This explains what comparative statics are and shows you how to calculate them. Most of the reason why we do game theory is to calculate comparative statics, so this is an important lecture for anyone serious about learning the subject.
Note that this lesson uses the equilibria from the soccer penalty kick game.
- Comparative statics are how equilibrium behaviors and outcomes change as a function of the exogenous parameters.
- Essentially, we want to know how manipulating the inputs changes the outputs.
- There is a four step process to calculating comparative statics:
- Solve for the game's Nash equilibria.
- Calculate the element of interest.
- Take the derivative of that element of interest with respect to the exogenous variable of choice.
- Use the derivative to see how changing the exogenous variable affects the element of interest.
- Each of these steps is fairly easy to do; just be careful not to make any silly mistakes in the process.