  Trusting in others and reciprocating that trust with trustworthy actions are
crucial to successful and prosperous societies. The Trust Game has been widely
used to quantitatively study trust and trustworthiness, involving a sequential
exchange between an investor and a trustee. The deterministic evolutionary game
theory predicts no trust and no trustworthiness whereas the behavioural
experiments with the one-shot anonymous Trust Game show that people
substantially trust and respond trustworthily. To explain these discrepancies,
previous works often turn to additional mechanisms, which are borrowed from
other games such as Prisoner's Dilemma. Although these mechanisms lead to the
evolution of trust and trustworthiness to an extent, the optimal or the most
common strategy often involves no trustworthiness. In this paper, we study the
impact of asymmetric demographic parameters (e.g. different population sizes)
on game dynamics of the Trust Game. We show that, in weak-mutation limit,
stochastic evolutionary dynamics with the asymmetric parameters can lead to the
evolution of high trust and high trustworthiness without any additional
mechanisms in well-mixed finite populations. Even full trust and near full
trustworthiness can be the most common strategy. These results are
qualitatively different from those of the previous works. Our results thereby
demonstrate rich evolutionary dynamics of the asymmetric Trust Game.
