Abstract
I study the path properties of adaptive heuristics that mimic the natural dynamics of play in a game and converge to the set of correlated equilibria. Despite their apparent differences, I show that these heuristics have an abstract representation as a sequence of probability distributions that satisfy a number of common properties. These properties arise due to the topological structure of the set of correlated equilibria. The characterizations that I obtain have useful applications in the study of the convergence of the heuristics.
Highlights
Given the large fraction of economic interactions intermediated by algorithms today, it is becoming increasingly important for economists to understand the collective play properties of algorithmic procedures
I need to establish a definition of convergence in terms of set containment relations, and this eventually provides the characterization of adaptive heuristics in terms of their paths
Even with the restriction that they converge to the set of correlated equilibria, there are myriads of approaches to generate heuristic schemes
Summary
Given the large fraction of economic interactions intermediated by algorithms today, it is becoming increasingly important for economists to understand the collective play properties of algorithmic procedures. The problem is still non-trivial because the probability distributions may inhabit a high dimensional space, and more importantly, the convergence is to a limit set, not a point For this reason, I need to establish a definition of convergence in terms of set containment relations, and this eventually provides the characterization of adaptive heuristics in terms of their paths. A useful result from this exercise is the insight that the outlines of a compact, convex set can be discerned from the path, as a sequence progresses, if a heuristic converges to the set of correlated equilibria This idea can have interesting applications, some of which I outline in the last part of the paper. The proof of Proposition 2 is in the Appendix A
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
