Two insurance companies that manage employee benefit programs are bidding for additional business in their area of expertise at a market rate of $200 per hour. The potential customers refuse to leave their current suppliers and award benefit management contracts to the new firms unless billing rates are cut by $50. Abbott, Abbott & Daughters (AA&D) decides to do just that. Your firm, Zekiel, Zekiel & Sons (ZZ&S), must decide whether to match the price cut and then allow customersto choose randomly between the two firms, or whether to lower rates still further to $100 per hour. Past experience suggests, however, that the price cutting may well not stop there. The clients will surely take their best current offer back and forth between the two firms, forcing a downward price spiral. The question therefore is, “How low will you go?” Crucially, this game has a stopping rule: At a price below your $40 cost, the additional business becomes unprofitable and must be refused. AA&D has higher costs at $66 per hour.
Again, your decision depends on an analysis of the sequence of predictable future events represented with a game tree or decision tree. Provide one. To simplify, assume that all rate cuts must be in $50 increments, that customers choose quickly between equal rate quotes using fair coin tosses (represented by capital letter N for Nature), that once a rate quote has been matched it cannot be lowered, and that many potential customers are present in the market. It is now your turn at node Z1 with rates at the $150-per-hour level. What should you do? Match rates or cut rates further?