Regret Minimization with Dynamic Benchmarks in Repeated Games

Regret minimization in repeated matrix games with variable stage duration

Regret minimization in repeated matrix games has been extensively studied ever since Hannan’s (1957) seminal paper. Several classes of no-regret strategies now exist; such strategies secure a longterm average payoff as high as could be obtained by the fixed action that is best, in hindsight, against the observed action sequence of the opponent. We consider an extension of this framework to repe...

Regret Minimization in Games with Incomplete Information

Extensive games are a powerful model of multiagent decision-making scenarioswith incomplete information. Finding a Nash equilibrium for very large instancesof these games has received a great deal of recent attention. In this paper, wedescribe a new technique for solving large games based on regret minimization.In particular, we introduce the notion of counterfactual regret, whi...

Regret Minimization in Games with Incomplete Information

Extensive games are a powerful model of multiagent decision-making scenarioswith incomplete information. Finding a Nash equilibrium for very large instancesof these games has received a great deal of recent attention. In this paper, wedescribe a new technique for solving large games based on regret minimization.In particular, we introduce the notion of counterfactual regret, whi...

Regret Minimization in Signal Space for Repeated Matrix Games with Partial Observations

Regret Minimization in Signal Space for Repeated Matrix Games with Partial Observations

The Bayes Envelope of a repeated matrix game traces the maximal payoo rate that a player (say P1) could secure for herself had she known in advance the empirical frequency of P2's actions. It was shown by J. Hannan (1957) that Regret Minimizing policies for P1 exist which asymptotically attain the Bayes Envelope even without such prior knowledge, but assuming a complete observation of the P2's ...