Control Meets Learning Seminar
System models often include the presence of relatively infrequent random events, such as exploration, mutations, or errors. The concept of stochastic stability concerns how such random effects can impact long run behavior, even as they become progressively infrequent. This talk presents an overview of stochastic stability as applied to finite state Markov chain models. The talk begins with a tutorial introduction to stochastic stability and its application in a variety of settings, with a particular emphasis on multi-agent systems, namely: (1) large population signaling games, (2) coordination games, and (3) programmable self-assembly. The talk continues with a comparison and contrast of stochastic stability with the concept of an evolutionarily stable strategy (ESS), a related notion that also examines the effect of random perturbations in multi-agent population dynamics. The comparison is through the introduction of a so-called transitive-stability graph, or TS-graph, that leverages the definition of an ESS to reach stochastic stability conclusions. The talk concludes with a discussion of how short and medium run behavior can distinguish dynamics that exhibit identical long run stochastic stability properties.