8 research outputs found
Learning Strong Substitutes Demand via Queries
This paper addresses the computational challenges of learning strong
substitutes demand when given access to a demand (or valuation) oracle. Strong
substitutes demand generalises the well-studied gross substitutes demand to a
multi-unit setting. Recent work by Baldwin and Klemperer shows that any such
demand can be expressed in a natural way as a finite list of weighted bid
vectors. A simplified version of this bidding language has been used by the
Bank of England.
Assuming access to a demand oracle, we provide an algorithm that computes the
unique list of weighted bid vectors corresponding to a bidder's demand
preferences. In the special case where their demand can be expressed using
positive bids only, we have an efficient algorithm that learns this list in
linear time. We also show super-polynomial lower bounds on the query complexity
of computing the list of bids in the general case where bids may be positive
and negative. Our algorithms constitute the first systematic approach for
bidders to construct a bid list corresponding to non-trivial demand, allowing
them to participate in `product-mix' auctions
Differential Liquidity Provision in Uniswap v3 and Implications for Contract Design
Decentralized exchanges (DEXs) provide a means for users to trade pairs of
assets on-chain without the need of a trusted third party to effectuate a
trade. Amongst these, constant function market maker (CFMM) DEXs such as
Uniswap handle the most volume of trades between ERC-20 tokens. With the
introduction of Uniswap v3, liquidity providers are given the option to
differentially allocate liquidity to be used for trades that occur within
specific price intervals. In this paper, we formalize the profit and loss that
liquidity providers can earn when providing specific liquidity positions to a
contract. With this in hand, we are able to compute optimal liquidity
allocations for liquidity providers who hold beliefs over how prices evolve
over time. Ultimately, we use this tool to shed light on the design question
regarding how v3 contracts should partition price space for permissible
liquidity allocations. Our results show that a richer space of potential
partitions can simultaneously benefit both liquidity providers and traders.Comment: 48 pages, 13 figure
Strategic Liquidity Provision in Uniswap v3
Uniswap v3 is the largest decentralized exchange for digital currencies. A
novelty of its design is that it allows a liquidity provider (LP) to allocate
liquidity to one or more closed intervals of the price of an asset instead of
the full range of possible prices. An LP earns fee rewards proportional to the
amount of its liquidity allocation when prices move in this interval. This
induces the problem of {\em strategic liquidity provision}: smaller intervals
result in higher concentration of liquidity and correspondingly larger fees
when the price remains in the interval, but with higher risk as prices may exit
the interval leaving the LP with no fee rewards. Although reallocating
liquidity to new intervals can mitigate this loss, it comes at a cost, as LPs
must expend gas fees to do so. We formalize the dynamic liquidity provision
problem and focus on a general class of strategies for which we provide a
neural network-based optimization framework for maximizing LP earnings. We
model a single LP that faces an exogenous sequence of price changes that arise
from arbitrage and non-arbitrage trades in the decentralized exchange. We
present experimental results informed by historical price data that demonstrate
large improvements in LP earnings over existing allocation strategy baselines.
Moreover we provide insight into qualitative differences in optimal LP
behaviour in different economic environments
Optimally Deceiving a Learning Leader in Stackelberg Games
Recent results have shown that algorithms for learning the optimal commitment in a Stackelberg game are susceptible to manipulation by the follower. These learning algorithms operate by querying the best responses of the follower, who consequently can deceive the algorithm by using fake best responses, typically by responding according to fake payoffs that are different from the actual ones. For this strategic behavior to be successful, the main challenge faced by the follower is to pinpoint the fake payoffs that would make the learning algorithm output a commitment that benefits them the most. While this problem has been considered before, the related literature has only focused on a simple setting where the follower can only choose from a finite set of payoff matrices, thus leaving the general version of the problem unanswered. In this paper, we fill this gap by showing that it is always possible for the follower to efficiently compute (near-)optimal fake payoffs, for various scenarios of learning interaction between the leader and the follower. Our results also establish an interesting connection between the follower’s deception and the leader’s maximin utility: through deception, the follower can induce almost any (fake) Stackelberg equilibrium if and only if the leader obtains at least their maximin utility in this equilibrium
Logarithmic Query Complexity for Approximate Nash Computation in Large Games
We investigate the problem of equilibrium computation for “large” n-player games. Large
games have a Lipschitz-type property that no single player’s utility is greatly affected by any
other individual player’s actions. In this paper, we mostly focus on the case where any change of
strategy by a player causes other players’ payoffs to change by at most 1
n
. We study algorithms
having query access to the game’s payoff function, aiming to find ε-Nash equilibria. We seek
algorithms that obtain ε as small as possible, in time polynomial in n.
Our main result is a randomised algorithm that achieves ε approaching 1
8
for 2-strategy games
in a completely uncoupled setting, where each player observes her own payoff to a query, and
adjusts her behaviour independently of other players’ payoffs/actions. O(log n) rounds/queries
are required. We also show how to obtain a slight improvement over 1
8
, by introducing a small
amount of communication between the players.
Finally, we give extension of our results to large games with more than two strategies per
player, and alternative largeness parameters
Welfare-Maximizing Pooled Testing
Accepted at EC'23. (Exemplary track paper award)International audienceLarge-scale testing is crucial in pandemic containment, but resources are often prohibitively constrained. We study the optimal application of pooled testing for populations that are heterogeneous with respect to an individual's infection probability and utility that materializes if included in a negative test. We show that the welfare gain from overlapping testing over non-overlapping testing is bounded. Moreover, non-overlapping allocations, which are both conceptually and logistically simpler to implement, are empirically near-optimal, and we design a heuristic mechanism for finding these near-optimal test allocations. In numerical experiments, we highlight the efficacy and viability of our heuristic in practice. We also implement and provide experimental evidence on the benefits of utility-weighted pooled testing in a real-world setting. Our pilot study at a higher education research institute in Mexico finds no evidence that performance and mental health outcomes of participants in our testing regime are worse than under the first-best counterfactual of full access for individuals without testing