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Game Theory

Overview​

This challenge is designed to test your ability to apply game-theoretic magic such as best responses, dominated strategies, and Nash equilibrium to real-world adversarial scenarios in DeFi. You will construct formal models, estimate key parameters, and analyze the economic feasibility of attacks and defenses across multiple settings.

Submission Requirements​

All work must be submitted to the GitHub repository assigned to you during onboarding. Organize your repository using the following directory structure:

  • /models: Include all mathematical models or formal derivations if applicable.
  • /diagrams: Provide visual illustrations such as payoff diagrams, equilibrium maps, or attack trees.
  • solution.md: Include your formal analysis, explanations, and conclusions.

Mandatory Task​

  • Validator Collusion and Slashing Risk (MANDATORY)

Analyze the strategic behavior of validators in a Cosmos-based staking network where validators can either follow the protocol honestly or attempt collusion for additional rewards. In Tendermint, if ≥ 1⁄3 of power is Byzantine, the chain can halt; if > 2⁄3, the coalition can finalize an arbitrary block.

  1. According to the Tendermint model, define the following parameters:

    • Reward RR for honest participation
    • Additional gain GG from successful collusion
    • Probability pp of detection and slashing
    • Slashing penalty SS

  2. Determine the best-response strategy for an individual validator given the parameters above.

  3. Analyze the Nash equilibrium among NN validators under different values of pp and SS.

  4. Explore how protocol-level changes to detection mechanisms or penalty sizes shift the equilibrium toward greater or lesser collusion risk.

Optional Tasks (You must choose one)​

Option A: MEV Sandwich Attack on DEX Users​

Model the incentives of a MEV searcher performing a sandwich attack against a large DEX trade.

  1. Construct the payoff matrix between:

    • A user who can either submit a large swap as a single transaction or split it across multiple smaller transactions
    • An MEV searcher who can choose to front-run and back-run (sandwich) the trade or abstain from interference

  2. Incorporate the following parameters:

    • Gas cost per transaction
    • Slippage effects on the user’s execution
    • Expected profit margin of the searcher from the sandwich

  3. Analyze the user’s best-response strategy under varying gas price and slippage protection levels.

  4. Evaluate the competitive equilibrium among multiple MEV searchers, considering the diminishing returns from overlapping attacks.

Option B: Attacks on Governance​

Governance Attack

Evaluate the feasibility of a governance attack under the Terra Blockchain governance, and identify the risks and implications that could arise given different situations. The analysis should propose a conceptual framework that enables the governance to systematically assess the risk of governance attacks, assuming that Quorum Q = 40 %, Approval T = 50 %, Veto V = 33.4 %, respond:

  • The feasibility of a governance attack under the current quorum rules.
  • The risks and trade-offs associated with potentially lowering the quorum threshold.
  • The impact of the current LUNA tokenomics on the potential distribution of voting power.
  • The potential return on investment (ROI) for a malicious actor attempting to carry out a successful attack.
  • Relevant factors such as token concentration, historical participation, and existing defense mechanisms.

Deliverables​

For each part of the challenge, you must provide:

  • Formal models: Include all mathematical expressions, payoff functions, and equilibrium characterizations.
  • Diagrams: Provide clear visualizations such as attack decision trees, cost-benefit plots, or equilibrium maps.
  • Final writeup: Deliver a formal summary explaining your models, outlining key insights, and assessing the effectiveness of different defensive strategies.

Purpose and Learning Outcomes​

This challenge is intended to cultivate your ability to:

  • Identify and formalize the economic incentives driving attacker and defender behavior in DeFi systems.
  • Apply game-theoretic tools to analyze adversarial interactions within protocol design.
  • Produce technically rigorous research artifacts suitable for internal use or external publication.

How to Submit Your Work​

  • All work for your chosen challenge must be committed to the GitHub repository assigned to you during onboarding.
  • Include diagrams/charts to illustrate key points.
  • Maintain a technical focus throughout.
  • No need to delve extremely deep into the underlying systems—focus on tokenomics, and wisely manage your time.
  • Structure your commits clearly, with meaningful messages that outline the progress of your work, see Git Practices for reference.
  • Ensure your final submission is well-organized, with supporting files, diagrams, or models included as needed.

Helpful Resources 🎓​

A quick knowledge boost before you dive in:

  1. Byzantine Consensus Algorithm in Tendermint.
  2. MEV and me.
  3. Cosmos Governance Module.

🍀 Good luck!