A simple case of rationality of escalation

Escalation is the fact that in a game (for instance an auction), the agents play forever. It is not necessary to consider complex examples to establish its rationality. In particular, the $0,1$-game is an extremely simple infinite game in which escalation arises naturally and rationally. In some sense, it can be considered as the paradigm of escalation. Through an example of economic games, we show the benefit economics can take of coinduction.