The Art of Strategy: A Game Theorist's Guide to Success in Business and Life

by Avinash K. Dixit

Begin by seeing if either side has a dominant strategy—one that outperforms all of that side’s other strategies, irrespective of the rival’s choice. This leads to Rule 2: If you have a dominant strategy, use it. If you don’t have a dominant strategy, but your rival does, then count on his using it, and choose your best response accordingly. Next, if neither side has a dominant strategy, see if either has a dominated strategy—one that is uniformly worse for the side playing it than all the rest of its strategies. If so, apply Rule 3: Eliminate dominated strategies from consideration. Go on doing so successively. If during the process any dominant strategies emerge in the smaller games, they should be chosen. If this procedure ends in a unique solution, you have found the prescriptions of action for the players and the outcome of the game. Even if the procedure does not lead to a unique outcome, it can reduce the size of the game to a more manageable level. Finally, if there are neither dominant nor dominated strategies, or after the game has been simplified as far as possible using the second step, apply Rule 4: Look for an equilibrium, a pair of strategies in which each player’s action is the best response to the other’s. If there is a unique equilibrium of this kind, there are good arguments why all players should choose it. If there are many such equilibria, one needs a commonly understood rule or convention for choosing one over the others. If there is no such equilibri...