Two-Firm Scenario

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**Two Firms with Incompatible Products**

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.

To the left, we've constructed a visual model corresponding to two firms that aren't connected in a network. This means that their products are incompatible. Each firm is represented by a colored circle. The number above the circle is its ID number. The first number below each circle is that firm's Equilibrium Mode. There are three possible Equilibrium Modes: 0, 1, and 2, and they refer to the type of equilibrium each firm is attempting to find with respect to its Equilibrium Reaction Correspondence curve. For a more detailed explanation of the Equilibrium modes, please see the Technical Appendix at the end of this tutorial. Lastly, the second number listed below each circle is β, a measure of the strength of network externality effect that will be discussed in future slides.

The size of each firm's circle is proportional to its output. The outputs of the two firms are plotted on the graph below. Press the "Go" button several times to see them converge to one of the possible equilibria. Press the "Restart" button to repeat the demonstration. In this case, they will always reach the same equilibrium - one where the outputs of the firms are equal to each other. The exact output both firms tend to is 10.37 under the chosen model parameters.

One result of "Network Externalities" is that a firm's profits increase with its outputs in a FECE. Therefore, in the rest of this tutorial, comparing firms' equilibrium outputs is equivalent to comparing their equilibrium profits. In other words, a firm always finds the equilibrium with highest output most preferable.

It is important to stress the meaning of this graphic. The agents are simply using a mathematical process to find solutions to the "Network Externalities" model. Think of this simulation as a specialized graphing calculator that solves a system of complicated equations. It doesn't, however, directly reflect any sort of progress of firm output through time.

Throughout the rest of this tutorial, we refer to simulations of this type as instances of the Equilibrium Calculator, to emphasize their meaning and function.

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