Game Theory

Game Theory for Crypto

Strategic analysis framework for understanding and designing incentive systems in web3. "Every protocol is a game. Every token is an incentive. Every user is a player. Understand the rules, or become the played."

When to Use This Skill

Analyzing tokenomics for exploits or misaligned incentives Evaluating governance proposals and voting mechanisms Understanding MEV and adversarial transaction ordering Designing auction mechanisms (NFT drops, token sales, liquidations) Predicting how rational actors will behave in a system Identifying attack vectors in DeFi protocols Modeling liquidity provision strategies Assessing protocol sustainability

The Five Questions

For any protocol or mechanism, ask: Who are the players? (Users, LPs, validators, searchers, governance token holders) What are their strategies? (Actions available to each player) What are the payoffs? (How does each outcome affect each player?) What information do they have? (Complete, incomplete, asymmetric?) What's the equilibrium? (Where do rational actors end up?)

Analysis Template

• ## Protocol: [Name]
• ### Players
• Player A: [Role, objectives, constraints]
• Player B: [Role, objectives, constraints]
• ...
• ### Strategy Space
• Player A can: [List possible actions]
• Player B can: [List possible actions]
• ### Payoff Structure
• If (A does X, B does Y): A gets [payoff], B gets [payoff]
• ...
• ### Information Structure
• Public information: [What everyone knows]
• Private information: [What only some players know]
• Observable actions: [What can be seen on-chain]
• ### Equilibrium Analysis
• Nash equilibrium: [Stable outcome where no player wants to deviate]
• Dominant strategies: [Strategies that are always best regardless of others]
• Potential exploits: [Deviations that benefit attackers]
• ### Recommendations
• [Design changes to improve incentive alignment]

Reference Documents

DocumentUse CaseNash EquilibriumFinding stable outcomes in strategic interactionsMechanism DesignDesigning systems with desired equilibriaAuction TheoryToken sales, NFT drops, liquidationsMEV Game TheoryAdversarial transaction orderingTokenomics AnalysisEvaluating token incentive structuresGovernance AttacksVoting manipulation and captureLiquidity GamesLP strategies and impermanent lossInformation EconomicsAsymmetric information and signaling

Nash Equilibrium

A state where no player can improve their payoff by unilaterally changing strategy. The "stable" outcome of a game. Crypto application: In a staking system, Nash equilibrium determines the stake distribution across validators.

Dominant Strategy

A strategy that's optimal regardless of what others do. Crypto application: In a second-price auction, bidding your true value is dominant.

Pareto Efficiency

An outcome where no one can be made better off without making someone worse off. Crypto application: AMM fee structures try to be Pareto efficient for traders and LPs.

Mechanism Design

"Reverse game theory" - designing rules to achieve desired outcomes. Crypto application: Designing token vesting schedules to align long-term incentives.

Schelling Point

A solution people converge on without communication. Crypto application: Why certain price levels act as psychological support/resistance.

Incentive Compatibility

When truthful behavior is optimal for participants. Crypto application: Oracle designs where honest reporting is the dominant strategy.

Common Knowledge

Everyone knows X, everyone knows everyone knows X, infinitely recursive. Crypto application: Public blockchain state creates common knowledge of balances/positions.

Pattern 1: The Tragedy of the Commons

Structure: Shared resource, individual incentive to overuse, collective harm. Crypto examples: Gas price bidding during congestion Governance token voting apathy MEV extraction degrading UX Solution approaches: Harberger taxes Quadratic mechanisms Commitment schemes

Pattern 2: The Prisoner's Dilemma

Structure: Individual rationality leads to collective irrationality. Crypto examples: Liquidity mining mercenaries (farm and dump) Race-to-bottom validator fees Bridge security (each chain wants others to secure) Solution approaches: Repeated games (reputation) Commitment mechanisms (staking/slashing) Mechanism redesign

Pattern 3: The Coordination Game

Structure: Multiple equilibria, players want to coordinate but may fail. Crypto examples: Which L2 to use? Token standard adoption Hard fork coordination Solution approaches: Focal points (Schelling points) Sequential moves (first mover advantage) Communication mechanisms

