
on Economic Design 
By:  Simon Jantschgi; Heinrich H. Nax; Bary S. R. Pradelski; Marek Pycia 
Abstract:  We address some open issues regarding the characterization of double auctions. Our model is a twosided commodity market with either finitely or infinitely many traders. We first unify existing formulations for both finite and infinite markets and generalize the characterization of market clearing in the presence of ties. Second, we define a mechanism that achieves market clearing in any, finite or infinite, market instance and show that it coincides with the kdouble auction by Rustichini et al. (1994) in the former case. In particular, it clarifies the consequences of ties in submissions and makes common regularity assumptions obsolete. Finally, we show that the resulting generalized mechanism implements Walrasian competitive equilibrium. 
Keywords:  Double auction, Walrasian equilibrium, finite and infinite markets, axiomatization 
JEL:  D44 D47 D50 
Date:  2022–02 
URL:  http://d.repec.org/n?u=RePEc:zur:econwp:404&r= 
By:  Simon Jantschgi; Heinrich H. Nax; Bary S. R. Pradelski; Marek Pycia 
Abstract:  Fees are omnipresent in markets but, with few exceptions, are omitted in economic models— such as Double Auctions—of these markets. Allowing for general fee structures, we show that their impact on incentives and efficiency in large Double Auctions hinges on whether the fees are homogeneous (as, e.g., fixed fees and price fees) or heterogeneous (as, e.g., bidask spread fees). Double Auctions with homogeneous fees share the key advantages of Double Auctions without fees: markets with homogeneous fees are asymptotically strategyproof and efficient. We further show that these advantages are preserved even if traders have misspecified beliefs. In contrast, heterogeneous fees lead to complex strategic behavior (price guessing) and may result in severe market failures. Allowing for aggregate uncertainty, we extend these insights to market organizations other than the Double Auction. 
Keywords:  Double auction, fees, transaction costs, incentives, strategyproofness, efficiency, robustness 
JEL:  C72 D44 D47 D81 D82 
Date:  2022–02 
URL:  http://d.repec.org/n?u=RePEc:zur:econwp:405&r= 
By:  Martino Banchio; Andrzej Skrzypacz 
Abstract:  Motivated by online advertising auctions, we study auction design in repeated auctions played by simple Artificial Intelligence algorithms (Qlearning). We find that firstprice auctions with no additional feedback lead to tacitcollusive outcomes (bids lower than values), while secondprice auctions do not. We show that the difference is driven by the incentive in firstprice auctions to outbid opponents by just one bid increment. This facilitates recoordination on low bids after a phase of experimentation. We also show that providing information about lowest bid to win, as introduced by Google at the time of switch to firstprice auctions, increases competitiveness of auctions. 
Date:  2022–02 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2202.05947&r= 
By:  Aaron BodohCreed; SangMok Lee 
Abstract:  Many school districts in the U.S. have replaced the Boston mechanism with deferred acceptance (DA) due to manipulability and unfairness. Nonetheless, the Boston mechanism Pareto dominates the DA in exante welfare, especially when students have similar ordinal preferences and schools have coarse priorities. We show that the DA's inefficiency relative to the Boston worsens if students have to acquire information about preferences at a cost before submitting rankorder lists to a given mechanism. Under the DA, greater homogeneity in rankorder reports and less information acquisition reinforce each other. A higher information cost intensifies this reinforcement and exacerbates the DA's inefficiency. 
Date:  2022–02 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2202.08366&r= 
By:  DoÄŸan, B.; Erdil, A. 
Abstract:  UK universities advertise the degree majors (courses) they offer, and every year over 700,000 students apply to their chosen courses. For each of their courses, universities have an intake target (the number of students to admit) and an access target (the number of disadvantaged students to admit). Depending on student demand, each university would like to adjust these courselevel targets to meet its aggregate (universitylevel) targets. We design a centralised system which provides universities with the exibility to optimally adjust their targets, makes it safe for students to reveal preferences truthfully, and quickly achieves fair and stable market clearing. 
Keywords:  Matching Theory, University Admissions, Affirmative Action 
JEL:  C70 D61 D63 I23 I24 
Date:  2022–03–10 
URL:  http://d.repec.org/n?u=RePEc:cam:camdae:2217&r= 
By:  Anna Bogomolnaia; Herve Moulin 
Abstract:  We must divide a finite number of indivisible goods and cash transfers between agents with quasilinear but otherwise arbitrary utilities over the subsets of goods. We compare two division rules with cognitively feasible and privacy preserving individual messages. In Sell&Buy agents bid for the role of Seller or Buyer: with two agents the smallest bid defines the Seller who then charges any a price constrained only by her winning bid. In Divide&Choose agents bid for the role of Divider, then everyone bids on the shares of the Divider's partition. S&B dominates D&C on two counts: its guaranteed utility in the worst case rewards (resp. penalises) more subadditive (resp. superadditive) utilities; playing safe is never ambiguous and is also better placed to collect a larger share of the efficient surplus. 
