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Register a new userDo Prices Coordinate Markets?
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Added by
Jamie Morgenstern
Publication date
2015
fields
Informatics Engineering
and research's language is
English
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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.
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Econometric inference allows an analyst to back out the values of agents in a mechanism from the rules of the mechanism and bids of the agents. This paper gives an algorithm to solve the problem of inferring the values of agents in a dominant-strategy mechanism from the social choice function implemented by the mechanism and the per-unit prices paid by the agents (the agent bids are not observed). For single-dimensional agents, this inference problem is a multi-dimensional inversion of the payment identity and is feasible only if the payment identity is uniquely invertible. The inversion is unique for single-unit proportional weights social choice functions (common, for example, in bandwidth allocation); and its inverse can be found efficiently. This inversion is not unique for social choice functions that exhibit complementarities. Of independent interest, we extend a result of Rosen (1965), that the Nash equilbria of concave games are unique and pure, to an alternative notion of concavity based on Gale and Nikaido (1965).
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Lampros Flokas
, Emmanouil-Vasileios Vlatakis-Gkaragkounis andn Thanasis Lianeas
, Panayotis Mertikopoulos
2020
Understanding the behavior of no-regret dynamics in general $N$-player games is a fundamental question in online learning and game theory. A folk result in the field states that, in finite games, the empirical frequency of play under no-regret learning converges to the games set of coarse correlated equilibria. By contrast, our understanding of how the day-to-day behavior of the dynamics correlates to the games Nash equilibria is much more limited, and only partial results are known for certain classes of games (such as zero-sum or congestion games). In this paper, we study the dynamics of follow-the-regularized-leader (FTRL), arguably the most well-studied class of no-regret dynamics, and we establish a sweeping negative result showing that the notion of mixed Nash equilibrium is antithetical to no-regret learning. Specifically, we show that any Nash equilibrium which is not strict (in that every player has a unique best response) cannot be stable and attracting under the dynamics of FTRL. This result has significant implications for predicting the outcome of a learning process as it shows unequivocally that only strict (and hence, pure) Nash equilibria can emerge as stable limit points thereof.
The growth of the sharing economy is driven by the emergence of sharing platforms, e.g., Uber and Lyft, that match owners looking to share their resources with customers looking to rent them. The design of such platforms is a complex mixture of economics and engineering, and how to optimally design such platforms is still an open problem. In this paper, we focus on the design of prices and subsidies in sharing platforms. Our results provide insights into the tradeoff between revenue maximizing prices and social welfare maximizing prices. Specifically, we introduce a novel model of sharing platforms and characterize the profit and social welfare maximizing prices in this model. Further, we bound the efficiency loss under profit maximizing prices, showing that there is a strong alignment between profit and efficiency in practical settings. Our results highlight that the revenue of platforms may be limited in practice due to supply shortages; thus platforms have a strong incentive to encourage sharing via subsidies. We provide an analytic characterization of when such subsidies are valuable and show how to optimize the size of the subsidy provided. Finally, we validate the insights from our analysis using data from Didi Chuxing, the largest ridesharing platform in China.
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.
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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