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Make Sure Players are Playing the Same Game

The Right Game

For many basic game theory concepts, a key assumption is that players, usually in pairs, play the same games, meaning that they look at exactly the same payoff tables. However, in reality, without incurring the costs of communication or information gathering, you can never know what payoff table your opponent is looking at. As a result, even when you make the perfectly rational decision, you may be forced into an undesirable outcome if your opponent is seeing the situation differently.

Many historical accounts have shown that, during the Battle of Waterloo, Prussian commander Blucher made an irrational decision based on very little military intelligence. His decision ultimately became a fatal surprise to Napoleon. During the battle, the Prussians had just suffered a major defeat from Napoleon’s left wing. They lost all communication with their allies and therefore the source of intel, faced a lot of uncertainties, and were still under the threat of Napoleon’s remaining troops. Napoleon thought the Prussians faced a choice of survival or annihilation. If they retreated, they would survive. If they attacked, they faced a high chance of being annihilated. Therefore, Napoleon concluded that the Prussians would retreat, withdrew his troops around the Prussian army, and sent them toward the British army. However, Blucher saw the situation very differently. He was much more concerned with his personal hatred toward Napoleon, whose survival might end all European monarchies, than with the lives of his troops. He saw himself facing a choice of defeating Napoleon or not. If he retreated, he forfeited the chance to defeat Napoleon. If he attacked, he still stood a chance. In the end, the Prussians advanced and, combined with the British force, outnumbered Napoleon 2 to 1. Clearly, Napoleon and Blucher were looking at different payoff tables. As the result of the clash of their decisions, the superior military leader lost to the inferior one.

How can we ensure our opponents are looking at the right payoff tables? Rupert Murdoch offered a solution. In 1994, Murdoch ran The Post in New York City. The Daily News was his main competitor. Both were priced at $0.50 apiece. However, in September, The Daily News reduced its price to $0.40 apiece, attracting many of Murdoch’s readers. Murdoch could have reduced Post’s price to $0.40 to stay competitive. Instead, he decided to reduce Post’s price for a limited time to $0.25 only in the Staten Island, stealing a significant percentage of Daily’s readers in that region. Now realizing the potential catastrophe of a price war, Daily raised its price back to $0.50, ending the potential price war.

Post and Daily were playing a very simple game, the Nash Equilibria of which were that both newspapers had the same price. If both had high prices, both enjoyed high margins, which was a win-win. If both had low prices, both suffered low margins, which was a lose-lose. However, there could never exist a situation where one had a high price while the other low, because whichever with the higher price would reduce it. When Daily reduced its price, it broke the Nash Equilibrium. If Post matched Daily’s price, Murdoch would effectively walk into a lose-lose situation. Instead, he reminded Daily the rules of the game by realizing the worst possible outcome, which was that both newspapers had extremely low prices. Clearly, Daily didn’t want that scenario, so they raised the price back and re-established the win-win equilibrium. Murdoch had shown that sometimes we need to play out some possible scenarios to reminder our opponents the right payoffs.

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