On the Rationality of Escalation

TL;DR

This paper uses coinduction to analyze infinite dollar auction games, revealing that rational escalation occurs under certain assumptions and challenging traditional views on equilibrium strategies.

Contribution

It formally demonstrates the rationality of escalation in infinite games using coinduction, and clarifies the conditions under which certain strategies are equilibria.

Findings

Escalation can be rational if the opponent always stops.

Stopping at every step is not a subgame perfect equilibrium.

Rational strategies depend on assumptions about the opponent’s behavior.

Abstract

Escalation is a typical feature of infinite games. Therefore tools conceived for studying infinite mathematical structures, namely those deriving from coinduction are essential. Here we use coinduction, or backward coinduction (to show its connection with the same concept for finite games) to study carefully and formally the infinite games especially those called dollar auctions, which are considered as the paradigm of escalation. Unlike what is commonly admitted, we show that, provided one assumes that the other agent will always stop, bidding is rational, because it results in a subgame perfect equilibrium. We show that this is not the only rational strategy profile (the only subgame perfect equilibrium). Indeed if an agent stops and will stop at every step, we claim that he is rational as well, if one admits that his opponent will never stop, because this corresponds to a subgame perfect equilibrium. Amazingly, in the infinite dollar auction game, the behavior in which both agents stop at each step is not a Nash equilibrium, hence is not a subgame perfect equilibrium, hence is not rational.