2.5. A SUMMARY OF LITERATURE
Note that δ is the most important parameter in EWA because it shows the way that EWA captures two learning principles, the law of actual effect and the law of simulated effect, is different from reinforcement and belief models.
In fact, EWA require that the strength of these two effects is only a matter of degree, while reinforcement assumes that only actual effect matters (δ = 0) and belief model supposes that actual and simulated effects are equally strong (δ = 1).
By investigating the empirical δ, we can identify the subjects as being reinforcement (δ = 0), belief learning (δ = 1) or in between (0 < δ < 1).
Would this heterogeneity in learning behavior corresponds to heterogeneity in cognitive capacity? In other words, would belief learning require more capacity than reinforcement learning? To distinguish the cognitive require-ment of learning models designed for calibrating heterogeneous agents, Chen (2012) has proposed three cognitive elements, including memory, conscious-ness and reasoning. Reinforcement learning agents requires some capacity of memory to retrieve their own past experience of success. However, they are not conscious about the existence of other players and it’s impossible for them to reason based on the entire environment they are embedded. On the other hand, belief learning agents are endowed with additional cognitive ability, said, some degree of consciousness and reasoning. They are aware of the presence of their opponents and also taking their opponents’ decisions into account. In fact, belief learning agents count the frequencies of their opponents’ past actions, calculate the foregone payoffs on which their future decisions are based. EWA allows the possibility that the agent’s cognitive ability to imagine all forgone payoffs is partial by introducing δ, ranging from 0 to 1. Chen(2012) actually gives us a correspondence between the spectrum of various learning models and the levels of cognitive capacity.
2.5 A Summary of Literature
Few studies investigated the relationship between cognitive capacity and cog-nitive hierarchy, two closely related concepts, one is from psychology and the other is from economics. Recent works began to address this issue, yet all of them applied at least one simplification of game structure. They either performed one-shot game to exclude the effect of learning or conducted two-person or three-two-person game to reduce game complexity. However, these two features reflect real economic decisions, in particular, investment decisions.
Investors compete with thousands of participants in the financial market.
They also make a sequence of decisions based on the experiences of previous trades. Our study was the first to investigate how cognitive capacity and
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2.5. A SUMMARY OF LITERATURE
cognitive hierarchy may related in a larger scale environment when learning takes effect.
The primary research questions to be addressed in this study are as fol-lows:
• First, would cognitive capacity have a positive effect on subjects’ re-vealed cognitive hierarchies?
• Second, would this effect endure when subjects become more experi-enced?
• Third, would cognitive capacity affect the way in which subjects learn?
Our predictions are as follows. According to the results of current studies, cognitive capacity should be related to cognitive hierarchy at least in initial rounds. Both the second and the third ones are open questions because many aspects of experimental design, such as time horizon and provided feedback information, would also affect the results. There is no clue from previous literature and we didn’t address these issues in this study. Our specific experimental design serves as initial attempts to answer the later two questions. In considering the the third question, in particular, we hope to related working memory capacity to the counterfactual simulation of forgone payoff, the parameter δ in EWA.
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Chapter 3 Method
3.1 Beauty Contest Experiment
The experiment consisted of 6 sessions and there were 15-20 subjects in each session, there being a total of 108 subjects involved. The subjects were required to complete both a repeated beauty contest game and then a working memory test. All experiments were conducted in the Experimental Economics Laboratory (EEL) of National Chengchi University from October 2009 to August 2010. Experiments were announced on the NCCU EEL web site1 and on the part-time job board in PPT, one of the most popular bulletin board systems in Taiwan. Subjects were required to register through the NCCU EEL Registration System2 and sign up for our experiments. After signing up for one experiment, subjects immediately received an e-mail for confirmation.
The BCG was conducted by means of a z-tree (Fischbacher, 2007). For each period, subjects were required to select an integer number between [0, 100] and competed with all of the others in the session. The prize was given to the one whose guess number was closest to the target number, denoted by τ , which was calculated by averaging all guesses and then multiplying the result by a factor p = 2/3. After collecting all subjects’ guesses, the screen would display feedback information regarding the target number, the subject’s chosen number, profit and cumulated profit. The BCG was repeated 10 times and it took about 60 minutes to finish. In addition to a fixed show-up fee of NT$125, we also provided a prize for the winner in each period of NT$100, and the prize was to be evenly split if there was more than one winner. The details of the instructions for the subjects are given in Appendix
1see http://eel.nccu.edu.tw/
2see http://eel.nccu.edu.tw/Registration/