Archive for the 'Game Theory' Category

Apr 20 2012

UPDATE: Golden Balls, Game Theory, the Prisoner’s Dilemma, and the cold rationality of human behavior!

In my original “Golden Balls” blog post (see below), written almost three years ago after I saw a clip of the finale in an episode of the British game show, Golden Balls, I analyzed the actions of Sarah and Steve, who  had to decide whether they would split or steal a jackpot of 100,000 British pounds. The contestants had one minute to try to convince one another that they would split the money; but when it came down to it Sarah stole and Steve split, meaning Sarah got to keep the whole jackpot and Steve went home with nothing.

In that original post, I proposed that Steve’s best chances for going home with any money would have been “for him to use the one minute of discussion time to convince Sarah that he would choose SPLIT, yet be willing to go home with something LESS THAN $50,000 and accept that Sarah was going to choose STEAL. He could have threatened to chose steal if she did not agree to share her winnings with him to some extent.”

In a recent episode of the same game show, a contestant followed a similar strategy to that I suggested Steve should have taken. Watch the clip below, from a February 2012 episode of Golden Balls.

In this episode, Nick immediately takes control of the negotiations by insisting that he is going to steal, which is a very unorthodox approach to this game, in which the traditional strategy is to try and convince your opponent that you are going to split. By establishing a credible threat to steal, Nick puts all the pressure on Ibraham to decide only one of two things:

  1. Does Ibraham trust that Nick will split the money with him after he has stolen the full jackpot, and
  2. Would Ibraham rather both of them go home without any money at all than Nick win the jackpot and possibly not split it with him later on?
Nick’s strategy is brilliant. By the end of the negotiation, Nick has convinced Ibraham 100% that he is going to steal the money. Ibraham may only have had a confidence level of 50% that Nick was honest about splitting the money with him after the show, but with a 50% confidence level, Ibrahim’s possible payoffs are:
  • Choose steal and go home with nothing.
  • Choose split and have a 50/50 chance of going home with half the jackpot (based on his level of confidence in Nick’s promise to split the money after the show).
In other words, with a jackpot of 14,000 pounds, the payoffs for Ibrahim became:
  • If he splits: 0 pounds or 0.5(14,000) = 7,000 pounds
  • If he steals: 0 pounds or 0 pounds (assuming his confidence level in Nick’s intention to steal is 100%).
Clearly Ibraham now has a dominant strategy: to split. In the typical version of this game, a player’s dominant strategy is always to steal (as explained below), since the possible payoffs are:
  • If you split: 0 pounds or half the jackpot
  • If you steal: 0 pounds or the whole jackpot.
But because Nick has convinced his opponent that he will steal, and then split the winnings, Ibraham’s dominant strategy shifted to split, since the possible payoffs have changed. Ultimately, Ibraham does what is most rational given his confidence in Nick’s threat to steal, and that is to split. Ibraham then chooses split (as he should), but then to everyone’s surprise, Nick chooses split, not steal as he had threatened to do throughout the negotiation. This a surprising twist, since from Nick’s perspective stealing is clearly now a dominant strategy! Nick had convinved Ibraham to split, which means Nick faced a greater payoff by stealing. But by splitting, Nick shows that he had intended to split all along, but first needed to convince Ibraham otherwise to establish splitting as Ibraham’s dominant strategy.
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What a thrilling game! I won’t even bother getting into how this relates to economics today, I’m still shaking with excitement over the outcome!
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Original Golden Balls post:
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Teaching the Prisoners’ Dilemma Will Never Be the Same Again « Cheap Talk

Rarely does such a perfect illustration of the Prisoner’s Dilemma come along for Econ teachers to use in their classroom:

The payoffs are clear:

Each player has a weakly dominant strategy, which is to choose to steal. By choosing to steal, the player has a chance at maximizing his own payoff, but will do no worse than he would if his opponent also chooses to steal and at least will have the satisfaction of thwarting his opponent’s attempt to steal the money.

There are three Nash equilibria in the game, which are outcomes at which a player can not do better on his or her own by changing his or her strategy. The outcome Steve was hoping for by chosing “split” (50/50) was not a Nash equilibrium because Sarah knows she can do better if she chooses steal when Steve chooses split. Steve doomed himself by choosing split because he should know that Sarah’s dominant strategy is to choose steal. However, Sarah would also have doomed herself by choosing split because she should assume that Steve would also chose steal since steal is a dominant strategy for him too.

John Nash, who pioneered the field of Game Theory, assumed that humans were coldly rational, self-interested, deceptive creatures that would not hesitate to stab one another in the back to get what was best for themselves. His theory of human behavior is only partially proven correct in this game, in which Steve is shown to be the sucker and Sarah the coldly rational self-interested player. The best chance for Steve to go home with any money would have been for him to use the one minute of discussion time to convince Sarah that he would choose SPLIT, yet be willing to go home with something LESS THAN $50,000 and accept that Sarah was going to choose STEAL. He could have threatened to chose steal if she did not agree to share her winnings with him to some extent. Then again, any promise Sarah makes she could later break, thus further empowering the players to choose steal.

