The Game Theory in the World of DeFi Part I

Game theory is an intrinsic component of the crypto ecosystem and has been particularly relevant in DeFi. From incentives models to governance voting dynamics, game theory is at the center of many of the protocol design aspects of DeFi. However, within the DeFi community, there is very little coverage about the foundations of game theory. So we thought we dedicate a small post to cover some of the fundamental ideas behind game theory.

The history of game theory is attached to the history of computer science. Much of the current research in game theory dates back to the work of computer science pioneers like Alan Turing or John Von Neumann. The famous Nash equilibrium popularized by the movie “A Beautiful Mind” is the cornerstone of many gamified interactions in modern systems. However, modeling a DeFi protocol using the principles of game theory many times goes beyond the Nash equilibrium. A good place to start understanding the implications architecting DeFi protocols using principles of game theory is to understand the different types of games that we typically encountered in our social or economic interactions.

DeFi protocols are an ideal candidate for applying game theorerical principles as they involve many participants in their interactions.

· Participant Design: Game theory can be used to optimize the decision of a participant in order to obtain the maximum utility.

· Mechanism Design: Inverse game theory focus on designing a game for a group of intelligent participant. Auctions are a classic example of mechanism design.

5 Types of Games Relevant to DeFi Protocols

Since its inception in the 1940s, game theory has focused on modeling the most common interaction patterns that now we are seeing every day in multi-agent AI systems. Understanding the different types of game dynamics in an environment is a key element to design the dynamics of DeFi protocols. At a high level there is a five-element criteria that I like to use to understand the game dynamics in DeFi protocols:

Symmetric vs. Asymmetric.

One of the simplest classifications of games is based on their symmetry. A symmetric game describes an environment in which each player has the same goals and the results will only depend on the strategies involved. Chess is a classic example of a symmetric game. Many of the situations we encountered in the real world lack the mathematical elegance of symmetry as participants often have different and even conflicting goals. A business negotiation is an example of asymmetric game in which each party has different goals and evaluates the results from a different perspective (ex: winning a contract vs. minimizing an investment).

Perfect vs. Imperfect Information

Another important categorization of games is based on the type of information available. A perfect information game refers to an environment in which each player can see the other player’s moves. Chess, again, is an example of a perfect information game. Many modern interactions are based on environments in which the moves from each player are hidden from other players and game theory classifies those scenarios as imperfect information games. From card games like poker to self-driving car scenarios, imperfect information games are all around us.

Cooperative vs. Non-Cooperative

A cooperative game environment is one in which the different participants can establish alliances in order to maximize the end result. Contractual negotiations are often modeled as cooperative games. Non-cooperative scenarios describe environments in which players are forbidden from forming alliances. Wars are the ultimate example of non-cooperative games.

Simultaneous vs. Sequential

A sequential game takes place in an environment in which each player has information about the other player earlier actions. Board games are mostly sequential in nature. Simultaneous games represent scenarios in which both players can take concurrent actions. Securities trading is an example of simultaneous games.

Zero-Sum vs. Non-Zero-Sum

A zero-sum game refers to a scenario in which the gains or one player always come translate into looses for other players. Board games are examples of zero-sum games. Non-zero-sum games are often encountered in scenarios in which multiple players can benefit from the actions of one players. Economic interactions in which multiple participants collaborate to increase the size of the market is an example of a non-zero-sum game.

These five types of games are very present in the current generation of DeFi protocols. In the second part of this essay, we will expand into other core aspects of game theory such as the Nash equilibrium which are, believe it or not, super relevant to DeFi.