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External Pressure on Alliances: What Does the Prisoners’ Dilemma Reveal?

Birmingham Business School, University House Edgbaston Park Road, Birmingham, B15 2TY, UK
School of Computing and Mathematical Sciences, Liverpool John Moores University, James Parsons Liverpool L3 3AF, UK
Department of Statistics, Zeeman Building, University of Warwick, Coventry CV4 7AL, UK
Author to whom correspondence should be addressed.
Games 2013, 4(4), 754-775;
Received: 15 September 2013 / Revised: 13 November 2013 / Accepted: 18 November 2013 / Published: 10 December 2013
PDF [222 KB, uploaded 10 December 2013]


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. View Full-Text
Keywords: business alliances; mathematical model; game theory; Prisoners’ Dilemma business alliances; mathematical model; game theory; Prisoners’ Dilemma

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This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Binner, J.M.; Fletcher, L.R.; Kolokoltsov, V.; Ciardiello, F. External Pressure on Alliances: What Does the Prisoners’ Dilemma Reveal? Games 2013, 4, 754-775.

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