A Multistage Game-Theoretic Model of International Environmental Agreements, Stability and Environmental Efficiency

The present paper deals with multistage dynamics [1], [2] of international environmental agreements (IEAs) and, in particular, with problem of IEA time-consistency, e.g. [3]. Let N be a set of players (countries of the world), each of which emits pollutant that damages a shared environment resource, and set S, S ⊆ N (S 6= ∅) be a coalition of players, which intend jointly to reduce emission. We consider a two level coalitional game Γ0(S) = 〈N , {q i , q i }i=1, {π i , π i }i=1〉, where q S(F ) i are players’ strategies and π S(F ) i are net benefits of players from S (and F = N \ S); the coalition S is the leader, and free-riders F are the followers, [4]. Assuming a certain agreement with structure S to be formed, we determine initial emission reduction targets (q ,q ) of agreement signatories and free-riders so that they constitute Stackelberg equilibrium in the game Γ0(S). Basing on results presented in [5]–[8], we construct a time-consistent abatement scheme, which reallocates abatement commitments over time periods [t, t + 1], t = 0, . . . ,m. Time-consistency of the scheme means that emission reduction ( q [t,m),q [t,m) ) during time period [t,m) should constitute Stackelberg equilibrium in the current game Γt ( S,q [0, t− 1),q [0, t− 1) ) . Stability of coalition S is associated with a principle of self-enforcement (conditions of internal/external stability), introduced in [9]. To analyze prospects for cooperation among players during stepwise emission reduction, we introduce a notion of time-consistency of a self-enforcing agreement, which is based on conditions of internal and