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Register a new userSecurities Based Decision Markets
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Added by
Wenlong Wang
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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Decision markets are mechanisms for selecting one among a set of actions based on forecasts about their consequences. Decision markets that are based on scoring rules have been proven to offer incentive compatibility analogous to properly incentivised prediction markets. However, in contrast to prediction markets, it is unclear how to implement decision markets such that forecasting is done through the trading of securities. We here propose such a securities based implementation, and show that it offers the same expected payoff as the corresponding scoring rules based decision market. The distribution of realised payoffs, however, might differ. Our analysis expands the knowledge on forecasting based decision making and provides novel insights for intuitive and easy-to-use decision market implementations.
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We design a prediction market to recover a complete and fully general probability distribution over a random variable. Traders buy and sell interval securities that pay $1 if the outcome falls into an interval and $0 otherwise. Our market takes the form of a central automated market maker and allows traders to express interval endpoints of arbitrary precision. We present two designs in both of which market operations take time logarithmic in the number of intervals (that traders distinguish), providing the first computationally efficient market for a continuous variable. Our first design replicates the popular logarithmic market scoring rule (LMSR), but operates exponentially faster than a standard LMSR by exploiting its modularity properties to construct a balanced binary tree and decompose computations along the tree nodes. The second design consists of two or more parallel LMSR market makers that mediate submarkets of increasingly fine-grained outcome partitions. This design remains computationally efficient for all operations, including arbitrage removal across submarkets. It adds two additional benefits for the market designer: (1) the ability to express utility for information at various resolutions by assigning different liquidity values, and (2) the ability to guarantee a true constant bounded loss by appropriately decreasing the liquidity in each submarket.
We consider a fundamental dynamic allocation problem motivated by the problem of $textit{securities lending}$ in financial markets, the mechanism underlying the short selling of stocks. A lender would like to distribute a finite number of identical copies of some scarce resource to $n$ clients, each of whom has a private demand that is unknown to the lender. The lender would like to maximize the usage of the resource $mbox{---}$ avoiding allocating more to a client than her true demand $mbox{---}$ but is constrained to sell the resource at a pre-specified price per unit, and thus cannot use prices to incentivize truthful reporting. We first show that the Bayesian optimal algorithm for the one-shot problem $mbox{---}$ which maximizes the resources expected usage according to the posterior expectation of demand, given reports $mbox{---}$ actually incentivizes truthful reporting as a dominant strategy. Because true demands in the securities lending problem are often sensitive information that the client would like to hide from competitors, we then consider the problem under the additional desideratum of (joint) differential privacy. We give an algorithm, based on simple dynamics for computing market equilibria, that is simultaneously private, approximately optimal, and approximately dominant-strategy truthful. Finally, we leverage this private algorithm to construct an approximately truthful, optimal mechanism for the extensive form multi-round auction where the lender does not have access to the true joint distributions between clients requests and demands.
This paper addresses the paucity of models of matching markets, both one-sided and two-sided, when utility functions of agents are cardinal. The classical Hylland-Zeckhauser scheme cite{hylland}, which is the most prominent such model in economics, can be viewed as corresponding to the linear Fisher model, which is most elementary model in market equilibria. Although HZ is based on the attractive idea of using a pricing mechanism, from the viewpoint of use in applications, it has a serious drawback, namely lack of computational efficiency, due to which solving instances of size even 4 or 5 is difficult. We propose a variety of Nash-bargaining-based models, several of which draw from general equilibrium theory, which has defined a rich collection of market models that generalize the linear Fisher model in order to address more specialized and realistic situations. The Nash bargaining solution satisfies Pareto optimality and symmetry and the allocations it yields are remarkably fair. Furthermore, since the solution is captured via a convex program, it is polynomial time computable. In order to be used in industrial grade applications, we give implementations for these models that are extremely time efficient, solving large instances, with $n = 2000$, in one hour on a PC, even for a two-sided matching market. The idea underlying our work has its origins in Vazirani (2012), which viewed the linear case of the Arrow-Debreu market model as a Nash bargaining game and gave a combinatorial, polynomial time algorithm for finding allocations via this solution concept, rather than the usual approach of using a pricing mechanism.
Walrasian equilibrium prices can be said to coordinate markets: They support a welfare optimal allocation in which each buyer is buying bundle of goods that is individually most preferred. However, this clean story has two caveats. First, the prices alone are not sufficient to coordinate the market, and buyers may need to select among their most preferred bundles in a coordinated way to find a feasible allocation. Second, we dont in practice expect to encounter exact equilibrium prices tailored to the market, but instead only approximate prices, somehow encoding distributional information about the market. How well do prices work to coordinate markets when tie-breaking is not coordinated, and they encode only distributional information? We answer this question. First, we provide a genericity condition such that for buyers with Matroid Based Valuations, overdemand with respect to equilibrium prices is at most 1, independent of the supply of goods, even when tie-breaking is done in an uncoordinated fashion. Second, we provide learning-theoretic results that show that such prices are robust to changing the buyers in the market, so long as all buyers are sampled from the same (unknown) distribution.
We study the power and limitations of posted prices in multi-unit markets, where agents arrive sequentially in an arbitrary order. We prove upper and lower bounds on the largest fraction of the optimal social welfare that can be guaranteed with posted prices, under a range of assumptions about the designers information and agents valuations. Our results provide insights about the relative power of uniform and non-uniform prices, the relative difficulty of different valuation classes, and the implications of different informational assumptions. Among other results, we prove constant-factor guarantees for agents with (symmetric) subadditive valuations, even in an incomplete-information setting and with uniform prices.
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