Incentive Compatibility in Two-Stage Repeated Stochastic Games

Abstract

We address the problem of mechanism design for two-stage repeated stochastic games -a novel setting using which many emerging problems in next-generation electricity markets can be readily modeled. Repeated playing affords the players a large class of strategies that adapt a player's actions to all past observations and inferences obtained therefrom. In other settings such as iterative auctions or dynamic games where a large strategy space of this sort manifests, it typically has an important implication for mechanism design: It may be impossible to obtain truth-telling as a dominant strategy equilibrium. Consequently, in such scenarios, it is common to settle for mechanisms that render truth-telling only a Nash equilibrium, or variants thereof, even though Nash equilibria are known to be poor models of real-world behavior owing to each player having to make overly specific assumptions about the behaviors of the other players in order for them to employ their Nash equilibrium strategy. In general, the lesser the burden of speculation in an equilibrium, the more plausible it is that it models real-world behavior. Guided by this maxim, we introduce a new notion of equilibrium called Dominant Strategy Non-Bankrupting Equilibrium (DNBE) which requires the players to make very little assumptions about the behavior of the other players to employ their equilibrium strategy. Consequently, a mechanism that renders truth-telling a DNBE as opposed to only a Nash equilibrium could be quite effective in molding real-world behavior along the desired lines. Finally, we present a mechanism for two-stage repeated stochastic games that renders truth-telling a Dominant Strategy Non-Bankrupting Equilibrium. The mechanism also guarantees individual rationality and maximizes social welfare. I. INTRODUCTIONThe power system is on the cusp of a revolution. The coming decade could witness increased renewable energy penetration, Electric Vehicle (EV) penetration, EV energy storage integration, demand response programs, etc. These changes have a profound impact on electricity market operations. New mechanisms must be devised to address a variety of important problems that are anticipated to arise in next-generation electricity markets. Most of the existing mechanism design settings are insufficient to model certain crucial features of these problems. To address this, we introduce the setting of Two-Stage Repeated Stochastic Games using which many problems that arise in the context of electricity markets can be readily modeled. The setting is an extension of the one-shot two-stage stochastic game introduced in [1] to repeated plays.At a high level, a two-stage stochastic game, as the name suggests, consists of two stages. In the first stage, the players do not know their valuation functions precisely, but rather only know the probability distribution of their valuation functions. It is only in the second stage of the game that the valuation functions realize. However, the social planner cannot wait until the second stage to decide on the out...

A Two-Stage Mechanism for Demand Response Markets

“…We have now have all quantities that are necessary to define a non-bankrupting strategy -a notion that was recently introduced in [15]. Definition 2.…”

“…The next section presents such a payment rule. The underlying equilibrium concept for incentive compatibility is the recently introduced notion of Dominant Strategy Non-Bankrupting Equilibrium (DNBE) [15].…”

“…, n} × N, the payment function p i,l consists of two components: (i) a first-stage payment p 1 i,l that is determined based on only the type distributions reported in the day-ahead market and (ii) a second-stage settlement p 2 i,l that is determined at the end of day l based on the history of type realizations reported until day l. We describe these payment rules next. They are an adaptation of the payment rule developed in [15] for two-stage repeated stochastic games.…”

“…In this paper, we present a mechanism that defers the challenge of determining the compensation for demand response providers to the markets, and circumvents the issues that arise from baseline estimation errors. It is based on the mechanism developed in [15] for two-stage repeated stochastic games. In the day-ahead market, participating consumers submit the probability distribution of their next-day consumption to the system operator and in real time, consumers report the realization of their baseline demand and receive credit for reductions below their reported baseline.…”

“…While the mechanism itself is adapted from [15], the main contribution of the paper lies in modeling the interaction between demand response providers and the system operator as a two-stage repeated stochastic game, thereby setting the stage for the application of the results developed in [15] to design an efficient and incentive-compatible demand response market.…”