Description

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

Category : GAMS EMP library

Main file : hark-stack.gms

$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;