MIT OpenCourseWareLecture 8: Mechanism Design and Incentives vs. Protocols and Notions of Trust
MIT OpenCourseWare
Bridging Economics and Computer Science 0:00
Robert Townsend opens the eighth lecture by framing the day's theme as a continued effort to put computer science and economics on the same page. The contrast for the day is mechanism design and incentives, the economist's way of thinking about trust, against protocols and notions of trust from computer science. He previews a plan to work through an information constrained allocation example, then move to implementing that allocation without a planner using computer science tools, and finally to revisit the trust question through the Byzantine Generals problem, drawing on a paper by Steve Morris and Hyun Shin.
Setting Up the Agrarian Insurance Example 2:34
Townsend introduces a pure exchange economy with two agents, a villa and a monastery, over one period. The villa, agent 1, has a privately observed random endowment described by a parameter theta, while the monastery, agent 2, has a publicly known endowment and is risk-neutral, compared to the villa which is risk-averse. The two agree on a rule that maps a message sent by the villa into transfers between them, framed as if the villa pays a tax to the monastery, though the transfer can run either direction, since this is fundamentally an insurance arrangement.
Turning Private Information Into a Truth Constraint 6:02
Townsend shows that once the villa knows its true theta, it chooses whatever message maximizes its own payoff, even if that message is a lie. Rather than track this indirectly, he defines a new allocation rule that only accepts direct announcements of theta and builds in the agent's optimal response automatically. This produces what looks like a truth-telling constraint, though he stresses it is not a demand for honesty, just a mathematical shortcut that reproduces exactly the same outcomes as the original message game, letting the same optimal mechanisms be found by imposing this constraint directly.
Why Lotteries Improve Risk Sharing 12:00
With only one good, the incentive constraint is severe: better allocations for one theta than another are impossible without inviting lies, which pushes the outcome toward autarky, no trade at all. Adding more goods or introducing randomness relaxes this. By turning the allocation into a lottery over transfers, a mean variance trade-off appears, agents with different risk attitudes can be steered toward truth by facing riskier payoffs for lying. This lottery formulation also turns the problem into a linear program, solvable with software like Gurobi even when there are hundreds of thousands of variables, useful both for farm economies with weather-driven harvests and for financial markets with private portfolios.
Extending to Two Periods 21:00
Townsend extends the model to two dates, with the villa's endowment following a Markov process and the allocation at date two allowed to depend on what was announced at date one. Working backward, incentive constraints must hold at date two given any history, and then at date one given that date-two truth-telling is guaranteed. Without private information, standard risk-sharing theory says the optimal rule reduces to a static one, pooling resources and always applying the same sharing rule. With private information, however, that full-insurance outcome is not incentive-compatible, since the villa would always claim low income.
Borrowing and Lending as a Compromise 27:02
Townsend notes that plain borrowing and lending, letting the agent decide whether to borrow when income is low or deposit when income is high, turns out to satisfy incentive-compatibility even under private information. But it is not optimal, since if both choices are strictly preferred at each state, the incentive constraints are slack, which would imply full insurance is achievable, contradicting its infeasibility. The truly optimal scheme is a hybrid that blends insurance and credit together, which mirrors real-world products like flexible loans allowing deferred repayment, and argues against separating insurance and lending businesses since they need to be coordinated within one contract.
Smart Contracts Without a Planner 32:01
Townsend reinterprets the "planner" of economics as something that need not be a trusted third party at all. The information-constrained allocation rule can be written as code, a smart contract, that agents enter voluntarily after understanding how it works, with their commitment publicly recorded so a judge could later verify consent. Resources can be placed in escrow up front, based on the worst-case payment the contract could require, solving the problem of limited commitment. Messages can also be encrypted so the contract computes on encrypted values without seeing the raw numbers, with the history of messages stored securely, similar to how Bitcoin's transaction history sits in Merkle tree archives.
Layer 1 Versus Layer 2 Execution 35:33
Townsend distinguishes between code that must be validated step by step by every node, as happens on Ethereum's layer 1, and a smart contract that agents have already agreed to and understand, which does not need line by line validation. This is the idea behind layer 2, where the contract's logic runs off-chain while the resulting balance transfers are recorded on-chain, on the ledgers agents hold. He corrects a labeling mistake in his own diagram, clarifying that the contract execution belongs off-chain while the ledger updates belong on-chain.
Comparing Validation Protocols 38:03
Townsend turns toward protocols and notions of trust, starting with a look at validation algorithms in systems like Bitcoin and Ethereum before returning to the tension between following a fixed protocol and following incentives. Bitcoin's validation relies on solving a costly cryptographic puzzle, using significant electricity and time, where whoever solves it first validates the batch of transactions, and since solving requires trial and error, the winner is effectively random. Because most participants are assumed honest, the odds that a randomly chosen validator is malicious stay low, but he notes that other, faster and cheaper validation algorithms exist beyond Bitcoin's approach.
Consensus methods beyond proof of work 40:03
Besides Bitcoin's proof of work, other ways exist to reach agreement even when some computers are faulty or malicious. Practical Byzantine Fault-Tolerant algorithms need three times the number of failing nodes plus one honest replica to determine the truth, and they pick a rotating leader from a known membership list, making this suited to closed systems like a company. Proof of authority puts one approver in charge, such as a central bank. Proof of stake picks validators at random and weights votes by how many coins someone holds. Federated Byzantine Agreement, developed by Ripple and Stellar, lets each node choose which other nodes it trusts, called a quorum slice, and overall agreement depends on how these slices overlap.
Miners, incentives, and Nash equilibrium 43:33
Economists first questioned whether Bitcoin's protocol truly forms a Nash equilibrium, since mining has often concentrated among few players who pool risk into syndicates. Validators can also be paid to prioritize a submitted block, which resembles bribery, raising further incentive concerns.
The Byzantine Generals Problem 45:34
Two generals must attack together to beat an unprepared enemy, but messages between them can get lost with small probability epsilon. Rubinstein's related "Email Problem" and Morris and Shin's analysis show that rational, self-interested behavior without commitment conflicts with the natural message-and-confirmation protocol.
Optimal protocol versus rational incentives 54:00
Under an optimal protocol, the first general attacks whenever he learns the enemy is unprepared, and the second attacks upon receiving just one message, without waiting for confirmation. This produces a coordinated attack almost whenever possible, but it only works if generals actually follow it rather than reasoning strategically about missing confirmations.
Why strategic reasoning breaks coordination 1:00:31
Once modeled as a genuine game, both generals never attack, even when messages almost always arrive, because each keeps calculating that the other, lacking confirmation, probably won't attack either. A student notes this suggests validation should sometimes be limited rather than expanded, and Townsend agrees that removing or committing not to send confirmation messages can fix the problem.
Trust, computer science, and economics 1:06:31
Townsend closes by distinguishing computer science's technical sense of trust from economics' broader one, arguing blockchain components, distributed ledgers, smart contracts, encryption, should be understood separately rather than assumed to require decentralized validation. He is comfortable relying on trusted third parties like Amazon or Google, since trust already pervades data systems, and the real task is deciding where trust lies and whether it works well. He closes by previewing the next lecture on cryptography and mechanism design.
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