A Game with No Equilibria

This lecture begins a unit in which we consider games so complex that we cannot easily draw out a matrix or game tree. It also shows an example of games without an equilibrium.

Takeaway Points

  1. Nash’s theorem states that every game with a finite number of players and a finite number of pure strategies has at least one Nash equilibrium.
  2. As a result, a game with infinitely many strategies might have no equilibria.
  3. Even if we cannot draw a game’s matrix or game tree, we can still analyze it. Doing so requires a different set of tools, though. Learning those tools is the task for this unit.