3. Bowden (1989, p 197) distinguishes these approaches as: ‘This simply means that the maximizing π1, π2, are completely laid out at the start of the horizon, as opposed to feedback or closed-loop control, where the optimizing would be given in terms of the then current state variable x1 resulting from the application of π1.’π1 and π2 are the policies for period one and period two respectively and x1 is the reaction function for period one.
4. The optimum values of A1 and A2 are determined as follows: Max G2 (r1, r2, A1, A2) = G2 (r1, A1) + G2 (r2, A2) (20.1)1 2
Subject to the reaction functions r1 and r2 of king one
r1 = R1 (A1, A2) (20.2) r2 = R2 (r1, A2) (20.3) Differentiating equation (20.1) with respect to A1 and A2 gives ∂G2 /∂A1 + (∂G2 /∂r1 + (∂G2 /∂R2) (∂R2/∂r1)) ∂R1/∂A1= 01 1 2
(∂G2 /r1) (∂R1/∂A2)+ ∂G2 /∂r2 ((∂R2/∂A2) (∂R1/∂A2) + ∂R2/∂A2)+ 1 2
∂G2 /∂A2 = 02
A* and A* are the optimum values obtained by solving these two1 2
equations. For a very lucid exposition of the time inconsistency problem (see Bowden (p 196-199).
5. See Bowden (p 200).
6. Kennan and Wilson (1993) note, ‘In this view, some conflicts stem from differing expectations due to differing information. Each party’s incentive to exploit its informational advantage prevents a quick, costless settlement.’ However, they add, ‘The idea that private information is a prime cause of costly conflict is currently an untested hypothesis.’
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