria for the dollar
auction game. The economically interesting feature is that in order to prove
these results we do not need to rely on continuity assumptions on the payoffs
which amount to discounting the future. In particular, we prove a form of
one-deviation principle without any such assumptions. This suggests that
coalgebra supports a more adequate treatment of infinite-horizon models in game
theory and economics.
