Joining the Nuke Club: A Forward Induction Approach

I investigate a two-country non-cooperative game where the status quo ante is asymmetric as one country is endowed with nuclear weapons while the other is not and is evaluating the opportunity of building up a nuclear arsenal. After identifying the conditions on pay-offs such that the resulting reduced form is a coordination game with two symmetric equilibria, I resort to forward induction to show that the implicit signalling mechanism in it may lead countries to select the peaceful equilibrium in a symmetric environment where both are endowed with analogous arsenals. Then I discuss the possibility for the nuclear power to give in to the rival so as to make the latter indifferent between entering the nuke club or not. This, however, turns out not to be a suitable route in absence of a commitment device or credible enforcement.