Consider an ongoing sequence of pairwise marketing competitions between three companies with promotional campaigns of varying degrees of success. Each campaign involves comparative advertising belittling the target company. The company with the most loyal customers (call this firm “Most”) enjoys 100 percent success when it attacks either of the others. The company with the least loyal customers (“Least”) has a 30 percent success rate when it belittles either Most or “More.” More experiences an 80 percent success rate. The firms each launch their advertising attacks one at a time in an arbitrary sequence. Least goes first and can attack either Most or More. More attacks second, and Most attacks third. If more than one of the opponents survives the first round of competition, the order of play repeats itself: Least, then More, then Most. Any player can skip his or her turn; that is, the three actions available to Least to initiate the game are as follows: attack More, attack Most, or do nothing and pass the turn.

Diagram the game tree and employ subgame perfect equilibrium analysis to identify the strategic equilibrium. What should the most vulnerable firm with the least loyal customers do to initiate play? What would be More’s best-reply response if attacked and More survives? What if Least did nothing? What would Most do when and if its turn arose?