The ultimatum game
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The ultimatum game
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[post_date] => 2025-01-02 10:14:39
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[post_content] => Practice Passage (Question 1-4)
*This passage is the property of Khan Academy and has been reformatted into an AAMC-style interface in their entirety by MedLife Mastery. MedLife Mastery does not endorse and is not an affiliate of Khan Academy.
Imagine that someone offers you and some other anonymous person $100 to share. The rules are strict and known to both players. The two of you are in separate rooms and cannot exchange information. A coin toss decides which of you will propose how to share the money. If you are the proposer you can make a single offer of how to split the sum, and the other person—the responder—can say yes or no. If the responder’s answer is yes, the deal goes ahead. If the answer is no, neither of you gets anything. In both cases, the game is over and will not be repeated. What will you do?
Instinctively, many people feel they should offer 50 percent, because such a division is “fair” and therefore likely to be accepted. More daring people, however, think they might get away with offering somewhat less than half of the sum.
You may not be surprised to learn that two-thirds of the offers are between 40 and 50 percent. Only four in 100 people offer less than 20 percent. Proposing such a small amount is risky, because it might be rejected. More than half of all responders reject offers that are less than 20 percent. But why should anyone reject an offer as “too small”? The responder has just two choices: take what is offered or receive nothing. The only rational option for a selfish individual is to accept any offer. A selfish proposer who is sure that the responder is also selfish will therefore make the smallest possible offer and keep the rest. This game-theory analysis, which assumes that people are selfish and rational, tells you that the proposer should offer the smallest possible share and the responder should accept it. But this is not how most people play the game.
The scenario just described, called the Ultimatum Game, was devised some twenty years ago. Experimenters subsequently studied the Ultimatum Game intensively in many places using diverse sums. The results proved remarkably robust. Behavior in the game did not appreciably depend on the players’ sex, age, schooling, or numeracy. Moreover, the amount of money involved had surprisingly little effect on results. Yet the range of players remained limited, because the studies primarily involved people in more developed countries and often university students.
Recently, a cross-cultural study in fifteen small-scale societies showed that there were sizable differences in the way some people play the Ultimatum Game. Within the Machiguenga tribe (from the Amazon) the mean offer was considerably lower than in typical Western-type civilizations—26 percent instead of 45 percent. Conversely, many members of the Au tribe (from Papua New Guinea) offered more than 50 percent. Cultural traditions in gift giving, and the strong obligations that result from accepting a gift, play a major role among some tribes, such as the Au. Yet despite these cultural variations, the outcome was always far from what rational analysis would dictate for selfish players. Most people all over the world place a high value on fair outcomes.
For a long time, theoretical economists postulated a being called Homo economicus—a rational individual relentlessly bent on maximizing a purely selfish reward. But the lesson from the Ultimatum Game and similar experiments is that real people are a crossbreed of H. economicus and H. emoticus, a complicated hybrid species that can be ruled as much by emotion as by cold logic and selfishness. An interesting challenge is to understand how Darwinian evolution would produce creatures instilled with emotions and behaviors that do not immediately seem geared toward reaping the greatest benefit for individuals or their genes.
Adapted from K. Sigmund, E. Fehr, and M.A. Nowak, “The economics of fair play.” ©2002 by Scientific American, Inc.
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[questions] => Array
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[question] => Which of the following statements is NOT as strongly supported by the passage?
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[answer] => 3
[description] => Reason for the Correct Answer:
This is a “Reasoning Within the Text” question, which means that it wants you to explore the key idea, claim, or theme that is being expressed in a passage. You will have to evaluate the soundness of an argument, the reasonableness of its conclusions, and/or the appropriateness of its generalizations. It is crucial to carefully examine the strengths and weaknesses of the key ideas based on the information given.
The second sentence explicitly states that “The rules are strict …” (option A). According to the fourth paragraph, the game has been studied “…intensively in many places using diverse sums. The results proved remarkably robust. Behavior did not appreciably depend on the players’ sex, age, schooling, or numeracy. Moreover, the amount of money had surprisingly little effect…” This evidence supports the claim that the results of the Ultimatum Game tend to be consistent (option B). The first sentence in paragraph 5 explicitly states that a recent study of the Ultimatum Game showed that there were “sizable differences in the way some people play the Ultimatum Game” (option D). There is a statement about people who “feel they should offer 50 percent because such a division is ‘fair’”; however, the passage provides no analysis of the decision-making process involved in responders. The passage is focusing on the decision-making process of the proposers.
Thus, option C is correct.
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[answers] => Array
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[each_answer] => A. The rules of the Ultimatum Game are strict.
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[each_answer] => B. The results of the Ultimatum Game tend to be consistent.
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[each_answer] => C. Responders reject offers that are less than 20 percent because they consider such offers unfair.
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[each_answer] => D. Studies of the Ultimatum Game show sizable differences in the way some people play.
