
on Economic Design 
By:  Yuya Wakabayashi; Ryosuke Sakai; Shigehiro Serizawa 
Abstract:  We consider the economy consisting of n agents and m heterogenous objects where the seller benefits v from objects. Our study focuses on the multiobject allocation problem with monetary transfers where each agent obtains at most one object (unitdemand). In the situation with arbitrary n, m and v, we show that the minimum price Walrasian rule with reserve prices adjusted to v on the classical domain is the only rule satisfying four desirable properties; efficiency, strategyproofness, individual rationality and nosubsidy. Our result is an extension of that of Morimoto and Serizawa (2015), and so we can consider more general situation than them. Moreover, we characterize the minimum price Walrasian rules by efficiency, strategyproofness and twosided individual rationality. 
Date:  2022–02 
URL:  http://d.repec.org/n?u=RePEc:dpr:wpaper:1161&r= 
By:  Felix Brandt; Patrick Lederer; Ren\'e Romen 
Abstract:  Social decision schemes (SDSs) map the preferences of a group of voters over some set of $m$ alternatives to a probability distribution over the alternatives. A seminal characterization of strategyproof SDSs by Gibbard implies that there are no strategyproof Condorcet extensions and that only random dictatorships satisfy ex post efficiency and strategyproofness. The latter is known as the random dictatorship theorem. We relax Condorcetconsistency and ex post efficiency by introducing a lower bound on the probability of Condorcet winners and an upper bound on the probability of Paretodominated alternatives, respectively. We then show that the SDS that assigns probabilities proportional to Copeland scores is the only anonymous, neutral, and strategyproof SDS that can guarantee the Condorcet winner a probability of at least 2/m. Moreover, no strategyproof SDS can exceed this bound, even when dropping anonymity and neutrality. Secondly, we prove a continuous strengthening of Gibbard's random dictatorship theorem: the less probability we put on Paretodominated alternatives, the closer to a random dictatorship is the resulting SDS. Finally, we show that the only anonymous, neutral, and strategyproof SDSs that maximize the probability of Condorcet winners while minimizing the probability of Paretodominated alternatives are mixtures of the uniform random dictatorship and the randomized Copeland rule. 
Date:  2022–01 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2201.10418&r= 
By:  Hiroki Shinozaki 
Abstract:  We consider the problem of allocating multiple units of an indivisible object among a set of agents and collecting payments. Each agent can receive multiple units of the object, and has a (possibly) nonquasilinear preference on the set of (consumption) bundles. We assume that preferences exhibit both nonincreasing marginal valuations and nonnegative income effects. We propose a new property of fairness: no price envy. It extends the standard no envy test (Foley, 1967) over bundles to prices (perunit payments), and requires no agent envy other agents' prices to his own in the sense that if he has a chance to receive some units at other agents' prices, then he gets better off than his own bundle. First, we show that a rule satisfies no price envy and no subsidy for losers if and only if it is an inverse uniformprice rule. Then, we identify the unique maximal domain for no price envy, strategyproofness, and no subsidy for losers: the domain with partly constant marginal valuations. We further establish that on the domain with partly constant marginal valuations, a rule satisfies no price envy, strategyproofness, and no subsidy for losers if and only if it is a minimum inverse uniformprice rule. Our maximal domain result implies that no rule satisfies no price envy, strategyproofness, and no subsidy for losers when agents have preferences with nonincreasing marginal valuations. Given this negative observation, we look for a minimally manipulable rule among the class of rules satisfying both no price envy and no subsidy for losers in the case of preferences with nonincreasing marginal valuations. We show that a rule is minimally manipulable among the class of rules satisfying no price envy and no subsidy for losers if and only if it is a minimum inverse uniformprice rule. Our results provide a rationale for the use of the popular minimum uniformprice rule in terms of fairness and nonmanipulability. 
