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Numeric solution: Nash Equilibrium (no trade, externality) ● Fictitious Play: Search for Nash Equilibrium as a fixed point of the iteration: REPEAT 8i max Wi feit g subject to economy and climate equations and ekt = ekt for k 6= i Kai Lessmann Kai Lessmann Numeric solution: Nash Equilibrium (trade + externality) ● Fictitious Play: Search for Nash Equilibrium as a fixed point of the iteration: REPEAT 8i max feit ; mijt ; xijt g Wi mijt : imports from j xijt : export to j subject to economy and climate equations and ekt = ekt for k 6= i ● Kai Lessmann Problem: mijt, xijt: market price levels unknown Kai Lessmann Numeric solution: Nash Equilibrium (trade, no externality) Determine competitive equilibrium using Negishi's Approach REPEAT ● ● Kai Lessmann max feit ; mijt ; xijt g X ±i Wi i subject to economy and climate equations Find δ i such that the intertemporal budget constraint R1P R1P holds: m x p m dt = p ijt ijt j6=i j6=i ijt xijt dt 0 0 Kai Lessmann My solution algorithm: Nash Equilibrium (trade + externality) ● Alternately fix emissions (in Negishi's Approach) and trade (in Fictitious Play) max fmijt ; xijt g X ±i Wi i subject to economy and climate equations and ejt = ejt 8i max Wi feit g subject to economy and climate equations and mijt = mijt ; xijt = xijt ; ekt = ekt for k 6= i Kai Lessmann ● ) mijt ; xijt ) eit Published as Lessmann et al. 2009, Economic Modelling Kai Lessmann