View All Pages

Lecture 18: Solving and estimating static games of incomplete information

We will start simple with static games, since many of the involved issues when solving and estimating dynamic games (such as multiple equilibria) can be illustrated with static games. In particular, we consider a simple entry model, where two firms need to decide whether or not to be active in a market. The model is completely static. In the model parameters can be set such that the model has multiple equilibria.

Multiple equilibria creates a lot of challenges that we have not discussed to far.   First, multiple equilibria means that the model has more that one solution, so we cannot expect to find all of them by successive approximations. Second, the likelihood function will be discontinuous, because the number of equilibria depends on the parameters we are trying to estimate.  Third, once we have to more than one equilibrium in the model, we need to figure out which one was played in the data. Does CCP types estimators help us here? Perhaps data is informative about equilibrium section. For NFXP, we need to solve for all equilibria implied by the model at all trial parameter values: While we can easily find all solutions here,  it is an extremely challenging task where considering dynamic games. Finding one solution is not enough, we need to find all. equilibria that could have been played in the data and then let the data inform us about which equilibrium is more likely (i.e.  the one with the highest likelihood). This is a subset of the many things that we will discuss in the lecture... and the discussion is general. Most of the challenges really also applies dynamic games although they are amplified by orders of magnitude.

In general, the lecture focus on comparing the properties of the different estimation methods that we have covered so far: NFXP, MPEC, CCP estimator and Nested Pseudo Likelihood.. and try to prepare us to visit the absolute frontier of dynamic structural econometrics: How to estimate dynamic games with multiple equilibria. 

The lecture and slides follows' Che-Lin Su's 2014 paper quite closely. He strongly advocates for the use of MPEC, but my lecture somewhat critically reviews his results and in some cases I think he somewhat oversell MPEC: My simulations show that MPEC often fails in case with multiplicity of equilibria, once the dimension of the problem increase. 

Preparation: 

Material: 

Video lecture

Lecture 18: Solving and estimating static games of incomplete information Links to an external site.