State-of-the-art driver-assist systems have failed to effectively mitigate driver inattention and had minimal impacts on the ever-growing number of road mishaps (e.g. life loss, physical injuries due to accidents caused by various factors that lead to driver inattention). This is because traditional human-machine interaction settings are modeled in classical and behavioral game-theoretic domains which are technically appropriate to characterize strategic interaction between either two utility maximizing agents, or human decision makers. Therefore, in an attempt to improve the persuasive effectiveness of driver-assist systems, we develop a novel strategic and personalized driver-assist system which adapts to the driver's mental state and choice behavior. First, we propose a novel equilibrium notion in human-system interaction games, where the system maximizes its expected utility and human decisions can be characterized using any general decision model. Then we use this novel equilibrium notion to investigate the strategic driver-vehicle interaction game where the car presents a persuasive recommendation to steer the driver towards safer driving decisions. We assume that the driver employs an open-quantum system cognition model, which captures complex aspects of human decision making such as violations to classical law of total probability and incompatibility of certain mental representations of information. We present closed-form expressions for players' final responses to each other's strategies so that we can numerically compute both pure and mixed equilibria. Numerical results are presented to illustrate both kinds of equilibria.

In the summer of 1967, Secretary of Defense Robert McNamara commissioned a group of thirty-six scholars to write a secret history of the Vietnam War. The project took a year and a half, ran to seven thousand pages, and filled forty-seven volumes. Only a handful of copies were made, and most were kept under lock and key in and around the Beltway. One set, however, ended up at the RAND Corporation, in Santa Monica, where it was read, from start to finish, by a young analyst there named Daniel Ellsberg. Ellsberg was dismayed by what he learned. For a generation, the U.S. government had been lying to the American people about the Vietnam War. He put the first of the volumes in his briefcase, praying that the security guards at RAND would not stop him, and made his way to a small advertising agency in West Hollywood, where a friend told him there was a Xerox machine he could use. "It was a big one, advanced for its time, but very slow by today's standards," Ellsberg writes in his 2002 autobiography, "Secrets: A Memoir of Vietnam and the Pentagon Papers": It could do only one page at a time, and it took several seconds to do each page. I tried pressing the book down on the glass to do two pages at a time, but the middle section was faint and uneven. Fortunately the books were bound with metal tapes through holes so they could be taken apart. . . . The machine didn't collate, and the bar had to come back and travel just as slowly for each copy.

Correlated equilibrium generalizes Nash equilibrium to allow correlation devices. Correlated equilibrium captures the idea that in many systems there exists a trusted administrator who can recommend behavior to a set of agents, but can not enforce such behavior. This makes this solution concept most appropriate to the study of multi-agent systems in AI. Aumann showed an example of a game, and of a correlated equilibrium in this game in which the agents' welfare (expected sum of players' utilities) is greater than their welfare in all mixed-strategy equilibria. Following the idea initiated by the price of anarchy literature this suggests the study of two major measures for the value of correlation in a game with nonnegative payoffs: 1. The ratio between the maximal welfare obtained in a correlated equilibrium to the maximal welfare obtained in a mixed-strategy equilibrium. We refer to this ratio as the mediation value. 2. The ratio between the maximal welfare to the maximal welfare obtained in a correlated equilibrium. We refer to this ratio as the enforcement value. In this work we initiate the study of the mediation and enforcement values, providing several general results on the value of correlation as captured by these concepts. We also present a set of results for the more specialized case of congestion games, a class of games that received a lot of attention in the recent literature.