Date:  2022–02 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2202.08117&r= 
By:  Oihane Gallo; Bettina Klaus 
Abstract:  We consider a set of agents, e.g., a group of researchers, who have claims on an endowment, e.g., a research budget from a national science foundation. The research budget is not large enough to cover all claims. Agents can form coalitions and coalitional funding is proportional to the sum of the claims of its members, except for singleton coalitions which receive no funding. We analyze the structure of stable partitions when coalition members use wellbehaved rules to allocate coalitional endowments, e.g., the wellknown constrained equal awards rule (CEA) or the constrained equal losses rule (CEL).For continuous, (strictly) resource monotonic, and consistent rules, stable partitions with (mostly) pairwise coalitions emerge. For CEA and CEL we provide algorithms to construct such a stable pairwise partition. While for CEL the resulting stable pairwise partition is assortative and sequentially matches up lowestclaims pairs, for CEA the resulting stable pairwise partition is obtained sequentially by matching up in each step either a highestclaims pair or a highestlowestclaims pair.More generally, we also assume that the minimal coalition size to have a positive endowment is larger or equal to two. We then show how all results described above are extended to this general case. 
Keywords:  Winnertakeall market, Market entry game, Excess entry, Cumulative Prospect Theory, Probability weighting, Experiment 
JEL:  C71 C78 D63 D71 D74 
Date:  2022–03 
URL:  http://d.repec.org/n?u=RePEc:lau:crdeep:22.03&r= 
By:  Yamashita, Takuro; Smolin, Alex 
Abstract:  We study information design in games with a continuum of actions such that the players’ payoffs are concave in their own actions. A designer chooses an information structure–a joint distribution of a state and a private signal of each player. The information structure induces a Bayesian game and is evaluated according to the expected designer’s payoff under the equilibrium play. We develop a method that facilitates the search for an optimal information structure, i.e., one that cannot be outperformed by any other information structure, however complex. We show an information structure is optimal whenever it induces the strategies that can be implemented by an incentive contract in a dual, principalagent problem which aggregates marginal payoffs of the players in the original game. We use this result to establish the optimality of Gaussian information structures in settings with quadratic payoffs and a multivariate normally distributed state. We analyze the details of optimal structures in a differentiated Bertrand competition and in a prediction game. 
Keywords:  Information design ; Bayesian persuasion ; Concave games ; Duality ; Firstorder approach 
JEL:  D42 D82 D83 
Date:  2022–03–08 
URL:  http://d.repec.org/n?u=RePEc:tse:wpaper:126692&r= 
By:  Dirk Bergemann (Cowles Foundation, Yale University); Yang Cai (Cowles Foundation, Yale University); Grigoris Velegkas (Yale University); Mingfei Zhao (Google Research) 
Abstract:  We study the problem of selling information to a databuyer who faces a decision problem under uncertainty. We consider the classic Bayesian decisiontheoretic model pioneered by Blackwell [Bla51, Bla53]. Initially, he data buyer has only partial information about the payoffrelevant state of the world. A data seller offers additional information about the state of the world. The information is revealed through signaling schemes, also referred to as experiments. In the singleagent setting, any mechanism can be represented as a menu of experiments. A recent paper by Bergemann et al.[BBS18] present a complete characterization of the revenueoptimal mechanism in a binary state and binary action environment. By contrast, no characterization is known for the case with more actions. In this paper, we consider more general environments and study arguably the simplest mechanism, which only sells the fully informative experiment. In the environment with binary state and m = 3 actions, we provide an O(m)approximation to the optimal revenue by selling only the fully informative experiment and show that the approximation ratio is tight up to an absolute constant factor. An important corollary of our lower bound is that the size of the optimal menu must grow at least linearly in the number of available actions, so no universal upper bound exists for the size of the optimal menu in the general singledimensional setting. We also provide a sufficient condition under which selling only the fully informative experiment achieves the optimal revenue. For multidimensional environments, we prove that even in arguably the simplest matching utility environment with 3 states and 3 actions, the ratio between the optimal revenue and the revenue by selling only the fully informative experiment can grow immediately to a polynomial of the number of agent types. Nonetheless, if the distribution is uniform, we show that selling only the fully informative experiment is indeed the optimal mechanism. 
Date:  2022–02 
URL:  http://d.repec.org/n?u=RePEc:cwl:cwldpp:2324&r= 
By:  Ian M. Schmutte; Nathan Yoder 
Abstract:  Firms and statistical agencies that publish aggregate data face practical and legal requirements to protect the privacy of individuals. Increasingly, these organizations meet these standards by using publication mechanisms which satisfy differential privacy. We consider the problem of choosing such a mechanism so as to maximize the value of its output to end users. We show that this is equivalent to a constrained information design problem, and characterize its solution. Moreover, by introducing a new order on information structures and showing that it ranks them by their usefulness to agents with supermodular payoffs, we show that the simple geometric mechanism is optimal whenever data users face supermodular decision problems. 
Date:  2022–02 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2202.05452&r= 