智能合约作为协调问题的解决方案：MIT公开课第4讲

[SQUEAKING] [RUSTLING] [CLICKING] ROBERT TOWNSEND: OK, we'll get started. Thank you for coming. Today is lecture 4, "Smart Contracts as a Solution to a Coordination Problem. It's still about distributed ledgers, but we're going to add on top of that not just information use, but also contracting. The longer subtitle, commodity space with location dates and states. The policy objective is the same. The Pareto criteria, we will also have fragmented markets the way we did last time.

The implementation is going to-- problem is going to have something to do with privately issued securities, which are circulating around as monies. And without the ability to coordinate with their smart contract, there will be market crises. And so we're featuring this multi-agent smart contract. So a little more detail. Extensions of the theory that we started to cover last time, but this time, explicitly about time and risk.

And then we'll talk about getting policy guidance from the data. As I said last time, I'm trying to put discipline on myself and the research, that we shouldn't just be exploring case studies or potential applications that potentially use these new technologies, we want to know what economic problem exists out there and whether or not we can help mitigate the problem. So we're going to use this efficiency benchmark that we did last time, and I'll show you how to use it with actual data, although that's a bit of a summary.

And then we'll, like last time, do some policy guidance that comes from theory. What's the logic according to the theory of what can go wrong when you have privately issued circulating debt? The idea is not to get rid of the debt, but to provide some coordination to avoid these financial crises. And this comes up in at least four seemingly distinct venues, but they have in common this underlying theory. So again, I think you've seen the pattern here, which is, take the theory seriously.

Even when it was designed and written without these kinds of considerations in mind, there are huge lessons to be learned from going back to it and thinking about the new technologies. So again, it's about multi-agent smart contracts on a common ledger, and in particular, at the end, we'll talk about Ethereum and what that is relative to Bitcoin. OK. So extensions of the theory to incorporate risk and intertemporal exchange.

So we had apples and wheat. It's easier to think about borrowing and lending as in getting-- or giving goods up today and receiving goods tomorrow, so the time date is there. But in addition, we're going to have mother nature drawing rainfall and weather realizations. So we need to talk about the state of nature, and that's that little s t. And actually, it could be the entire history from the genesis of states that have been realized over time.

So we index commodities by time and by this history, including contemporary realizations. So little t superscript denotes the history, sub t denotes the contemporary value. The utility of the agents is going to be-- I'll say it in words, discounted expected utility. So we're going to add up the utilities over the time horizon, and we're going to take expectations over these underlying states of nature. So it's discounted by beta, and the expectations are formed with these probabilities of states of nature.

And then we're going to, with this notation, do what we said we were going to do last time, which is turn this into a programming problem. So we're going to maximize this lambda-weighted sum of the utilities of the participants subject to resource constraints. The words are easy. The notation is a little more demanding, but lambdas are the weights, here's the discounted expected utility summing over dates and states with that probability distribution.

And this resource constraint says that consumption in a pure exchange economy, consumption should equal income. So we're just summing up over all the, quote, "endowments" of the finite number-- capital I, it is-- of participants. That's the resources available for, say, distribution. So consumptions can add up to more than that. Again, a very powerful tool, and I'm happy to elaborate on this. We set this max problem up as a Lagrangian, so we kind of repeat the objective function.

And then we have these auxiliary terms which are shadow prices times constraint. So we have the resource constraint written out for each date and state. For every date in state, it's preceded by this shadow price, this Lagrange multiplier, theta, of s of t. And the very nice thing about Lagrangians is as long as we have concavity of the objective functions and convexity of the underlying constraints, the first-order conditions of this max problem are necessary and sufficient for characterizing an optimum.

Here are the first-order conditions. And it simply states in words that the lambda-weighted discounted marginal utility of consumption in a certain history of states should equal the common Lagrange multiplier across all the households. For every date and state, we're equating-- we're reallocating consumption in a way that equates the weighted marginal utilities. So this is-- and we repeat the resource constraint. Just a word about the math, and I'm trying not to do too much of that, there's a lot of these guys for every date and every history of states, and we're writing it out conditionally, but there are tons of them-- of these constraints, tons of Lagrange multipliers.

So this just says weighted marginal utilities for person 1 should be equated to any other person i, repeat the resource constraints, and we get, as a solution, something that looks deceptively simple, which is that the consumption allocation for an agent type i can be captured by a household i specific function g i, which has, as its argument, only the aggregate income. Now the intuition for this is that we're operating kind of a mutual insurance society.

And it's as if everybody were contributing their rice to a community fund, and then that is pooled together, here's the big pile of rice. And now, maybe under the auspices of the monks, that is handed back to households depending on whether their own harvest was high or low. So the implication is, individual harvests are in there, but they're in the stockpile. And once you control for the stockpile in terms of its aggregate income y, the individual harvests don't enter.

So you have this surprising result that consumption should depend on the aggregate and not on the individual shocks. And that's, as you'll see, a benchmark, which is taken to data. There is another implication, because of the concavity, that you'll have co-movement in consumption. People's consumption should go up and down together. Not everyone should eat the same amount. Some will be eating more, some less, but if you track their consumption, it should never cross.

You should never have any period where consumption of one household or region is going up while consumption in the other region is going down. And that's testable. So again, we're working on policy guidance from the data, and the idea is, OK, that's the implication of the theory. How well are people doing? Maybe they're doing just fine. That would be wonderful. It sometimes happens. Or in other instances, things that look terrible, is there a remedy?

That's the simple logic of it. So we're going to take a peek at village India, village Thailand, and come back to this idea of targeting based on the theory more generally. So this is a picture of villages in India that were sampled for 10 years by a crops institute where the economists and business folks were not telling households how to grow crops, but they were gathering the data. ICRISAT data. And here, you can see the year, 70-- 10 years, basically.

The numbers here are 76 through 84. And here are household numbers. And for every household, we're tracking the ups and downs of income. It's normalized around the overall average. So a negative number doesn't mean it

原文超出正文长度上限，此处截断——上游还有内容，完整版见上方「原文 ↗」。