In this lab, you will consider two different applications. The first is a simulation of of the Prisoner's Dilemma. Using an existing Web page that conducts repeated Prisoner's Dilemma transactions, you will experiment with the basic starategies such as coop, defect, and titForTat, and consider their biological analogies. The second application in this lab is a rather silly Web page for translating English words and phrases into pirate talk. You will expand the page to include a variety of words and phrases, and will consider ways to simplify the page.
For each round of play, two players independently choose to cooperate or defect.
The goal for each player is to accumulate as many points as they can.
- if both players cooperate, then both receive 3 points
- if both players defect, then both receive 1 point
- if one cooperates and one defects, then the defector receives 5 points
In his paper, Hofstadter describes several basic strategies for playing the repeated Prisoner's Dilemma. The coop strategy always cooperates, the defect strategy always defects, while the randomness strategy cooperates or defects at random. The titForTat strategy cooperates in the first round, and then mimics whatever the opponent did in the previous round. It is interesting to note that the defect strategy will never "lose" to an opponent, meaning that it will never accumulate fewer points than any opponent. Similarly, coop and titForTat will never "win" against an opponent. However, the number of points accumulated in "winning" and "losing" may vary greatly.
EXERCISE 1: For each of the following pairings, predict the outcome if the two strategies were to compete in a repeated Prisoner's Dilemma. In particular, how many points would each strategy accumulate (assuming 50 rounds)?
coop vs. coop defect vs. defect titForTat vs. titForTat coop vs. defect coop vs. titForTat defect vs. titForTat
Which of the strategies would tend to do best against randomness? Which would do worst? Explain.
Load this page into the browser and use it to verify your predictions from the previous exercise.
What makes the Prisoner's Dilemma interesting is that locally optimal behavior is not necessarily globally optimal. Consider a round-robin tournament between defect and two copies of titForTat (assuming 50 rounds per contest). Even though defect outscores each opponent in head-to-head contests, it only earns 54 points in each, for a total of 108. When one copy of titForTat plays the other, however, they both earn 150 points. Adding this to the 49 points earned against defect, each copy of titForTat earns a total of 199 points. Thus, defect wins all of its battles, but loses the war!
A Prisoner's Dilemma tournament can be described nicely in ecological terms. The defect and coop strategies, because of their aggressive and passive natures, can be characterized as hawks and doves. The titForTat strategy, which is passive by nature but will become aggressive when provoked, may be characterized as a sparrow. According to this analogy, the fact that defect outscores titForTat in a head-to-head contest shows that a lone hawk dominates a lone sparrow. However, the tournament shows that two sparrows support each other and can fight off a lone hawk. Using this type of analogy, the Prisoner's Dilemma has been used by researchers as a way of explaining how cooperative behavior can evolve without consciousness. In fact, studies done on the hunting patterns of lions and the defensive behaviors of fish have supported the Prisoner's Dilemma model of cooperation.
The results of a round-robin tournament can be displayed neatly in a table. The above tournament between a hawk (defect) and two sparrows (titForTat) would appear as follows. The entries across a row contain the points earned by a strategy playing against each of the other strategies. For example, the hawk earns 54 points when it goes against sparrow1, so there is a 54 in the table at the row labeled hawk and column labeled sparrow1. Conversely, sparrow1 only earns 49 points against the hawk, so there is a 49 in the table at the row labeled sparrow1 and column labeled hawk.
EXERCISE 3: In the table below, show the results of a round-robin tournament between a hawk, a dove, and two sparrows. How does the addition of the dove affect the dynamics between the hawk and the sparrows compared to the example above?
hawk dove sparrow1 sparrow2 TOTAL hawk dove sparrow1 sparrow2
EXERCISE 4: In the table below, show the results of a round-robin tournament between a hawk, a dove, and three sparrows. How does the additional sparrow affect the results when compared to the previous exercise?
hawk dove sparrow1 sparrow2 sparrow3 TOTAL hawk dove sparrow1 sparrow2 sparrow3
EXERCISE 5: Suppose we characterized the titFor2Tats strategy as a robin. Would robins be more or less effective than sparrows (titForTat) in protecting a lone dove (coop) from a lone hawk (defect)? In other words, would a round-robin tournament involving a dove, hawk, and some number of robins result in the dove and each robin earning more points than the hawk? Does it take more or fewer robins than it took sparrows to acheive this? Why would this be the case?
The following Web page is a framework for an alternative English-to-Pirate translator. As is, it contains two buttons, labeled "hello" and "friend", and a text area. When the user clicks on a button, the corresponding Pirate word or phrase is added to the text area. For example, if the user were to click on the "hello" button, the word "ahoy" will appear in the text area. If he then clicks on the "friend" button, then "me matey" is added to the text area, resulting in the phrase "ahoy me matey."
Land Lubber's Pirate Translator
Simply click on the buttons to translate
EXERCISE 6: Cut-and-paste this HTML text into a Web page named pirate1.html and verify that it behaves as described.
As the page is currently written, multiple translations are awkward. If you finish translating one phrase and want to begin a new one, simply refreshing the page does not suffice to clear the text area. Instead, you must click the mouse in the browser's Address box and hit enter to reload the page and reset the text area. To make repeated translations easier, add a button directly below the text area labeled "Clear". When the user clicks on this button, a function should be called to clear the text area (i.e., set its contents to be the empty string).
EXERCISE 7: Extend pirate1.html by adding new words and phrases. For each new word or phrase, you will need to add a button with the appropriate label and translated pirate phrase. At a minimum, you must add the new words and phrases below. However, feel free to add a larger vocabulary (see www.talklikeapirate.com for ideas).
English Pirate talk hey you avast ye stranger ye scurvy dog where is whar be is that be that how far is it to thar be how many leagues til the restroom th' stinkin' head a restaurant a briney galley a pub th' Skull & Scuppers
Hand in printouts of pirate1.html and pirate2.html, attached to these sheets.