Theory of Backward Induction:

We  solve the  games  from the class we  just  discussed  by  the method  of backward Induction. When the player  2  gets the move  in  the second  stage, she  will face  the following problem: given the action a, previously chosen by player,  

We assume that for each al  in  A₁, player  2's  optimisation  problem has  a unique solution R₂(a,). This is player 2's  best response  to player  1's action. Since  player  1 can  solve the  problem  of  player 2 as well  as  player  2  can, player  1 should anticipate player 2's reaction to each  of player  1's action a, that  player  1 might  take. Therefore, player 1's  problem  at  the first stage amounts to  

Assume  that  this optimisation  problem  for  player  one has a unique solution denoted by  a₁*. We will call the back ward  iriduction outcome of  this game.