Download Numeric solution: Nash Equilibrium (no trade, externality)

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