Dynamic zero-sum games are an important class of problems with applications ranging from evasion-pursuit and heads-up poker to certain adversarial versions of control problems such as multi-armed bandit and multiclass queuing problems. These games are generally very difficult to solve even when one player’s strategy is fixed, and so constructing and evaluating good sub-optimal policies for each...

We develop a unifying approach for approximating a “limit" zero-sum game by a sequence of approximating games. We discuss both the convergence of the values and the convergence of optimal (or “almost" optimal) strategies. Moreover, based on optimal policies for the limit game, we construct policies which are almost optimal for the approximating games. We then apply the general framework to stat...

In this lecture we formulate and prove the celebrated approachability theorem of Blackwell, which extends von Neumann's minimax theorem to zero-sum games with vector-valued payoffs [1]. (The proof here is based on the presentation in [2]; a similar presentation was given by Foster and Vohra [3].) This theorem is powerful in its own right, but also has significant implications for regret minimiz...

In this invited contribution [7], we summarize new solution concepts useful for the synthesis of reactive systems that we have introduced in several recent publications. These solution concepts are developed in the context of non-zero sum games played on graphs. They are part of the contributions obtained in the inVEST project funded by the European Research Council.

We develop a unifying approach for approximating a \limit" zero-sum game by a sequence of approximating games. We discuss both the convergence of the values and the convergence of optimal (or \almost" optimal) strategies. Moreover, based on optimal policies for the limit game, we construct policies which are almost optimal for the approximating games. We then apply the general framework to stat...

An inspection game is here a non-cooperative two-person-game between an inspector and an inspectee. It models a situation where the inspector controls the inspectee who has an incentive to violate certain legal obligations. A recent survey of inspection games applied to data verification, for example in nuclear material safeguards, is given in [1]. Dresher [2] described a sequential inspection ...