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on Economic Design |
| By: | Vitali Gretschko; Helene Mass |
| Abstract: | The usual analysis of bidding in first-price auctions assumes that bidders know the distribution of valuations. We analyze first-price auctions in which bidders do not know the precise distribution of their competitors’ valuations, but only the mean of the distribution. We propose a novel equilibrium solution concept based on worst-case reasoning. We find an essentially unique and efficient worst-case equilibrium of the first-price auction, which has appealing properties from both the bidders’ and the seller’s point of view. |
| Keywords: | Auctions, worst-case equilibria, uncertainty |
| JEL: | D44 D81 D82 |
| Date: | 2023–06 |
| URL: | http://d.repec.org/n?u=RePEc:bon:boncrc:crctr224_2023_434&r=des |
| By: | Jason Shachat (Durham University Business School); Lijia Wei (School of Economics and Management, Wuhan University) |
| Abstract: | We present a hidden Markov model of discrete strategic heterogeneity and learning in first price independent private values auctions. The model includes three latent bidding rules: constant absolute mark-up, constant percentage mark-up, and strategic best response. Rule switching probabilities depend upon a bidder's past auction outcomes and a myopic reinforcement learning dynamic. We apply this model to a new experiment that varies the number of bidders and the auction frame between forward and reverse. We find the proportion of bidders following constant absolute mark-up increases with experience, and is higher when the number of bidders is large. The primary driver here is subjects' increased propensity to switch strategies when they experience a loss (win) reinforcement when following a strategic (heuristic) rule. |
| Keywords: | private value auction; discrete heterogeneity; learning; hidden Markov model; laboratory experiment |
| JEL: | D44 C72 C92 D87 C15 |
| Date: | 2023 |
| URL: | http://d.repec.org/n?u=RePEc:chu:wpaper:23-07&r=des |
| By: | Pranjal Rawat |
| Abstract: | This paper examines the impact of different payment rules on efficiency when algorithms learn to bid. We use a fully randomized experiment of 427 trials, where Q-learning bidders participate in up to 250, 000 auctions for a commonly valued item. The findings reveal that the first price auction, where winners pay the winning bid, is susceptible to coordinated bid suppression, with winning bids averaging roughly 20% below the true values. In contrast, the second price auction, where winners pay the second highest bid, aligns winning bids with actual values, reduces the volatility during learning and speeds up convergence. Regression analysis, incorporating design elements such as payment rules, number of participants, algorithmic factors including the discount and learning rate, asynchronous/synchronous updating, feedback, and exploration strategies, discovers the critical role of payment rules on efficiency. Furthermore, machine learning estimators find that payment rules matter even more with few bidders, high discount factors, asynchronous learning, and coarse bid spaces. This paper underscores the importance of auction design in algorithmic bidding. It suggests that computerized auctions like Google AdSense, which rely on the first price auction, can mitigate the risk of algorithmic collusion by adopting the second price auction. |
| Date: | 2023–06 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2306.09437&r=des |
| By: | Yurong Chen; Qian Wang; Zhijian Duan; Haoran Sun; Zhaohua Chen; Xiang Yan; Xiaotie Deng |
| Abstract: | In online ad markets, a rising number of advertisers are employing bidding agencies to participate in ad auctions. These agencies are specialized in designing online algorithms and bidding on behalf of their clients. Typically, an agency usually has information on multiple advertisers, so she can potentially coordinate bids to help her clients achieve higher utilities than those under independent bidding. In this paper, we study coordinated online bidding algorithms in repeated second-price auctions with budgets. We propose algorithms that guarantee every client a higher utility than the best she can get under independent bidding. We show that these algorithms achieve maximal coalition welfare and discuss bidders' incentives to misreport their budgets, in symmetric cases. Our proofs combine the techniques of online learning and equilibrium analysis, overcoming the difficulty of competing with a multi-dimensional benchmark. The performance of our algorithms is further evaluated by experiments on both synthetic and real data. To the best of our knowledge, we are the first to consider bidder coordination in online repeated auctions with constraints. |
| Date: | 2023–06 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2306.07709&r=des |
| By: | Bo Young Chang |
| Abstract: | We use detailed data on the bids at auctions for Government of Canada bonds between 1999 and 2021 to gauge the yield sensitivity of these bonds to the issuance amount. We propose a new metric that captures the slope of the demand function at each auction by using the information in the multiple bids (quantity and yield) that each bidder submits. In the absence of an established theoretical framework, we estimate the slope of the aggregate demand function simply by weighing the slopes of the individual demand functions, where the weights are the maximum bids of each participant. We show that these slopes can provide insights into the relationship between the supply and yield of a government debt security. |
| Keywords: | Debt management; Interest rates |
| JEL: | G12 D44 |
| Date: | 2023–06 |
| URL: | http://d.repec.org/n?u=RePEc:bca:bocadp:23-12&r=des |
