166 CHAPTER 6 Fully Distributed Learning Algorithms 6.5 REGRET MATCHING-BASED LEARNING: LEARNING CORRELATED EQUILIBRIA In this section we present a procedure for converging to the set of correlated equilib- ria in terms of an empirical distribution of play, based on Foster and Vohra (1997), Hart and Mas-Colell (2000) no-regret dynamics. Compared to the previous, fully distributed algorithms, this algorithm will be based on frequencies of play and may lead to a correlated equilibrium as a steady state. To make the section sufficiently self-contained we review correlated equilibria and some known related results. 6.5.1 Review of Correlated Equilibrium In this section we present a procedure for converging to the set of correlated equilib- ria in terms of empirical distribution of play. The section is based on Foster and Vohra (1997), Hart and Mas-Colell (2000) no-regret dynamics. Compared to the previous fully distributed algorithms, this algorithm will be based on frequencies of play. The notion of correlated equilibrium (CE) was introduced by Aumann (1974) and can be described as follows: Assume that, before the game is played, each player receives