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 ## Core Framework ### The Five Questions For any protocol or mechanism, ask: 1. **Who are the players?** (Users, LPs, validators, searchers, governance token holders) 2. **What are their strategies?** (Actions available to each player) 3. **What are the payoffs?** (How does each outcome affect each player?) 4. **What information do they have?** (Complete, incomplete, asymmetric?) 5. **What's the equilibrium?** (Where do rational actors end up?) ### Analysis Template ```markdown ## 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 | Document | Use Case | |----------|----------| | [Nash Equilibrium](references/nash-equilibrium.md) | Finding stable outcomes in strategic interactions | | [Mechanism Design](references/mechanism-design.md) | Designing systems with desired equilibria | | [Auction Theory](references/auction-theory.md) | Token sales, NFT drops, liquidations | | [MEV Game Theory](references/mev-strategies.md) | Adversarial transaction ordering | | [Tokenomics Analysis](references/tokenomics-analysis.md) | Evaluating token incentive structures | | [Governance Attacks](references/governance-attacks.md) | Voting manipulation and capture | | [Liquidity Games](references/liquidity-games.md) | LP strategies and impermanent loss | | [Information Economics](references/information-economics.md) | Asymmetric information and signaling | ## Quick Concepts ### 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. ## Analysis Patterns ### 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 ## Common Crypto Games ### The MEV Game **Players:** Users, searchers, builders, validators **Key insight:** Transaction ordering is a game; users are often the losers See: [MEV Strategies](references/mev-strategies.md) ### The Liquidity Game **Players:** LPs, traders, arbitrageurs **Key insight:** Impermanent loss is the cost of being adversely selected against See: [Liquidity Games](references/liquidity-games.md) ### The Governance Game **Players:** Token holders, delegates, protocol team **Key insight:** Rational apathy + concentrated interests = capture See: [Governance Attacks](references/governance-attacks.md) ### The Staking Game **Players:** Stakers, validators, delegators **Key insight:** Security budget must exceed attack profit See: [Tokenomics Analysis](references/tokenomics-analysis.md) ### The Oracle Game **Players:** Data providers, consumers, attackers **Key insight:** Profit from manipulation must be less than cost See: [Mechanism Design](references/mechanism-design.md) ## Red Flags in Protocol 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) ## Advanced Topics ### 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. ## Methodology ### 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 ## Resources ### 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