  A common assumption employed in most previous works on evolutionary game
dynamics is that every individual player has full knowledge about and full
access to the complete set of available strategies. In realistic social,
economical, and political systems, diversity in the knowledge, experience, and
background among the individuals can be expected. Games in which the players do
not have an identical strategy set are hypergames. Studies of hypergame
dynamics have been scarce, especially those on networks. We investigate
evolutionary hypergame dynamics on regular lattices using a prototypical model
of three available strategies, in which the strategy set of each player
contains two of the three strategies. Our computations reveal that more complex
dynamical phases emerge from the system than those from the traditional
evolutionary game dynamics with full knowledge of the complete set of available
strategies, which include single-strategy absorption phases, a cyclic
competition (`rock-paper-scissors') type of phase, and an uncertain phase in
which the dominant strategy adopted by the population is unpredictable.
Exploiting the pair interaction and mean field approximations, we obtain a
qualitative understanding of the emergence of the single strategy and uncertain
phases. We find the striking phenomenon of strategy revival associated with the
cyclic competition phase and provide a qualitative explanation.Our work
demonstrates that the diversity in the individuals' strategy set can play an
important role in the evolution of strategy distribution in the system. From
the point of view of control, the emergence of the complex phases offers the
possibility for harnessing evolutionary game dynamics through small changes in
individuals' probability of strategy adoption.