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[1] => Array
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[quiz_unique_key] => 3873426850
[question] => In some trials of the Ultimatum Game, the proposed split is determined by a computer. When responders are aware of this, they are willing to accept considerably lower offers. Based on the passage, compared to the standard game played without a computer, these responses are more:
[value] => Array
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[answer] => 1
[description] => Reason for the Correct Answer:
This is a “Reasoning Beyond the Text” question, which means that it wants you to either apply or extrapolate the ideas in the passage to new situations or to assess how new information would impact the ideas presented in the passage. It is important to understand the assumptions underlying the article, and how new information may or may not shift the central thesis.
Two of the response options (options A and B) are concerned with what rational analysis would dictate for responders. According to the third paragraph: “The responder has just two choices: take what is offered or receive nothing. The only rational option for a selfish individual is to accept any offer… This game-theory analysis, which assumes that people are selfish and rational, tells you that the proposer should offer the smallest possible share and the responder should accept it.” When a computer determines the proposed split, we learn that responders are willing to accept considerably lower offers. Therefore, the responders are acting more in keeping with what rational analysis would dictate because they are more likely accept any offer (option A). In contrast, the responders are out of keeping with what one would expect from Homo emoticus, which is a term used to reflect emotional thinking in paragraph 6 to explain why people might not act in a purely selfish manner (option C). Since the two studies done in small-scale societies did not show consistent results, and the 15 studies showed sizeable differences, there is not a clear expectation set up for non-Western cultures (assuming this term is being used as a synonym for small-scale societies). Since there is no expectation, a new finding cannot be either consistent or inconsistent with it (option D).
Thus, option A is correct.
)
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[each_answer] => A. in keeping with what rational analysis would dictate.
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[each_answer] => B. out of keeping with what rational analysis would dictate.
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[each_answer] => C. in keeping with what one would expect from Homo emoticus.
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[each_answer] => D. in keeping with what researchers would expect of the responses from people of non-Western cultures.
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[2] => Array
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[quiz_unique_key] => 83407773
[question] => Assume a “fair” offer is defined as 50 percent, and responders behave rationally. Based on the discussion in paragraph 5, it can be reasonably assumed that the author believes that the Machiguenga tribe had a:
[value] => Array
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[answer] => 3
[description] => Reason for the Correct Answer:
This is a “Reasoning Beyond the Text” question, which means that it wants you to either apply or extrapolate the ideas in the passage to new situations or to assess how new information would impact the ideas presented in the passage. It is important to understand the assumptions underlying the article, and how new information may or may not shift the central thesis.
All responses make an assertion about the percentage of fair offers compared to typical Western societies. The passage states that among the Machiguenga tribe, the “mean offer was considerably lower than in typical Western-type civilizations—26 percent instead of 45 percent” (Paragraph 5). Since the mean (or average) Machiguenga tribe offer is 26 percent, it seems very unlikely that there would be a higher percentage of individual offers above 50 percent as compared to typical Western societies with a mean offer of 45 percent. This excludes options B and D. The second part of all responses makes an assertion about the percentage of fair offers that would be made by rational selfish players. This requires determining what that expected percentage might be from the text. Based on game-theory analysis (which assumes that people are selfish and rational), the rational selfish player should propose the smallest possible offer and the responder should accept this offer. This is based on the fact the responder has only two choices: take what is offered or receive nothing. This means that the rational selfish player should propose an offer of 1% (or 0.01% which would be one cent), and never offer a “fair” offer of 50%. The Machiguenga tribe had a mean offer of 26%, which is higher than the 1% we might expect for rational selfish players. This excludes options A and D.
Thus, option C is correct.
)
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[each_answer] => A. lower percentage of fair offers than both typical Western societies and rational selfish players.
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[each_answer] => B. higher percentage of fair offers than both typical Western societies, and rational selfish players.
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[each_answer] => C. lower percentage of fair offers than typical Western societies, and a higher percentage of fair offers than rational selfish players.
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[each_answer] => D. higher percentage of fair offers than typical Western societies, and a lower percentage of fair offers than rational selfish players.
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[quiz_unique_key] => 4240073053
[question] => In the discussion of the Ultimatum Game, what is the significance of the statement that “the range of players remained limited” (paragraph 4)?
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[answer] => 1
[description] => Reason for the Correct Answer:
This is a “Foundations of Comprehension” question, which means that it wants you to interpret the meaning of a particular statement made by the author.
The full statement reads “Yet the range of players remained limited, because the studies primarily involved people in more developed countries and often university students” (paragraph 4). The cause for the limited range of players is explained by the fact that they came from specific countries and educational settings. The following paragraph describes a cross-cultural study that showed “sizable differences in the way some people play” (paragraph 5), demonstrating that the previous body of literature could not be generalized to all people. There is no evidence the experimenters wanted to limit the range of players to better control the game (option B) or range of variables (option D) or that there were any limitations on the game itself that led to mistaken conclusions (option C).
Thus, option A is correct.
)
[answers] => Array
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[each_answer] => A. The limited sample did not allow the experimenters to generalize about all people.
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[each_answer] => B. Limiting the range of players allowed the experimenters to better control the outcome of the game.
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[each_answer] => C. Limitations on the game led to mistaken conclusions by experimenters at that time.
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[each_answer] => D. The limited sample allowed the experimenters to better control the range of variables in the experiment.
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[559752|1] => C
[559752|2] => A
[559752|3] => C
[559752|4] => A
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