Economic Perspectives II
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Importance Of Risk-Neutrality In Agent Behavior
Note: in order to run the simulation referred to in this slide, go here, to the Java Applet version. You will be directed to download the latest version of the Java plug-in.
In the previous couple of slides we described a mechanism behind the fact that some agents are risk-averse, some are risk-neutral, and some - risk-loving. Yet why should a risk-averse agent be less productive than a risk-neutral one? To answer this question, we must present the agent with a choice of several options, and see which one she is bound to choose.
Consider the graphic to your left. Each of the agents in the left column picks one of the options in the right column at every other time step. Each option is just like the one discussed in the previous slide. The size of its circle represents x - the expected payoff of the option, and the circle's color represents v - the option's variance. Risky options with high variances are red, those that are less risky - yellow, and the safest options are green.
In the spirit of our previous discussion, the Risk Neutral Agent's utility curve is u(x) = x, with a risk-love factor r equal to 1. The Risk Averse and Risk Loving Agents have r's equal to 0.25 and 4, respectively. Each of them calculates her own expected utility of the available options, and connects to the one with highest returns. Every other time step the set of options changes, and the agents make their choices again.
Note how the agents behave. Sometimes they pick the same option. Quite often, however, the Risk Averse Agent will choose a safer option than the Risk Neutral one, even if it comes at a cost in terms of the expected value. The Risk Loving Agent, on the other hand, will sometimes forgo high expected value in favor of a greater variance in the outcome.
However, in the long term, only the options' expected values matter, and the Risk Neutral strategy is bound to win. After a few "Go" steps, the simulation process speeds up, and you should be able to note that the total output of the Risk Neutral Agent (yellow line) surpasses that of the Risk Averse and the Risk Loving ones (green and red lines, respectively).
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