| By: | Labrini Zarpala |
| Abstract: | This paper examines how risk and budget limits on investment mandates affect the bidding strategy in a uniform-price auction for issuing corporate bonds. I prove the existence of symmetric Bayesian Nash equilibrium and explore how the risk limits imposed on the mandate may mitigate severe underpricing, as the symmetric equilibrium's yield positively relates to the risk limit. Investment mandates with low-risk acceptance inversely affect the equilibrium bid. The equilibrium bid provides insights into the optimal mechanism for pricing corporate bonds conveying information about the bond's valuation, market power, and the number of bidders. These findings contribute to auction theory and have implications for empirical research in the corporate bond market. |
| Date: | 2023–06 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2306.07134&r=des |
| By: | Noelia Juarez; Paola B. Manasero; Jorge Oviedo |
| Abstract: | In a many-to-one matching market with substitutable preferences, we analyze the game induced by a stable rule. When both sides of the market play strategically, we show that any stable rule implements, in Nash equilibrium, the individually rational matchings. Also, when only workers play strategically and firms' preferences satisfy the law of aggregated demand, we show that any stable rule implements, in Nash equilibrium, the stable matchings. |
| Date: | 2023–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2305.13956&r=des |
| By: | Eric Kamwa (LC2S - Laboratoire caribéen de sciences sociales - CNRS - Centre National de la Recherche Scientifique - UA - Université des Antilles) |
| Abstract: | Preference Approval Voting (PAV) and Fallback Voting (FV) are two voting rules that combine approval and preferences. They were first introduced by Brams and Sanver (2009). Under PAV, voters rank the candidates and indicate which ones they approve of; with FV, they rank only those candidates they approve of. In this paper, we supplement the work of Brams and Sanver (2009) by exploring some other normative properties of FV and PAV. We show among other that FV and PAV satisfy and fail the same criteria; they possess two properties that AV does not: Pareto optimality and the fact of always electing the absolute Condorcet winner when he exists. For threecandidate elections and a very large electorate, we compare FV and PAV to other voting rules by evaluating the probabilities of satisfying the Condorcet majority criteria. We find that PAV performs better than the Borda rule. We also find that in terms of agreement, FV and PAV are closer to scoring rules than to Approval voting. Our analysis is performed under the Impartial Anonymous Culture assumption. |
| Keywords: | Approval Voting, Rankings, Condorcet, Properties, Impartial and Anonymous Culture |
| Date: | 2023 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:hal-03614585&r=des |
| By: | Will Sandholtz; Andrew Tai |
| Abstract: | We study the classic house-swapping problem of Shapley and Scarf (1974) in a setting where agents may have "objective" indifferences, i.e., indifferences that are shared by all agents. In other words, if any one agent is indifferent between two houses, then all agents are indifferent between those two houses. The most direct interpretation is the presence of multiple copies of the same object. Our setting is a special case of the house-swapping problem with general indifferences. We derive a simple, easily interpretable algorithm that produces the unique strict core allocation of the house-swapping market, if it exists. Our algorithm runs in square polynomial time, a substantial improvement over the cubed time methods for the more general problem. |
| Date: | 2023–06 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2306.09529&r=des |
| By: | Denizalp Goktas; Jiayi Zhao; Amy Greenwald |
| Abstract: | A prevalent theme in the economics and computation literature is to identify natural price-adjustment processes by which sellers and buyers in a market can discover equilibrium prices. An example of such a process is t\^atonnement, an auction-like algorithm first proposed in 1874 by French economist Walras in which sellers adjust prices based on the Marshallian demands of buyers. A dual concept in consumer theory is a buyer's Hicksian demand. In this paper, we identify the maximum of the absolute value of the elasticity of the Hicksian demand, as an economic parameter sufficient to capture and explain a range of convergent and non-convergent t\^atonnement behaviors in a broad class of markets. In particular, we prove the convergence of t\^atonnement at a rate of $O((1+\varepsilon^2)/T)$, in homothetic Fisher markets with bounded price elasticity of Hicksian demand, i.e., Fisher markets in which consumers have preferences represented by homogeneous utility functions and the price elasticity of their Hicksian demand is bounded, where $\varepsilon \geq 0$ is the maximum absolute value of the price elasticity of Hicksian demand across all buyers. Our result not only generalizes known convergence results for CES Fisher markets, but extends them to mixed nested CES markets and Fisher markets with continuous, possibly non-concave, homogeneous utility functions. Our convergence rate covers the full spectrum of nested CES utilities, including Leontief and linear utilities, unifying previously existing disparate convergence and non-convergence results. In particular, for $\varepsilon = 0$, i.e., Leontief markets, we recover the best-known convergence rate of $O(1/T)$, and as $\varepsilon \to \infty$, e.g., linear Fisher markets, we obtain non-convergent behavior, as expected. |
| Date: | 2023–06 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2306.04890&r=des |