Solving a nonlinear system with parameters

Click For Summary
SUMMARY

The discussion centers on solving a system of nonlinear equations relevant to game theory for an economics thesis. The equations presented are: a0x² + a1xy + a2x + a3y + a4 = 0 and b0y² + b1xy + b2x + b3y + b4 = 0. It is established that if all constants (a0, a1, a2, a3, a4, b0, b1, b2, b3, b4) are known, one can isolate y from the first equation and substitute it into the second, leading to a fourth-degree polynomial in x. This method provides a clear pathway to finding solutions despite the complexity of the nonlinear system.

PREREQUISITES
  • Understanding of nonlinear equations
  • Familiarity with polynomial equations
  • Knowledge of game theory concepts
  • Proficiency in algebraic manipulation
NEXT STEPS
  • Research methods for solving fourth-degree polynomials
  • Learn about numerical methods for nonlinear equation systems
  • Explore software tools like MATLAB or Mathematica for symbolic computation
  • Study the implications of reaction functions in game theory
USEFUL FOR

Students and researchers in economics, particularly those focusing on game theory, as well as mathematicians dealing with nonlinear systems and polynomial equations.

KevinL
Messages
37
Reaction score
0
I'm doing my economics thesis on game theory, and need to solve a system of nonlinear equations (these will be the reaction functions). Unfortunately, I have no idea how to solve it explicitly--indeed, I am a bit worried its impossible with the parameters. It is rather symmetric though.

The system is as such:

a0x2 + a1xy + a2x + a3y + a4 = 0

b0y2 + b1xy + b2x + b3y + b4 = 0

Any help pointing me in the right direction is much appreciated!
 
Physics news on Phys.org
If all 'a' and 'b' constants are known, you can isolate, say, y from the first equation and insert the resulting into the second equation...a few line of expanding everything and multiplying, etc., you will end up with a forth degree polynomial for x
 

Similar threads

Graduate Need help solving 1st order pde numerically
  • · Replies 5 ·
Replies
5
Views
3K
Failure of Optimisation for Nonlinear Equation Systems
  • · Replies 8 ·
Replies
8
Views
3K
Graduate Solving nonlinear differential to emulate Newtonian gravity
  • · Replies 8 ·
Replies
8
Views
2K
Program to solve system of nonlinear equations
  • · Replies 7 ·
Replies
7
Views
3K
MATLAB MATLAB: How to solve a system of Nonlinear Differential Equations?
  • · Replies 1 ·
Replies
1
Views
5K
Graduate How do you solve a nonlinear recurrence relation?
  • · Replies 6 ·
Replies
6
Views
4K
Need some advice about graduate studies in nonlinear dynamics
  • · Replies 3 ·
Replies
3
Views
3K
Graduate Solve Nonlinear System of Equations
  • · Replies 1 ·
Replies
1
Views
3K
Angle determination of Sum-Frequency Generation in BBO
  • · Replies 1 ·
Replies
1
Views
3K
MATLAB Solving Nonlinear System of Equations for x and y as a Function of r
  • · Replies 3 ·
Replies
3
Views
6K