In the extended deterrence literature, third party defenders play an important role in resolving a crisis primarily due to their credibility to retaliate. But the strategic dynamics in South Asia provide a complex environment for third party defenders/mediators where extended deterrence relationship is not formalized by any agreement and the hostile parties are also nuclear weapon states. It is however ironic that though the third, neutral state party, does not exercise any control over deterrence dynamics between the two hostile states, it remains the most important contributing factor in the region for crisis stability.

Let us examine two hypotheses: (a) presence of third party with high resolve in a crisis where both states have nuclear weapons bolsters the chances of limited war and extends the duration of the crisis (b) presence of third party with low resolve in a crisis where both states have nuclear weapons will push the two states away from crisis escalation thus shortening the duration of the crisis.

Now lets play a game.

The Game

Two states A and B are two nuclear weapon states moving towards a nuclear crisis. C is a third party that is also a nuclear weapon state. Nature (N) moves about the resolve of third party C (high resolve, low/no resolve). C with high resolve offers mediation. C with low or no resolve offers no mediation. Players A and B do not know the true nature of C’s resolve. But they believe that they accept C with high resolve with a probability p and C with low resolve with a probability 1-p. A and B after perceiving C with a high resolve have two options each: either to accept the offer of C’s mediation or to escalate. If they accept the offer of mediation without any concessions/carrots by C, the game ends. But if they reject the offer the game continues to the next level where both A and B choose to escalate. If they choose to escalate, C offers concessions/carrots (f) to both A and B. If A and B accept, the crisis does not escalate and A and B choose the negotiating table. If A and B do not accept, the crisis escalates to the next level. If the crisis escalates and inches towards limited war, C at this time offers better concessions/carrots (2f) to both A and B. If both accept, crisis is managed. If not, game continues till they accept offers by C that are lucrative for both. During this time of steady escalation, A and B dangerously continue to exploit C’s vulnerability and proceed with the game. C has stakes in the game, which could come from C’s forces stationed in close proximity to A and B; C’s past reputation as a mediator or C’s credibility as a superpower.

When both A and B perceive C with low resolve with a probability (1-p) with no offer of mediation, they realize that they can only push it too far before crisis spirals out of control. In this scenario, A and B have only two choices each, to escalate or not escalate. If they choose not to escalate the game ends and crisis is managed bilaterally without third party mediation. If they choose to escalate, both suffer the risks of actual war fighting. The payoffs for not escalating, for both, are greater than the payoffs for fighting and thus like the game of chicken, both A and B would find an equilibrium in not escalating.


 Extensive Game of Crisis Bargaining and Third Party Intervention

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