Direct reciprocity between individuals that use different strategy spaces.

Area of Science:

• Game Theory
• Evolutionary Biology
• Behavioral Economics

Background:

• Direct reciprocity models often assume uniform strategy spaces.
• Players in repeated interactions can adapt strategies based on prior outcomes.
• Understanding strategy space dynamics is crucial for cooperation models.

Purpose of the Study:

• To investigate learning and evolutionary dynamics when players utilize different strategy spaces.
• To compare the long-term payoffs of memory-1, reactive, and unconditional strategies in the iterated donation game.
• To analyze the impact of selection strength and cost-to-benefit ratios on strategy dominance.

Main Methods:

• Analysis of pairwise learning processes in an infinitely repeated donation game.
• Comparison of three distinct strategy spaces: memory-1, reactive, and unconditional.
• Computation of long-term average payoffs under varying selection pressures.

Main Results:

• Smaller strategy spaces can outperform larger ones, challenging existing assumptions.
• Unconditional strategies dominate reactive and memory-1 strategies under weak selection.
• Reactive strategies dominate memory-1 strategies under intermediate selection.
• Memory-1 strategies dominate only under strong selection with a low cost-to-benefit ratio.
• A social dilemma emerges: maximal payoff requires larger spaces, but smaller spaces dominate.

Conclusions:

• Strategy space size significantly impacts outcomes in direct reciprocity.
• The dominance hierarchy of strategies is contingent on selection intensity and game parameters.
• The interaction between different strategy spaces can lead to suboptimal collective outcomes, resembling a social dilemma.