War of Attrition exercise

Two firmsyour team's and one otherare competing in "winner take all" market, meaning that after an initial period of competition, there will be one survivor who'll capture the entire market and earn substantial economic profits. During the initial period of competition, in each year that both firms are in the market, each firm suffers a loss of $20 million. If one firm drops out, the other firm becomes a monopolist and wins a pile of money, which you can think of as the NPV of all future economic profits in the market.

Before the competition begins, each firm estimates (e.g., through internal strategy studies and market research) the profit that it will get if it "wins" the market.

While each firm obviously knows its own valuation of the monopoly franchise, neither firm knows its competitor's valuation. That is, both firms are operating in the "fog of business." Each firm does know that its competitor's estimate will fall within a range between $100 million and $500 million, and that any estimate within this range is equally likely. For the statistically inclined, we would say the values are uniformly distributed between $100 and $500 million.

The way that a firm forms strategy in this game is to choose an amount of time that it fights in this market. If Firm 1's "fight time" is greater than Firm 2's "fight time", then the battle between the firms rages until Firm 2 drops out of the market, and Firm 1 becomes the monopolist.

What are the payoffs? Both firms lose the cost of fighting ($20 million x the number of periods.)So, the losing firm suffers this cost and gains nothing.The winning firm also suffers the cost from fighting, but the winner gets its valuation of the monopoly.

To illustrate, if Firm 1 chooses to fight for 11 years and Firm 2 chooses to fight for 15 years and if the value to Firm 2 of the monopoly franchise is $460 million, then: Firm 1 drops out first, so Firm 2 wins the war. Firm 1 loses $20 million per year for 11 years, a cumulative loss of $220 million. Firm 2 also incurs a cumulative loss of $220 million. But it also gains a monopoly franchise that is worth $460 million. Its net profit is thus $460 million - $220 million = $240 million.

The Exercise:

valuation V is 450 million. This valuation is known only to your team. You are playing against another team whose identity and valuation are unknown to you. All you know about that team is that it has a valuation drawn at random between $100 million and $500 million. You may discuss your strategy within your team. Please do not discuss either your strategy or the value you have received with other teams. Do not attempt to solve this game mathematically (trust me); just formulate good analytical reasoning to support your strategy.