  Finite objects and more specifically finite games are formalized using
induction, whereas infinite objects are formalized using coinduction. In this
article, after an introduction to the concept of coinduction, we revisit on
infinite (discrete) extensive games the basic notions of game theory. Among
others, we introduce a definition of Nash equilibrium and a notion of subgame
perfect equilibrium for infinite games. We use those concepts to analyze well
known infinite games, like the dollar auction game and the centipede game and
we show that human behaviors that are often considered as illogic are perfectly
rational, if one admits that human agents reason coinductively.
