This paper considers repeated games in which one player has a different objective than others. In particular, we investigate repeated two-player zero-sum games where the column player not only aims to minimize her regret but also stabilize the actions. Suppose that while repeatedly playing this game, the row player chooses her strategy at each round by using a no-regret algorithm to minimize her regret. We develop a no-dynamic regret algorithm for the column player to exhibit last round convergence to a minimax equilibrium. We show that our algorithm is efficient against a large set of popular no-regret algorithms the row player can use, including the multiplicative weights update algorithm, general follow-the-regularized-leader and any no-regret algorithms satisfy a property so called “stability”.

A descending (multi-item) clock auction (DCA) is a mechanism for buying items from multiple potential sellers. In the DCA, bidder-specific prices are decremented over the course of the auction. In each round, each bidder might accept or decline his offer price. Accepting means the bidder is willing to sell at that price. Rejecting means the bidder will not sell at that price or a lower price. DCAs have been proposed as the method for procuring spectrum from existing holders in the FCC's imminent incentive auctions so spectrum can be repurposed to higher-value uses. However, the DCA design has lacked a way to determine the prices to offer the bidders in each round. This is a recognized, important, and timely problem.