Date:  2022–02 
URL:  http://d.repec.org/n?u=RePEc:dpr:wpaper:1164&r= 
By:  Michael Curry; Tuomas Sandholm; John Dickerson 
Abstract:  A recent approach to automated mechanism design, differentiable economics, represents auctions by rich function approximators and optimizes their performance by gradient descent. The ideal auction architecture for differentiable economics would be perfectly strategyproof, support multiple bidders and items, and be rich enough to represent the optimal (i.e. revenuemaximizing) mechanism. So far, such an architecture does not exist. There are singlebidder approaches (MenuNet, RochetNet) which are always strategyproof and can represent optimal mechanisms. RegretNet is multibidder and can approximate any mechanism, but is only approximately strategyproof. We present an architecture that supports multiple bidders and is perfectly strategyproof, but cannot necessarily represent the optimal mechanism. This architecture is the classic affine maximizer auction (AMA), modified to offer lotteries. By using the gradientbased optimization tools of differentiable economics, we can now train lottery AMAs, competing with or outperforming prior approaches in revenue. 
Date:  2022–02 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2202.02872&r= 
By:  Isenhardt, Lars; Seifert, Stefan; Hüttel, Silke 
Abstract:  Current European Union legislation offers public authorities to grant a Right of First Refusal (RFR) in farmland auctions with public tenders in favour of the current tenant. That is, tenants can purchase the auctioned lot by matching the highest bid. Granting this right secures tenants to buy the land they use; however, it may deter other potential buyers’ auction participation and incentivise bidders to adjust their strategies. An RFR for tenants is thus hypothesised to decrease the number of bidders and lower sales prices. Empirical evidence seems lacking thus far and in this paper, we target to closing this gap by analysing a tenants’ RFR effect on the number of bidders and winning bids in firstprice privatization auctions in eastern Germany. Using around 4,000 land auction results in one German Federal State over 2007–2018 by two agencies that differ in granting the RFR to tenants, we combine nonparametric nearest neighbour matching based on the Mahalanobis distance with parametric postmatching regressions. Our results indicate that the RFR reduces competition by an average of 9.3% bidders per auction and lowers the prices paid in land auctions by 16.4 %. 
Keywords:  Agricultural and Food Policy, Industrial Organization, Land Economics/Use, Political Economy 
Date:  2021–11–18 
URL:  http://d.repec.org/n?u=RePEc:ags:gewi21:317062&r= 
By:  Sanjay Chandlekar; Easwar Subramanian; Sanjay Bhat; Praveen Paruchuri; Sujit Gujar 
Abstract:  Periodic double auctions (PDA) have applications in many areas such as in ecommerce, intraday equity markets, and dayahead energy markets in smartgrids. While the trades accomplished using PDAs are worth trillions of dollars, finding a reliable bidding strategy in such auctions is still a challenge as it requires the consideration of future auctions. A participating buyer in a PDA has to design its bidding strategy by planning for current and future auctions. Many equilibriumbased bidding strategies proposed are complex to use in realtime. In the current exposition, we propose a scalebased bidding strategy for buyers participating in PDA. We first present an equilibrium analysis for singlebuyer singleseller multiunit singleshot kDouble auctions. Specifically, we analyze the situation when a seller and a buyer trade two identical units of quantity in a double auction where both the buyer and the seller deploy a simple, scalebased bidding strategy. The equilibrium analysis becomes intractable as the number of participants increases. To be useful in more complex settings such as wholesale markets in smartgrids, we model equilibrium bidding strategy as a learning problem. We develop a deep deterministic policy gradient (DDPG) based learning strategy, DDPGBBS, for a participating agent in PDAs to suggest an action at any auction instance. DDPGBBS, which empirically follows the obtained theoretical equilibrium, is easily extendable when the number of buyers/sellers increases. We take Power Trading Agent Competition's (PowerTAC) wholesale market PDA as a testbed to evaluate our novel bidding strategy. We benchmark our DDPG based strategy against several baselines and stateoftheart bidding strategies of the PowerTAC wholesale market PDA and demonstrate the efficacy of DDPGBBS against several benchmarked strategies. 
Date:  2022–01 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2201.10127&r= 