  Cooperation is fundamental for human prosperity. Blockchain, as a trust
machine, is a cooperative institution in cyberspace that supports cooperation
through distributed trust with consensus protocols. While studies in computer
science focus on fault tolerance problems with consensus algorithms, economic
research utilizes incentive designs to analyze agent behaviors. To achieve
cooperation on blockchains, emerging interdisciplinary research introduces
rationality and game-theoretical solution concepts to study the equilibrium
outcomes of various consensus protocols. However, existing studies do not
consider the possibility for agents to learn from historical observations.
Therefore, we abstract a general consensus protocol as a dynamic game
environment, apply a solution concept of bounded rationality to model agent
behavior, and resolve the initial conditions for three different stable
equilibria. In our game, agents imitatively learn the global history in an
evolutionary process toward equilibria, for which we evaluate the outcomes from
both computing and economic perspectives in terms of safety, liveness,
validity, and social welfare. Our research contributes to the literature across
disciplines, including distributed consensus in computer science, game theory
in economics on blockchain consensus, evolutionary game theory at the
intersection of biology and economics, bounded rationality at the interplay
between psychology and economics, and cooperative AI with joint insights into
computing and social science. Finally, we discuss that future protocol design
can better achieve the most desired outcomes of our honest stable equilibria by
increasing the reward-punishment ratio and lowering both the cost-punishment
ratio and the pivotality rate.