Discussion questions:

  1. What in the world is going on here? Why did Sarah choose steal rather than collaborate with Steve and share the $100,000?
  2. Was Steve totally wrong to choose split? What would you have done in his situation?
  3. How do the choices faced by Steve and Sarah relate to the choices faced by firms in oligopolitic markets? Now that you’ve seen this video, can you explain why collusive agreements between oligopolists often fall apart? Why do cartels such as OPEC often fail to achieve the high price targets agreed upon in meetings of their leaders?

110 responses so far

Mar 23 2012

Understanding Oligopoly Behavior – a Game Theory overview

What makes oligopolistic markets, which are characterized by a few large firms, so different from the other market structures we study in Microeconomics? Unlike in more competitive markets in which firms are of much smaller size and one firm’s behavior has little or no effect on its competitors, an oligopolist that decides to lower its prices, change its output, expand into a new market, offer new services, or adverstise, will have powerful and consequential effects on the profitability of its competitors. For this reason, firms in oligopolistic markets are always considering the behavior of their competitors when making their own economic decisions.

To understand the behavior of non-collusive oligopolists (non-collusive meaning a few firms that do NOT cooperate on output and price), economists have employed a mathematical tool called Game Theory. The assumption is that large firms in competition will behave similarly to individual players in a game such as poker. Firms, which are the “players” will make “moves” (referring to economic decisions such as whether or not to advertise, whether to offer discounts or certain services, make particular changes to their products, charge a high or low price, or any other of a number of economic actions) based on the predicted behavior of their competitors.

If a large firm competing with other large firms understands the various “payoffs” (referring to the profits or losses that will result from a particular economic decision made by itself and its competitors) then it will be better able to make a rational, profit-maximizing (or loss minimizing) decision based on the likely actions of its competitors. The outcome of such a situation, or game, can be predicted using payoff matrixes. Below is an illustration of a game between two coffee shops competing in a small town.

In the game above, both SF Coffee and Starbuck have what is called a dominant strategy. Regardless of what its competitor does, both companies would maximize their outcome by advertising. If SF coffee were to not advertise, Starbucks will earn more profits ($20 vs $10) by advertising. If SF coffee were to advertise, Starbucks will earn more profits ($12 vs $10) by advertising. The payoffs are the same given both options for SF Coffee. Since both firms will do best by advertising given the behavior of its competitor, both firms will advertise. Clearly, the total profits earned are less when both firms advertise than if they both did NOT advertise, but such an outcome is unstable because the incentive for both firms would be to advertise. We say that advertise/advertise is a “Nash Equilibrium since neither firm has an incentive to vary its strategy at this point, since less profits will be earned by the firm that stops advertising.

As illustrated above, the tools of Game Theory, including the “payoff matrix”, can prove helpful to firms deciding how to respond to particular actions by their competitors in oligopolistic markets. Of course, in the real world there are often more than two firms in competition in a particular market, and the decisions that they must make include more than simply to advertise or not. Much more complicated, multi-player games with several possible “moves” have also been developed and used to help make tough economic decisions a little easier in the world of competition.

Game theory as a mathematical tool can be applied in realms beyond oligopoly behavior in Economics.  In each of the videos below, game theory can be applied to predict the behavior of different “players”. None of the videos portray a Microeconomic scenario like the one above, but in each case a payoff matrix can be created and behavior can be predicted based on an analysis of the incentives given the player’s possible behaviors.

Assignment: Watch each of the five videos below. For each one, create a payoff matrix showing the possible “plays” and the possible “payoffs” of the game portrayed in the video. Predict the outcome of each game based on your understanding of incentives and the assumption that humans act rationally and in their own self-interest.

“Batman – the Dark Night” – the Joker’s ferry game:

“Princess Bride” – where’s the poison?:

“Golden Balls” – split or steal:

“The Trap” – the delicate balance of terror

“Murder by Numbers” – the interrogation

Discussion Questions:

  1. Why is oligopoly behavior more like a game of poker than the behavior of firms in more competitive markets?
  2. What does it mean that firms in oligopolistic markets are “inter-dependent” of one another?
  3. Among the videos above, which games ended in the way that your payoff matrix and understanding of human behavior and rational decision making would have predicted?
  4. How often did the equilibrium outcomes according to your analysis of the payoff matrices correspond with the socially optimal outcome (i.e. the one where total payoffs for all players are maximized or the total losses minimized)?

