Question

Can backward induction be readily applied when a sequential game is presented as a payoff matrix? Discuss.

Answer 1

Yes, backward induction can be applied readily when a sequential game is presented as a payoff matrix. Backward induction, like all game theory, uses the assumptions of rationality and maximization, meaning that Player 2 will maximize his payoff in any given situation. Moreover the backward induction requires sequential rationality which indicates that the players should play optimally at every point in the game

For example: In a below there is a sequential game between two players. The Player 1 makes the first decision (right or left) and Player 2 makes its decision after Player 1 (down or up). If we eliminate the choices that Player 2 will not choose, thus can narrow down the tree; and now will bold the lines that maximize the player's payoff at the provided information set. Thus the result is an equilibrium found by backwards induction of Player 1 selecting the "right" and Player 2 selecting "up"