Networked Decision-Making Dynamics Based on Fair, Extortionate and Generous Strategies in Iterated Public Goods Games

Iterated games constitute an important topic of evolutionary game theory and shape the human long-run behaviors in social systems. A new class of memory-one strategies for iterated game contexts, called zero-determinant (ZD) strategies, have received considerable attention. Based on the iterated public goods games (IPGG), we investigates the evolutionary dynamics of three ZDs, which formulate three typical human behaviors: the fair strategy (proportional Tit-for-Tat,
$pTFT$
), the exploitative strategy (extortion,
$E$
) and generous strategy (generosity,
$G$
). In the context of replicator dynamics, the evolutionary prospects of
$E$
and
$G$
are shown to be susceptible to both the group size of IPGG and the slope of the linear ZD relation. Next, decision-makings between
$G$
and
$E$
are explored on complex networks, and the theoretical analyses show that the gaming system can converge to one of the equilibria full-
$E$
or full-
$G$
, depending on the ZD slope and the number of neighbors. For network topologies with fewer neighbors and the linear ZD relation with larger slope, agents tend to choose the generous strategies. In the competition with
$pTFT$
, generous strategy gains an upper hand, while the extortionate strategy will be suppressed. The results provide some new insights into the evolutionary outcomes of iterated games on complex networks.