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立 政 治 大 學
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Chapter 1 Introduction
1.1 Background
This study attempts to investigate the relation between cognitive hierarchy, recently formulated in behavioral game theory, and cognitive capacity, long studied in cognitive psychology. These two concepts, while being quite closely related, belong to two different bodies of knowledge, one in economics and one in psychology. Cognitive hierarchy is a concept developed from the recent behavioral experimental games which involve iterative reasoning or depth of reasoning. Among many such games, one of the most famous is the Keynes’
beauty contest game (Nagel, 1995, 1998), which is also known as the out-guessing game. Cognitive hierarchy is a core concept, shared by a family of models, which aims to explain subjects’ behavior observed in this kind of experiment. Cognitive capacity, as is well known, is a concept related to the psychological study of human intelligence.
As we can see from Figure 1.1, attempts to connect the two intuitively close concepts have not been frequently made by either economists or psy-chologists. In this study, we shall formally examine the relation between the two; in particular, we would like to see whether cognitive capacity as a psychological trait of a subject can help predict his/her revealed cognitive hi-erarchy in game experiments which explicitly involve depth of reasoning, such as the beauty contest game (BCG). Therefore, this study naturally makes economics meet psychology. While the possible cooperation between the two disciplines has been long ignored, it has picked up significant momentum in recent years (Earl,1990;Frey and Stutzer,2007;DellaVigna,2009), and this research is just one of many on-going interactions between the two.
Let us start from the side of economics, the cognitive hierarchy. There are two possible ways to think of the observed cognitive hierarchy from
ex-‧
perimental games (to be briefly reviewed in Section 2.1). One way is to think that it is only an ex post representation of our experimental results; as to who correspond to the upper levels of the hierarchy and who correspond to the lower levels, that may just be stochastically determined by subjects’
choices based on their own experiences and beliefs.1 In this case, the cogni-tive hierarchy is emerged from the interaction of agents, or, simply stated, it is endogenously formed. If this is so, the cognitive hierarchy of a group of subjects observed in one game may have limited applicability to the cognitive hierarchy of the same group of subjects in the other game. Subjects whose behavior was regarded as having a high cognitive hierarchy may switch to a lower one in different experiments, and vice versa.
Alternatively, one may think that cognitive hierarchy is exogenously de-termined by some fundamental attributes of the participating subjects. In other words, the cognitive hierarchy with which the subjects are associated has a functional relation with these fundamental attributes. If so, then a further inquiry into what these fundamental attributes are and whether cog-nitive capacity is one of the them define the research question of this research.
In sum, the scope of this research is, given the success of the cognitive hi-erarchy model in experimental games, to decide whether we should include personal traits as part of the given conditions (the exogenous variables) of the game so that it can help us either better predict or better explain the strategic sophistication observed in the game.
Figure 1.1, using a blue triangle, shows the main backgrounds of the research question and the related literature. The three vertices of the triangle are the Keynes’ beauty contest game (top left), cognitive hierarchy (top right) and cognitive capacity (bottom). The three arrows which connect the three vertices correspond to three strands of the literature. The arrow number one shows the research that applies the cognitive hierarchy models to explain the behavior observed in the beauty contest game. This belongs to the typical game-theoretic literature. The arrow number two shows the research trying to examine the significance of cognitive capacity in subjects’ performance in beauty contest games, and the arrow number three shows the research trying to examine the effects of cognitive capacity upon cognitive hierarchy.
These latter two belong to the literature on psychological studies of game
1For example,McCain (2010) used the Brock-Hommes adaptive belief system (Brock and Hommes, 1998) to build an agent-based model to simulate the evolution of the dis-tribution over different depths of reasoning. In this model, agents can in principle choose whatever depth of reasoning they prefer; however, based on the experienced rewards and costs they may choose different depths of reasoning at different points in time. The point is that all depths are available for all agents, regardless of their personal attributes, not to mention cognitive capacity.
‧ 國
立 政 治 大 學
‧
N a tio na
l C h engchi U ni ve rs it y
1.1. BACKGROUND
Figure 1.1: An Overview of the Research Backgrounds
Due to the space limitation, three arrows are only numbered without related literature.
They are given as follows. Direction 4 includes Nagel (1995); Stahl (1996); Duffy and Nagel (1997); Stahl (1998); Ho, Camerer, and Weigelt (1998); Camerer and Ho (1999).
Both direction 5 and 6 include onlyGill and Prowse(2012)
experiments, which are also known as cognitive game experiments.
As we can see from the figure, studies distributed over these three arrows are not even. There have been numerous studies in the literature addressing the usefulness of the cognitive hierarchy models in BCG (arrow number one, colored in black) since 1995. In addition, a growing number of researches are now available to shed some light on the the significance of cognitive capacity on BCG (arrow number two, colored in black). However, few studies on arrow number three (colored in white), until very recently, complete the circle. A complete circle means that the beauty contest game specifically and the iterated dominance game in general may be given a unified structure overarching psychology and economics. This is exactly what this study aims to do.
If we successfully complete the circle, a next legitimate question would be what role does learning play? In particular, given the fact that the relation