1. The Risk Preference and the Matthew Effect on Wealth Distributions
Kunyu Song1, Kenan An1, Jiping Huang1
(1Department of Physics and Surface Physics Laboratory (National Key Laboratory), Fudan University, Shanghai , China)
Abstract:
By introducing the revised MDRAG model, we can see the market can still adjust the allocation of resources efficiently. Also, we can get that the stronger risk preference can lead to lower income, which is also improved to be true by the experiment. Further, in order to observe the influence of the Matthew effect on wealth distributions, the “rich get richer” rule is added into the model. It is impressive that the introduction of the Matthew effect can lead to bigger gap between the rich and the poor.
There are two rooms with different resources (namely M1, M2) for agents to invest in.
The payoff function in the game given as:
(pay_w for the payoff of the agent j; w1(or w2) for the total wealth invested in room 1 (or 2); in_wj for invested wealth of agent j; Mi for the room agent j invested and wi for the total invested wealth in the room.)
Model:
Varied weight
Agents can choose different weight in the game.
We carried out the experiment with 18 students in Fudan University
Both the experiment and the simulation result show that stronger risk preference can lead to lower income.
Fixed weight
Agents have the same fixed weight in the game.
longitudinal
horizontal
In simulation, we set 1000 agents in the game to play 2000 times in on round(fixed weight and fixed M1/M2). In the whole picture, weight is varied from 0.02 to 1.0, and M1/M2 from 1 to 10.
Higher weight just can be seen as Matthew Effect. We can see that:
►In lower weight, gini-index is much lower than it in higher weight. Then, Matthew Effect do lead to bigger gap between the rich and the poor.(Longitudinal comparison)
►In lower weight and higher weight, gini-index show different trends with growth of M1/M2.(Horizontal comparison)
Conclusion:
Simulating by the revised MDRAG model, we can get some results as follows:
1. In some investment game, the heavier risk preference you present, the more you lose, unless you are the King of the game.
2. The Matthew Effect can lead the society to a more uneven station.
Besides we can see the same situation in the real life or economic market.
W. Wang, Y. Chen and J.P. Huang(2009) Heterogeneous preferences, decision-making capacity, and phase transitions in a complex adaptive system. Proc Natl Acad Sci USA 106 :
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