We have worked on a class of new game-play strategies, called zero-determinant strategies. In particular, we have focused on multi-player games. Many of today’s most pressing societal concerns require decisions which take into account a distant and uncertain future. Recent developments in strategic decision-making suggest that individuals, or a small group of individuals, can unilaterally influence the collective outcome of complex social dilemmas. However, these results do not account for the extent to which decisions are moderated by uncertainty in the probability or timing of future outcomes that characterize the valuation of a (distant) uncertain future. We have developed a general framework that captures interactions among uncertainty, the resulting time-inconsistent discounting, and their consequences for decision-making processes. In deterministic limits, existing theories can be recovered. More importantly, new insights have been obtained into the possibilities for strategic influence when the valuation of the future is uncertain. We have shown that in order to unilaterally promote and sustain cooperation in social dilemmas, decisions of generous and extortionate strategies should be adjusted to the level of uncertainty. In particular, generous payoff relations cannot be enforced during periods of greater risk (which we term the “generosity gap”), unless the strategic enforcer orients their strategy towards a more distant future by consistently choosing “selfless” cooperative decisions; likewise, the possibilities for extortion are directly limited by the level of uncertainty. Our results have implications for policies that aim at solving societal concerns with consequences for a distant future and provides a theoretical starting point for investigating how collaborative decision-making can help solve long-standing societal dilemmas.
We have identified a surprising relationship between observability and privacy. As a quantitative criterion for privacy of “mechanisms” in the form of data-generating processes, the concept of differential privacy was first proposed in computer science and has later been applied to linear dynamical systems. However, differential privacy has not been studied in depth together with other properties of dynamical systems, and it has not been fully utilized for controller design. We have clarified that a classical concept in systems and control, input observability (sometimes referred to as left invertibility) has a strong connection with differential privacy. In particular, we have shown that the Gaussian mechanism can be made highly differentially private by adding small noise if the corresponding system is less input observable. In addition, enabled by our new insight into privacy, we have developed a method to design dynamic controllers for the classic tracking control problem while addressing privacy concerns. We call the obtained controller through our design method the privacy preserving controller.
