Discussion on “Game Theory for Swingers: What states should the candidates visit before Election Day?” by Jordan Ellenberg (Slate Magazine, October 2004).
Summary
Jordan Ellenberg’s article, “Game Theory for Swingers,” uses the 2004 election to explain game theory. Ellenberg describes a scenario in which each candidate believes on the last day of the election that Pennsylvania, Florida, and Ohio are key to winning the election. Each candidate can improve their chances of winning one of the states by visiting it on the last day before the election, but this is dependent on what the other candidate does. In one scenario we assume that Kerry will win Pennsylvania and the election comes down to Ohio and Florida. We assume that Bush has a 30% chance of winning Ohio and a 70% of winning Florida. Both candidates can increase their chances of winning by 10% by visiting one state on the final day before the election (unless both candidates visit the same state, since the increases would cancel each other out). In this scenario, both candidates should visit Ohio and ignore the other candidate since it increases both of their odds regardless of what the other does. This is an example of a Nash Equilibrium.
Say Bush and Kerry both visit Ohio. Their odds of winning both Florida and Ohio remain the same at (.7)x(.3)=.21. If Bush visits Florida and Kerry visits Ohio, both candidates’ odds of winning both decrease to (.8)x(.2)=.16. If Kerry visits Florida and Bush visits Ohio, both candidates’ odds of winning both states increase to (.4)x(.6)=.24. As mentioned above, both candidates are better off visiting Ohio, no matter what the opponent does. However, it is not always this simple. If each candidate had a 50% chance of winning each Florida and Ohio and each candidate’s odds increased 10% by visiting a state, there would be no Nash Equilibrium because each candidate will be better off if he chooses the state the other candidate did not select. There would be a Nash Equilibrium if the odds of which candidate will go to which state are considered, however. If each candidate flips a coin to determine which state to go to, each of their odds of winning will be (.5)x(.5)x(.5) (the coin flip times a 50% chance of winning each state if both candidates go to the same state) + (.5)x(.6)x(.4) (the coin flip times a 60% chance of winning one state and a 40% chance of winning the other state if the candidates choose different states)=.245, the Nash Equilibrium.
The element of chance from the coin flip reduces predictability and is called a mixed strategy. In order for a mixed strategy to work, both candidates must act simultaneously. It should be noted that this simulation ignores 47 states in the election and the differences in electoral votes from each state.
Class-Room Relevance
Game theory applies to managerial economics because producers are constantly trying to predict how competitors are going to price their goods. Especially in a monopolistic competition, where there is a possibility of long-run profit, it is important for companies to accurately predict how the competition will price substitutes for the goods it is producing so that it can swiftly react to changes in the market.
Commentary
he article states that “rational behavior tends to be predictable, and in a game of strategy, predictability will leave you with a decided disadvantage.” This means that people expect you to act in a rational manner, so if you act rationally it is easier for your competitor to anticipate what you are going to do. For example, suppose Apple comes out with a new iPad. The market for iPads has boomed with the price set at $499 for an entry-level model. The competition has adjusted to this price point, and have even started selling tablets at a loss to try to undercut Apple’s price. Common sense would dictate that Apple would continue to sell the iPad at $499 even if costs go down since it is such a hot seller. But Apple could also choose to cut into its margins and drop the price to $399 just to take sales away from the competition. History and common sense tell us that Apple would not cut into its margins, especially with a product selling as well as the iPad, and that is why such a move would cause such a stir in the market.
The article states that an element of chance, such as flipping a coin, helps keep your moves random and therefore more difficult for your competition to predict. Apple would not leave a pricing decision such as this up to chance since it has so much market power, but Amazon has changed the market for tablets by offering a tablet for $199, a move many saw as unexpected. Even though they are selling the tablets at a loss, they make up for it by controlling the content sold on the devices. The Amazon Kindle Fire may not be outselling the iPad, but it has been more successful than any other iPad competitor because it offered a different and unexpected pricing strategy: a tablet nearly as good as the iPad for less than half of the price. In short, tablet makers should learn to expect the unexpected and make decisions that their competition will not be ready to combat.
Real World Application
Game theory exists in many different negotiations and interactions in the real world. For example, one can see the theory at work in salary negotiations. This situation will be very relevant to us since we will all be working and receiving offers soon. Suppose that a company offers you a starting salary that doesn’t meet your expectations. You can either A:Take the offer or B: Try to negotiate a better offer. If you believe your skills and what is expected of you deserves a higher salary, you can request a higher salary and the company can either refuse to go higher, or accept it.
Another example of the game theory at work is when cigarette advertising was legal in the United States. The cigarette market realized that any advertising they did was cancelled out when another firm responded with the same amount of advertising. This created a prisoner’s dilemma. The firm had to advertise or they would lose customers to the rival, however it was very expensive to. Interestingly enough, when the government decided to ban cigarette advertising on TV, the companies at first fought the decision. However, tobacco firm’s profits improved after the ban.
Posted by Chris, Andrew and Mariah (Section 2)
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