12 responses so far

Sep 14 2010

Bali’s Oligopolistic Scuba operators

A few summers ago, my wife and I spent three weeks travelling around the island of Bali in Indonesia. For six of those days we rented a jeep and circumnavigated the island. Our first stop was for two days of scuba diving in the northeast region of Ahmed. As we drove along the seven beaches near Ahmed, we observed there were around ten dive operators offering packages for the local dive spots (including one of Asia’s most famous dives, the WWII-era USS Liberty wreck). Based on our Lonely Planet recommendation, we settled on Eco-Dive, where we paid $60 a day for two dives and all our gear rental. We felt good about this rate and agreed that $60 was a fair and competitive price for a day of diving.Jukung- traditional wind powered trimaran used for fishing in Ahmed

Our next stop, Pemuteran, a remote and relatively undeveloped area on the northwest coast just across the straits from Java, is also known for its great diving. On our first morning in Pemuteran, my wife and I strolled along the beach and found that there were only three dive operators to choose from! And guess what, they all charged between $95-$105 for a day of diving. That’s around 60% more than the operators in Ahmed charged! In the end, we decided to do only one day of diving in Pemuteran, and elected to spend our second day there reading by the pool.

Discussion Questions:

  1. What was the difference between the scuba diving markets in Ahmed and Pemuteran? Which market was more competitive? Which of the four market structures did the two markets most resemble: perfectly competitive, monopolistically competitive, oligopolistic or monopolistic?
  2. How were the dive operators in Pemuteran able to charge 60% more than the operators in Ahmed?
  3. What do you think is keeping one of the three dive operators in Pemuteran from lowering their price to, say, $60 for a day of diving? How would the other two operators respond? Would this be good or bad for the dive operators of Pemuteran? Would it be good or bad for scuba divers?
  4. Assuming that the cost of opening a dive operation was relatively low, and there were no government or other barriers to doing so in Pemuteran, what do you suspect will happen in the Scuba diving market as the tourism industry continues to develop in the remote town of Pemuteran? Explain.
  5. Which village’s dive operators do you think were more “efficient” in their use of resources? Explain.

50 responses so far

Feb 27 2009

The “delicate balance of terror”: How game theory can be used to predict firm behavior (oh, and save the human race from utter annihilation)

This week in AP Microeconomics students get to play online games, watch movies, and compete with their classmates in strategic competitions in which there are proud winners and sad losers. That’s right, we’re studying oligopoly!

What makes oligopolistic markets, which characterized by a few large firms, so different from the other market structures we study in Microeconomics? The answer is that unlike in more competitive markets in which firms are of much smaller size and one firm’s behavior has little or no effect on its competitors, an oligopolist that decides to lower its prices, change its output, expand into a new market, offer new services, or adverstise, will have powerful and consequential effects on the profitability of its competitors. For this reason, firms in oligopolistic markets are always considering the behavior of their competitors when making their own economic decisions.

To understand the behavior of non-collusive oligopolists, economists have employed a mathematical tool called Game Theory. The assumption is that large firms in competition will behave similarly to individual players in a game such as poker. Firms, which are the “players” will make “moves” (referring to economic decisions such as whether or not to advertise, whether to offer discounts or certain services, make particular changes to their products, charge a high or low price, or any other of a number of economic actions) based on the predicted behavior of their competitors.

If a large firm competing with other large firms understands the various “payoffs” (referring to the profits or losses that will result from a particular economic decision made by itself and its competitors) then it will be better able to make a rational, profit-maximizing (or loss minimizing) decision based on the likely actions of its competitors. The outcome of such a situation, or game, can be predicted using payoff matrixes. Below is an illustration of a game between two coffee shops competing in a small town.

As illustrated above, the tools of Game Theory, including the “payoff matrix”, can prove helpful in helping firms decide how to respond to particular actions by their competitors in oligopolistic markets. Of course, in the real world there are often more than two firms in competition in a particular market, and the decisions that they must make include more than simply to advertise or not. Much more complicated, multi-player games with several possible “moves” have also been developed and used to help make tough economic decisions a little easier in the world of competition.

While Game Theory can be useful in predicting firm behavior in oligopolistic markets, believe it or not that is not its most useful application developed. In fact, would you believe me if I told you that Game Theory may be precisely what saved the world from nuclear holocaust during the 20th Century? It’s true. The US government employed Game Theory to avert annihilation by nuclear attack from the Soviet Union during much of the 20th Century. This video tells the story!

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11 responses so far

May 28 2007

Irrational behavior leads to larger rewards

Scientific American: The Traveler’s Dilemma

A student sent me the above article. It’s late, and tomorrow I only have one class, so I think I’ll have to tackle this one in the morning! I can already tell this is going to be a good one to use in AP when we study Game Theory, dominant strategy and Nash Equilibrium. Can’t wait to read it!

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