Free Literature Review On Cooperative Game Theory

Acknowledgement

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Abstract

This paper is a review of Fairness through the Lens of Cooperative Game Theory: An Experimental Approach by Georoy de Clippely and Kareen Rozen (de Clippel and Rozen 1). This paper is a summary of the journal, detailing the primary ideas addressed and there significances to the readers. It will also examine the methods used and if they were the best choice in addition to the data used (de Clippel and Rozen 2). The primary argument of Fairness through the Lens of Cooperative Game Theory is that extensive research exists on the solution concepts and style of thinking on non-cooperative game theory but this is not the case for cooperative game theory (de Clippel and Rozen 2). Clippely and Rozen have used a normative approach to try to find out whether there is fairness in the cooperative game theory. From this normative perspective, they experimentally tested self-evident principles and solution concepts of the cooperative game theory (Lui 4). We will also analyze at the results of the experiment where Clippely and Rozen say that the fairness of the game varies from person to person and may not be based on pay-offs (de Clippel and Rozen 2).

Review

Game theory is divided into two categories namely; cooperative game theory and non-cooperative game theory (Brandenburger 1). Fairness through the Lens of Cooperative Game Theory: An Experimental Approach by Georoy de Clippely and Kareen Rozen tries to find out whether a cooperative game theory has a fair outcome for all subjects. There have been few researchers prior to Georoy de Clippely and Kareen Rozen (de Clippel and Rozen 2). Some gave the recipients of the money a chance to bargain with other recipients then from there determined whether the results were the same as the predicted solutions of the game. Other researchers like the Kalisch, Milnor, Nash and Nering (1954) gave their recipients information about their role using the characteristic function then they allowed them to agree on the fair outcome. Other past studies combined both the aspect of characteristic function and allowed their subjects to bargain on a payoff (de Clippel and Rozen 2). Therefore, these past studies researched on whether there is fairness in cooperative game of theory using normative experiments only, however; Fairness through the Lens of Cooperative Game Theory: An Experimental Approach by Georoy de Clippely and Kareen Rozen went ahead and combined normative experiments and axiomatic principles. Axiomatic principles here refer to the rule in the cooperative game theory (University of Pennsylvania 9). Hence, the importance of this paper is to explain to the reader whether there is fairness in cooperative game theory by using a different approach that has not been used before (de Clippel and Rozen 2).

Methodology

The two researchers used three recipients for every stage of the experiment, while the rest were decision makers (de Clippel and Rozen 5). The responsibility of the decision makers was to determine how much money was to be paid to the recipients based on the value of the different coalitions (de Clippel and Rozen 5). Though there were many decision makers, only one recommendation is used for the experiment. In the research design, the decision makers were not allowed to any of the recipients. This is because the main of the experiment to determine fairness in the cooperative game of theory, therefore favoritism would lead to incorrect results (de Clippel and Rozen 6). The researchers went ahead and tested the reliability of the behaviors that are shared by many solutions. They examined whether the principles for both individuals and the groups. They used linear regression to analyze the effects of aggregate value on the payoffs that are given to the recipients of the game. This helped them to identify how the principles of the game become a hindrance (de Clippel and Rozen 7). At this stage, the researchers found out that the decision makers adhered to the principles of the games namely, the symmetry, additivity, and so on. This was witnessed when they played as individuals. However, in groups, they did not respect the rule that advocates for the protection of the dummy player. A dummy player, in game theory, is one who has no worth in the game hence they do not receive any payoffs (de Clippel and Rozen 9).
The researchers also used theory to prove that using symmetry and additivity implies that decision makers’ selections have to be categorized as a linear combination (de Clippel and Rozen 10). This means that a regression framework that has less factors, links coefficients in different values of the coalitions and makes them equal to all recipients. The researchers used seven different characteristic functions that showed the level of the payoffs being at different positions between Shapley value and equal split. They used a Gaussian mixture that showed that there were varying opinions on what is fair based on the individual characteristic functions, and the extent of fairness was based on the overall characteristic functions (de Clippel and Rozen 12).

Conclusions

The decision makers consider fairness as based on the value of the sub-coalitions. These decision makers use the value of the sub-coalitions to allocate money to the recipients. On the other hand, the decision makers took equal payoffs in when a completely symmetric function was used but in case of other characteristic functions, their payoffs were not the same. Additionally, Georoy de Clippely and Kareen Rozen concluded that the decision makers’ allocation of payoffs to themselves or the recipients seemed to vary according to various rules of the cooperative game theory.
The paper is very useful in the topic of game theory because it contributes information that was not presently available. This paper teaches the readers that cooperative game theory is a fair game and the factors or players affect its fairness. It offers more information to the literature of game theory by researching on an area that little research has been carried out. The authors started out by saying that little research has been done on cooperative game theory hence the need to concentrate on it rather than non-cooperative game theory. It is a readable paper and the authors did a good job.

Works Cited

Brandenburger, Adam. 'Cooperative Game Theory: Characteristic Functions, Allocations, Marginal Contrib Ution'. uib. N.p., 2007. Web. 8 Apr. 2015 < http://www.uib.cat/depart/deeweb/pdi/lbm/arxius_decisions_and_games/cooperative_game_theory-brandenburger.pdf>
de Clippel, Geoffroy, and Kareen Rozen. 'Fairness through the Lens of Cooperative Game Theory: An Experimental Approach'. Brown, 2013. Web. 8 Apr. 2015 2015.http://www.econ.brown.edu/fac/Geoffroy_declippel/fairness.pdf
Lui, John. 'Introduction To Game Theory; Cooperative Game Thory'. cse. Web. 8 Apr. 2015. <http://www.cse.cuhk.edu.hk/~cslui/CSC6480/cooperative_game.pdf>