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Top1. Introduction
Are economic agents rational? Since Herbert A. Simon was awarded the Nobel Prize for Economic Sciences in 1978, the term and idea of “bounded rationality” has become widespread in economics, especially in the research field of behavioral economics. Whereas standard economic theory assumes that economic agents are quite rational, recent behavioral economic theory shows empirically and experimentally that economic agents are not necessarily rational, arguing that they are often merely boundedly rational.1
To investigate the rationality of economic agents, guessing games, first discussed by Moulin (1986) as a useful tool in theory, and studied experimentally by Nagel (1995), are often used in the behavioral economics literature (For various other studies using guessing games, see, e.g., Duffy et al. (1997), Ho et al. (1998), Bosch-Domenech et al. (2002), and Grosskopf and Nagel (2008). Nagel (1999) and Camerer (2003) present a useful survey of the literature that analyzes the guessing games.). In a guessing game, which is a type of “coordination game”—a special case is the so-called “beauty contest game” described by John Maynard Keynes (1936)—the test subjects are first asked to choose a certain number from a given number interval, anticipating what numbers other test subjects will choose. Next, the experimenter calculates the average value (with no constant value) and obtains a “target value” that is equal to a fraction p (0 < p < 1) of the average value.2 Finally, the test subject(s) who predicted a number closest to the target value wins (win) a fixed prize. If the test subjects playing this guessing game are perfectly rational, they believe that other test subjects are also perfectly rational, and these beliefs are common knowledge among all test subjects, there exists only one Nash equilibrium prediction, i.e., the minimum number of the given interval (if 0 < p < 1), which is uniquely selected through the iterated deletion of dominated strategies. Thus, in carrying out experiments of this type of guessing game, it is expected that we can investigate the rationality of economic agents, which is usually assumed in the standard economic (game) theory.
However, many experimental studies reveal that the test subjects in guessing games seldom chose such a uniquely expected Nash equilibrium prediction number; therefore, the rationality of economic agents as a whole may arguably be questionable. These results in the literature may occur because the test subjects are not perfectly rational in the first place and/or they do not have common beliefs that other subjects are perfectly rational. “Rationality” is hard to characterize in general, as the works above and the literature show, but it is expected that we can investigate the rationality of (economic) agents using various appropriate ways and approaches.
In this paper, the author uses a typical guessing game to examine not only the rationality of the test subjects but also the degree of their strategic uncertainty in playing the guessing game. In our experiment, the author asks the test subjects not only to choose a predicted target number but also to provide a value for the predicted standard deviation of the answered numbers in the classroom. A number of experimental studies asked their test subjects to choose a predicted target number; however, to the best of our knowledge, no study also asked their test subjects to predict the value of the standard deviation, which can be considered to be a proxy measure of the (subjective) “strategic uncertainty” facing the test subjects in playing the guessing game.3,4 As larger predicted values of the standard deviation can be assumed to imply that the test subjects feel greater strategic uncertainty in playing the guessing game, the author considers the standard deviation of the answers to provide a proximate measure of the subjective (rather than objective) strategic uncertainty they feel in playing the guessing game.