  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. This is
owing to each player having to make overly specific assumptions about the
behaviors of the other players to employ their Nash equilibrium strategy, which
they may not make. 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 truthful lines. 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. Finally, we describe an application
of the mechanism to design demand response markets.
