What is Equilibrium? How do we define it in social sciences, economy, game theory and engineering? Do these different fields crossover?
This session is an attempt to relate the topic of Equilibrium as explained in game theory to Equilibrium as defined in structural engineering. The session starts with an analysis of a scene in “A Beautiful Mind” movie, where Nash - sitting among his coursemates who are all attracted to the same beautiful blonde - finds himself criticising Adam Smith by arguing that “the interests of a group are best served by each of its members taking into account one another's decisions as well as his own self-interest”. In the scene, this translates in Nash’s advice of going for the four less enchanting brunette girls rather than the glamorous blonde in order to achieve what has later become known as Nash Equilibrium.
But what is Equilibrium in engineering then? A structure is said to be in equilibrium when all forces or moments acting upon it are balanced. This means that each force acting upon a body, or part of the body, is resisted by either another equal and opposite force or set of forces whose net result is zero. In different words, Cecil Balmond defines Equilibrium as “a stable relationship of forces about a point of symmetry” (Informal, 2007).
Lets draw a diagram of forces around the blonde and see what happens!!! When the forces are going towards the blonde, there is no equilibrium. When the forces are inverted outwards, they balance each other and equilibrium is achieved. According to Balmond’s definition then, the blonde is a point of symmetry, and achieving stability of forces about it means going for the brunettes.
