By Ngo Van Long
This e-book presents readers with a finished survey of versions of dynamic video games in economics, together with an in depth insurance of diverse fields of purposes. it is going to additionally talk about and clarify major techniques and strategies utilized in dynamic video games, and tell readers of its significant advancements whereas equipping them with instruments and ideas that may relief within the formula of ideas for difficulties. A Survey of Dynamic video games in Economics will curiosity those that desire to research extra in regards to the conceptions, techniques and versions which are utilized within the area of dynamic video games.
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Extra info for A Survey of Dynamic Games in Economics (Surveys on Theories in Economics and Business Administration)
70) cS + (δ + ρ)ψ2 = 0. 72) Thus, we have obtained the interesting result that the open-loop Stackelberg game leads to a higher steady-state pollution stock than the OLNE S a in Eq. 34). It can be veriﬁed that in the OLSE, the leader’s level of emissions is greater, and the follower’s level is smaller, than in their OLNE counterparts. At the steady state, the leader’s shadow price γ of the follower’s shadow price is positive: γ= cS > 0. c + δ(ρ + δ) The leader’s steady-state shadow price θ of the pollution stock is θ = −δγ = − δcS <0 c + δ(ρ + δ) and the follower’s steady-state shadow price is ψ2 = − cS < 0.
67) 15 An important point is that for the Stackelberg leader’s problem, one should ask what primitive assumptions of the speciﬁc models at hand imply ψ2 (0) can (or cannot) be inﬂuenced by the leader. This is a type of “controllability problem”, see Xie (1997) and Dockner et al. (2000, Chap. 5) for details. 16 This is technically a transversality condition at the beginning of the time horizon, when the initial state variable is not ﬁxed; see, for example, L´eonard and Long (1992, Chap. 7). If you can choose the initial level of a state variable, you should set that variable at the level where its marginal contribution to your objective function is zero.
Finally, it can be shown that the equilibrium feedback strategies are, for all Z ≤ ar/δ τ = g(Z) = a + p = φ(Z) = 2A2 − 2δ(2 + η)2 r(2 + η)3 δ(2 + η)2 + 2bA2 r(2 + η)3 ar −Z δ ar −Z δ Along the equilibrium path, the producer price falls monotonically to zero, and the tax τ rises steadily toward a. It can be shown that the time path of consumer price in the Nash equilibrium is above the one that a world social planner would choose. This is because the seller aims at restricting output in the early phase of the program.