oligomcp.gms : Oligopolistic Competition - Examples from MP
Oligopolistic Competition - Examples from MP
References:
- 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, A Variational Inequality Approach for the Determination of Oligopolistic Market Equilibrium. Mathematical Programming 30 (1984), 105-111.
Small Model of Type: MCP
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$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.
$Offtext
sets 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 variables
p price,
q(f) supply;
equations
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;
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