The target projection dynamic

This paper studies the target projection dynamic, which is a model of myopic adjustment for population games. We put it into the standard microeconomic framework of utility maximization with control costs. We also show that it is well-behaved, since it satisfies the desirable properties: Nash stationarity, positive correlation, and existence, uniqueness, and continuity of solutions. We also show that, similarly to other well-behaved dynamics, a general result for elimination of strictly dominated strategies cannot be established. Instead we rule out survival of strictly dominated strategies in certain classes of games. We relate it to the projection dynamic, by showing that the two dynamics coincide in a subset of the strategy space. We show that strict equilibria, and evolutionarily stable strategies in $2\times2$ games are asymptotically stable under the target projection dynamic. Finally, we show that the stability results that hold under the projection dynamic for stable games, hold under the target projection dynamic too, for interior Nash equilibria.