$title Oligopolistic Competition - Examples from MP (OLIGOMCP,SEQ=133)

$onText
Oligopolistic Competition - Examples from MP.

Murphy, F H, Sherali, H D, and Soyster, A L, A mathematical programming
approach for determining oligopolistic market equilibrium. Mathematical
Programming 24 (1982), 92-106.

Harker, P T, Oligopolistic equilibrium. Mathematical Programming 30
(1984), 105-111.

Keywords: mixed complementarity problem, oligopoly, general equilibrium model,
          Nash equilibria
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Set f 'firms' / f1*f5 /;

* f (q) = c q + beta/(beta+1) l^(-1/beta) q^(beta+1)/beta
* f'(q) = c + (q/l)^(1/beta)

Table data(f,*) 'cost function data'
         c  l  beta
   f1   10  5   1.2
   f2    8  5   1.1
   f3    6  5   1.0
   f4    4  5   0.9
   f5    2  5   0.8;

Parameter
   c(f)
   l(f)
   beta(f);

c(f)    = data(f,"c");
l(f)    = data(f,"l");
beta(f) = data(f,"beta");

Positive Variable
   p    'price'
   q(f) 'supply';

Equation
   demand    'supply - demand balance'
   profit(f) 'Nash first order condition';

demand..    sum(f, q(f)) =g= 5000*p**(-1.1);

profit(f).. c(f) + (q(f)/l(f))**(1/beta(f)) =g= p - q(f)*p**2.1/5500;

Model oligop / demand.p, profit.q /;

* initial guess:
q.l(f) =  10;
p.l    = (5000/sum(f, q.l(f)))**(1/1.1);

solve oligop using mcp;