%0 Journal Article
%T External Pressure on Alliances: What Does the Prisoners¡¯ Dilemma Reveal?
%A Jane M. Binner
%A Leslie R. Fletcher
%A Vassili Kolokoltsov
%A Francesco Ciardiello
%J Games
%D 2013
%I MDPI AG
%R 10.3390/g4040754
%X Prompted by a real-life observation in the UK retail market, a two-player Prisoners¡¯ Dilemma model of an alliance between two firms is adapted to include the response of a rival firm, resulting in a version of a three-player Prisoners¡¯ Dilemma. We use this to analyse the impact on the stability of the alliance of the rival¡¯s competition, either with the alliance or with the individual partners. We show that, while strong external pressure on both partners can cause Ally-Ally to become a Nash equilibrium for the two-player Prisoners¡¯ Dilemma, weak or asymmetric pressure that plays on the partners¡¯ differing objectives can undermine the alliance. As well as providing new insights into how allies should respond if the alliance is to continue, this also illustrates how a third party can most effectively cause the alliance to become unsustainable. We create a new game theoretic framework, adding value to existing theory and the practice of alliance formation and sustainability.
%K business alliances
%K mathematical model
%K game theory
%K Prisoners¡¯ Dilemma
%U http://www.mdpi.com/2073-4336/4/4/754