  Trusting others and reciprocating the received trust with trustworthy actions
are fundaments of economic and social interactions. The trust game (TG) is
widely used for studying trust and trustworthiness and entails a sequential
interaction between two players, an investor and a trustee. It requires at
least two strategies or options for an investor (e.g. to trust versus not to
trust a trustee). According to the evolutionary game theory, the antisocial
strategies (e.g. not to trust) evolve such that the investor and trustee end up
with lower payoffs than those that they would get with the prosocial strategies
(e.g.to trust). A generalisation of the TG to a multiplayer (i.e.more than two
players) TG was recently proposed. However, its outcomes hinge upon two
assumptions that various real situations may substantially deviate from: (i)
investors are forced to trust trustees and (ii) investors can turn into
trustees by imitation and vice versa. We propose an asymmetric multiplayer TG
that allows investors not to trust and prohibits the imitation between players
of different roles; instead, investors learn from other investors and the same
for trustees. We show that the evolutionary game dynamics of the proposed TG
qualitatively depends on the nonlinearity of the payoff function and the amount
of incentives collected from and distributed to players through an institution.
We also show that incentives given to trustees can be useful and sufficient to
cost-effectively promote trust and trustworthiness among self-interested
players.
