Final answer:
In a trust game, a self-interested Person A may theoretically offer a minimal amount like $1 to Person B; however, experimental data suggests offers tend to be more generous due to considerations of fairness and rejection of inequitable offers.
Step-by-step explanation:
If Person A believes that people act solely in their own self-interest, the optimal amount to give to Person B would theoretically be very small to maximize their own returns in a trust game. In a scenario where both players are assumed to be rational and only concerned with personal gain, Person A might offer as little as $1 to Person B, assuming that something is better than nothing for Person B. However, experimental data shows that real players often reject offers that are too far from equitable.
In a restructured game where Person B gets to keep their amount when rejecting an offer, the balance of power shifts, and Person A is likely to make more generous offers. Political scientists suggest that players also consider fairness and are willing to refuse unfair offers, and may even punish those who violate this fairness by rejecting the offers completely. This means that in practice, offers are typically larger than the minimal amount, as rational players would expect offers to be rejected if they are perceived as unfair.
Therefore, while ensuring self-interest, Person A might consider offering an amount that is more generous than the minimal possible to avoid rejection, looking towards results seen in practical experiments, where players often settle for $6-$4 or $7-$3 splits. Trust and fairness are significant factors in the dynamics of trust games, influencing the decision of how much to offer.