1Z.
(9) II1S
[1 - q(r)]δs.II0* + K
[1 - q ( r ) δs ]
After substituting (9) into (8), the expression for the total expected pay-off at time ts for the
opposition party is obtained:
(10) II0*
[1 - p ( r )]. δ,K
(1 - δs )[1 + δs - 2δsp(r)]
Finally, the total discounted pay-off for both parties is given by:
11 ■■ + II0 ' = —K— where δ, = δ (W,, μ)
(1 - δ, ) s t
From this last expression the Pareto-optimum or efficient result for the level of reserves WP can
be derived. This corresponds to the level that make the total discount factor equal to the pure
myopia value, i.e., Wp / δs (W, μ) = μ.
After introducing the game and characterised the non-cooperative equilibrium, the next step is
to present the conditions for the emergence of co-operation between both parties.
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