Probabilistic Choice in Games: Properties of Rosenthal’s t-Solutions

The t-solutions introduced in R. W. Rosenthal (1989, Int J Game Theory 18:273–292) are quantal response equilibria based on the linear probability model. Choice probabilities in t-solutions are related to the determination of leveling taxes in taxation problems. The set of t-solutions coincides with the set of Nash equilibria of a game with quadratic control costs. Evaluating the set of t-solutions for increasing values of t yields that players become increasingly capable of iteratively eliminating never-best replies and eventually only play rationalizable actions with positive probability. These features are not shared by logit quantal response equilibria. Moreover, there exists a path of t-solutions linking uniform randomization to Nash equilibrium