  In this paper, we address the much-anticipated deployment of connected and
automated vehicles (CAVs) in society by modeling and analyzing the
social-mobility dilemma in a game-theoretic approach. We formulate this dilemma
as a normal-form game of players making a binary decision: whether to travel
with a CAV (CAV travel) or not (non-CAV travel) and by constructing an
intuitive payoff function inspired by the socially beneficial outcomes of a
mobility system consisting of CAVs. We show that the game is equivalent to the
Prisoner's dilemma, which implies that the rational collective decision is the
opposite of the socially optimum. We present two different solutions to tackle
this phenomenon: one with a preference structure and the other with
institutional arrangements. In the first approach, we implement a social
mechanism that incentivizes players to non-CAV travel and derive a lower bound
on the players that ensures an equilibrium of non-CAV travel. In the second
approach, we investigate the possibility of players bargaining to create an
institution that enforces non-CAV travel and show that as the number of players
increases, the incentive ratio of non-CAV travel over CAV travel tends to zero.
We conclude by showcasing the last result with a numerical study.
