Evolutionary Game Theory and Cooperation

Summary & takeaways

This literature review is about cooperation under the lens of evolutionary game theory.

Understanding how cooperation forms, in a more or less emergent or institutionalized way, instructs how to better design mechanisms that incentivize it correctly.

Cooperation, in turn, is a key ally of the protocol designer who wants to rely on community and a DAO to perform the duties of this protocol, including but not limited to governance.

Key concepts

  • Evolutionary games where strategies evolve and are selected over time among participants.
  • Incentive games where rewards and punishments are awarded by game participants to other game participants. Importantly, a distinction is to be made between pool incentives (akin to institutions) and peer incentives (akin to emergent behavior).
  • Networks, notably network topology and gossip, which heavily influence how strategies will evolve.
  • Automata, as formal description of player strategies based on local interactions.

Remarks on applicability to on-chain protocols

Cooperation has a limited applicability. Nowak defines it as “A cooperator is someone who pays a cost, c, for another individual to receive a benefit, b.”. Sigmund et al. describe public goods games that rely on an objective notion of cooperation. Depending on any non-objective definition of cooperation, eg. intersubjective, will require another mechanism to define it.

Literature review: Evolutionary Cooperation

The Evolution of Cooperation

Five Rules for the Evolution of Cooperation

  • Source: Five rules for the evolution of cooperation - PMC
  • Authors: Martin A Nowak
  • Year: 2006
  • Description: Overview of how cooperation evolves based on 5 cooperation rules. For each, are given conditions for the network-wide success of cooperation over competition induced by natural selection.
  • Relevance: Direct reciprocity, indirect reciprocity, network reciprocity and group selection are rules that can be observed or engineered in crypto-networks.

Social learning promotes institutions for governing the commons

  • Source: https://core.ac.uk/download/pdf/33900899.pdf
  • Authors: Karl Sigmund, Hannelore De Silva, Christoph Hauert, Arne Traulsen
  • Year: 2011
  • Description: Study of pool punishment versus peer punishment in public goods games. Pool punishment produces more stable outcomes, as it allows preventing free-riders. Institutions are instances of pool punishment mechanisms.
  • Relevance: Provides additional nuance to the incentives games and the free-rider problem.

Axelrod’s Metanorm Games on Networks

  • Source: Axelrod's Metanorm Games on Networks
  • Authors: José M. Galán, Maciej M. Łatek, Seyed M. Mussavi Rizi
  • Year: 2011
  • Description: Metanorms are games where players punish those who fail to punish norm violators. Mathematical analysis and simulations. Different network topolgies and initial populations heavily influence whether cooperation spreads. 2 attraction zones appear: norm collapse or norm establishment.
  • Relevance: Useful mathematical model and simulation results.

The Effect of Incentives and Meta-incentives on the Evolution of Cooperation

  • Source: The Effect of Incentives and Meta-incentives on the Evolution of Cooperation
  • Authors: Isamu Okada , Hitoshi Yamamoto, Fujio Toriumi, Tatsuya Sasaki
  • Year: 2015
  • Description: Meta-incentives games (MIGs, a generalization of metanorms games) are games with incentives given to cooperators (or free-riders) and meta-incentives given to players who should be giving incentives. Cooperation will be reached if rewards, punishments, meta-rewards and meta-punishments are present. Relies on meta-incentives being given unquestionably as long as incentives are themselves given.
  • Relevance: Extensive classification and nomenclature. Discussion on how to design MIGs.

How to keep punishment to maintain cooperation: Introducing social vaccine

  • Source: https://www.sciencedirect.com/science/article/pii/S0378437115007189
  • Authors: Hitoshi Yamamoto, Isamu Okada
  • Year: 2016
  • Description: Introduction of perturbation in metanorms game in the form of non-cooperators. This results in heightened strength of the cooperative regime.
  • Relevance: Improvement on metanorms and MIGs via perturbations, of practical use to the game designer. Agent based simulation.
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Comparison to Peer Prediction

The peer prediction literature shares common roots in the analysis of strategic behavior of agents and study of equilibrium conditions leveraging game theory.

But they differ in key points:

  • Methodologically, Evolutionary Game Theory relies fundamentally on Agent Based Modeling, leveraging local properties of each agent then deducing equilibrium conditions of a network of agents depending on initial conditions. Instead, Peer Prediction is rooted in on formal analysis of peer prediction games, where each peer is considered a rational agent and strong epistemic assumptions are taken (like shared beliefs).
  • Evolutionary Game Theory will look into how individual strategies propagate in a network of agents, with a fundamentally dynamic view and try to understand under which conditions (incentive mechanism, topology…) different equilibria emerge. Peer prediction will rather try to achieve DSIC mechanisms, where all agents are expected to adapt their behavior to the mechanism. If not DSIC, Bayes-Nash equilibria are studied, characterizing equilibrium without guaranteeing it happens.

Let’s note that a peer prediction mechanism that doesn’t display DSIC but has interesting Bayes-Nash equilibria might be interesting to further study under the evolutionary framework.

As noted in Resnick et al., “Eliciting Informative Feedback: The Peer-Prediction Method”:

Subjective evaluations of ratings could be elicited directly instead of relying on correlations between ratings. For example, the news and commentary site Slashdot.org allows meta-moderators to rate the ratings of comments given by regular moderators. Meta-evaluation incurs an obvious inefficiency, since the effort to rate evaluations could presumably be put to better use in rating comments or other products that are a site’s primary product of interest. Moreover, meta-evaluation merely pushes the problem of motivating effort and honest reporting up one level, to ratings of evaluations. Thus, scoring evaluations in comparison to other evaluations is preferable.