hark-stack.gms : SPE model from Harker - Stackelberg version
A spatial price equilibrium model is used to demonstrate different
ways of modeling market behavior. In this variant, we look at
the Stackelberg model that arises when we assume an oligopoly,
i.e. the production in each region is controlled by a single firm,
where the regional firms are independent, and one of the firms takes
the leader position, i.e. is assumed to have knowledge of the other
firms' decision problems.
Harker, P T, Alternative Models of Spatial Competition. Operations
Research 34, 3 (1986), 410-425.
Contributor: Steven Dirkse, June 2011
either include hark-oligop or
run with a restart from the hark-oligop save file
Small Model of Type: BP
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$title SPE model from Harker - Stackelberg version (HARK-STACK,SEQ=67)
$ontext
A spatial price equilibrium model is used to demonstrate different
ways of modeling market behavior. In this variant, we look at
the Stackelberg model that arises when we assume an oligopoly,
i.e. the production in each region is controlled by a single firm,
where the regional firms are independent, and one of the firms takes
the leader position, i.e. is assumed to have knowledge of the other
firms' decision problems.
Harker, P T, Alternative Models of Spatial Competition. Operations
Research 34, 3 (1986), 410-425.
Contributor: Steven Dirkse, June 2011
$offtext
* either include hark-oligop or
* run with a restart from the hark-oligop save file
$include hark-oligop.gms
$eolcom //
variable obj;
equations objdef;
;
objdef.. obj =E= sum{Q1(Q), z(Q)};
model stack / nash, objdef /;
parameter profit (*,*) 'profit for firm Q under different scenarios';
profit('nash',Q) = z.l(Q);
loop {Qi,
put myinfo '* Stackelberg version of Harker model: leader is firm' Qi.tl;
put / 'bilevel';
Q1(Q) = sameas(Qi,Q); // leader
// first write the leader's vars
put /' 'z(Qi)/' ';
loop{L,
put dl(L,Qi) dlq(L,Qi);
};
put s(Qi) /' ';
loop{arc(i,j),
put t(i,j,Qi);
};
// now write the follower problems
loop {Q$[not Q1(Q)],
put / 'max' z(Q)/' ';
loop{L,
put dl(L,Q) dlq(L,Q);
};
put s(Q) /' ';
loop{arc(i,j),
put t(i,j,Q);
};
put /' ' objDefD(Q);
loop{NL(n),
put flowBal(n,Q);
};
put /' ';
loop{L,
put dlBalD(L,Q);
};
put /' ';
loop{L$[not sameas(L,Q)],
put in(L,Q);
};
put / ' ' out(Q) sBal(Q);
};
put / 'vi';
put / ' ttVarDef ttVar';
put / ' cVarDef cVar';
put / ' dlqVarDef dlqVar';
putclose;
solve stack using emp max obj;
profit(Qi,Q) = z.l(Q);
};
execute_unload 'oliProfit', profit;
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