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Raiffa-Kalai-Smorodinsky Analysis

The Raiffa-Kalai-Smorodinsky (RKS) bargaining solution is defined with respect to a “ideal” outcome in which each player’s utility is maximized (26). Figure 6 demonstrates the two-person situation. There is again a default position and feasible set. The point represents an ideal outcome in which each player’s share is the maximum possible within the feasible set, regardless of the consequences for the other players. The RKS solution is the best feasible point on the line segment from to .

Figure 6. Raiffa-Kalai-Smorodinsky solution.

We can see the RKS solution as the result of making proportional allocations to the players. Each player has a maximum gain . First, allot each player 10% of his or her maximum gain, then 20%, and so on until further allocations are infeasible. It is clear that enlarging the feasible set can never cause a player’s allocation to decrease.

Again, The axiomatic derivation of the RKS solution assumes "cardinal non-comparability", anonymity and a Pareto condition. However, it replaces the independence of irrelevant alternatives with the monotonicity property just mentioned (27). The derivation is problematic for the same reason as the derivation of the Nash solution: cardinal non comparability is a very strong assumption that rules out meaningful comparison of utilities as quantities.

A possible bargaining justification is that the RKS solution achieves the minimax relative concession mentioned earlier. If player accepts offer , the player’s concession (with respect to the ideal) is . The concession if negotiation fails is , which means that the relative concession is . It might be argued that the players will try to minimize their relative concessions and will reach equilibrium when they minimize the maximum relative concession among them. Algebraically , minimizing the maximum relative concession is the same as maximizing the minimum relative gain , which is what the RKS point accomplishes.

Figure 7. Anomalous example for the RKS bargaining solution, which in this case is the default position . The feasible set is the shaded triangular area, and the Rawlsian minimax solution is .

So, in the two-player case, the RKS solution resembles the Rawlsian maximin solution, except that it maximizes the minimum relative gain rather than the minimum utility. It might be seen as having ideological content on that basis. However, it leads to some anomalies when there are three or more players (Figure 7). The line segment from to leaves the feasible set at , which means that is the RKS solution-scarcely a rational outcome. is solution for The Rawlsian maximin.

Ideological Factor in National Security

This part of strategic Ideology consists of assumptions at a more operational level, about what strategic options are the most efficacious for dealing with the threat environment as defined by the central paradigm. It is at this second level that strategic Ideology begins to...

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