  Mutual relationships, such as cooperation and exploitation, are the basis of
human and other biological societies. The foundations of these relationships
are rooted in the decision making of individuals, and whether they choose to be
selfish or altruistic. How individuals choose their behaviors can be analyzed
using a strategy optimization process in the framework of game theory. Previous
studies have shown that reference to individuals' previous actions plays an
important role in their choice of strategies and establishment of social
relationships. A fundamental question remains as to whether an individual with
more information can exploit another who has less information when learning the
choice of strategies. Here we demonstrate that a player using a memory-one
strategy, who can refer to their own previous action and that of their
opponent, can be exploited by a reactive player, who only has the information
of the other player, based on mutual adaptive learning. This is
counterintuitive because the former has more choice in strategies and can
potentially obtain a higher payoff. We demonstrated this by formulating the
learning process of strategy choices to optimize the payoffs in terms of
coupled replicator dynamics and applying it to the prisoner's dilemma game.
Further, we show that the player using a memory-one strategy, by referring to
their previous experience, can sometimes act more generous toward the
opponent's defection, thereby accepting the opponent's exploitation. Mainly, we
found that through adaptive learning, a player with limited information usually
exploits the player with more information, leading to asymmetric exploitation.