Pattern 4: The Principal-Agent Problem

Structure: One party acts on behalf of another with misaligned incentives. Crypto examples: Protocol team vs token holders Delegates in governance Fund managers Solution approaches: Incentive alignment (token vesting) Monitoring (transparency) Bonding (skin in game)

Pattern 5: Adverse Selection

Structure: Information asymmetry leads to market breakdown. Crypto examples: Token launches (team knows more than buyers) Insurance protocols (risky users more likely to buy) Lending (borrowers know their risk better) Solution approaches: Signaling (lock-ups, audits) Screening (credit scores, history) Pooling equilibria

Pattern 6: Moral Hazard

Structure: Hidden action after agreement leads to risk-taking. Crypto examples: Protocols with insurance may take more risk Bailout expectations encourage leverage Anonymous teams may rug Solution approaches: Monitoring and transparency Incentive alignment Reputation systems

The MEV Game

Players: Users, searchers, builders, validators Key insight: Transaction ordering is a game; users are often the losers See: MEV Strategies

The Liquidity Game

Players: LPs, traders, arbitrageurs Key insight: Impermanent loss is the cost of being adversely selected against See: Liquidity Games

The Governance Game

Players: Token holders, delegates, protocol team Key insight: Rational apathy + concentrated interests = capture See: Governance Attacks

The Staking Game

Players: Stakers, validators, delegators Key insight: Security budget must exceed attack profit See: Tokenomics Analysis

The Oracle Game

Players: Data providers, consumers, attackers Key insight: Profit from manipulation must be less than cost See: Mechanism Design

Tokenomics Red Flags

Insiders can sell before others (vesting asymmetry) Inflation benefits few, dilutes many No sink mechanisms (perpetual selling pressure) Rewards without risk (free money = someone else paying)

Governance Red Flags

Low quorum thresholds (minority capture) No time delay (flash loan attacks) Token voting only (plutocracy) Delegates with no skin in game

Mechanism Red Flags

First-come-first-served (bot advantage) Sealed bids without commitment (frontrunning) Rebates/refunds (MEV extraction) Complex formulas (hidden exploits)

Repeated Games and Reputation

Single-shot games often have bad equilibria. Repetition enables cooperation through: Trigger strategies (cooperate until defection) Reputation building (costly to destroy) Future value (patient players cooperate more) Crypto application: Why anonymous actors behave worse than doxxed teams.

Evolutionary Game Theory

Strategies that survive competitive selection. Relevant for: Which protocols survive long-term Memetic competition between narratives Bot strategy evolution

Bayesian Games

Games with incomplete information. Players have beliefs about others' types. Crypto application: Trading with unknown counterparties, evaluating anonymous teams.

Cooperative Game Theory

When players can form binding coalitions. Crypto application: MEV extraction coalitions, validator cartels, governance blocs.

Algorithmic Game Theory

Computational aspects of game theory. Crypto application: On-chain game computation limits, gas-efficient mechanism design.

Step 1: Model the Game

Identify all players (including those not obvious) Map complete strategy spaces Define payoff functions precisely Specify information structure

Step 2: Find Equilibria

Check for dominant strategies Compute Nash equilibria Identify Pareto improvements Consider trembling-hand perfection

Step 3: Stress Test

What if players collude? What if new players enter? What if information leaks? What if parameters change?

Step 4: Recommend

Mechanism changes to improve equilibrium Monitoring to detect deviations Parameter bounds to maintain stability

Foundational Texts

"Theory of Games and Economic Behavior" - von Neumann & Morgenstern "A Beautiful Mind" (Nash's life, accessible intro) "The Strategy of Conflict" - Schelling "Mechanism Design Theory" - Myerson (Nobel lecture)

Crypto-Specific

"Flash Boys 2.0" - MEV paper "SoK: DeFi Attacks" - Systemization of DeFi exploits "Clockwork Finance" - MEV and mechanism design Paradigm research blog

Tools

Nashpy (Python game theory library) Gambit (game theory software) Agent-based modeling frameworks