Log Tracing: Searching the prior space

The logarithmic tracing homotopy crucially depends on the prior belief about players’ strategies. For different priors, the homotopy path leads to potentially different equilibria. By searching the prior space, either randomly or systematically, one can find multiple equilibria for a given game, and assess the basins of attractions for each equilibrium.

Note, however, that this method does generally not allow to find all equilibria of a given game. For unstable equilibria, the corresponding basins of attraction reduce to single points in the prior space, which are likely to be missed.

• Example: Stag hunt
• Example: Sequential price competition