
on Microeconomics 
By:  Dirk Bergemann (Cowles Foundation, Yale University); Alessandro Bonatti (MIT); Andreas Haupt (Institute for Data, Systems, and Society, MIT); Alex Smolin (Dept. of Economics, Yale University) 
Abstract:  We consider a multiproduct monopoly pricing model. We provide sufficient conditions under which the optimal mechanism can be implemented via upgrade pricingâ€”a menu of product bundles that are nested in the strong set order. Our approach exploits duality methods to identify conditions on the distribution of consumer types under which (a) each product is purchased by the same set of buyers as under separate monopoly pricing (though the transfers can be different), and (b) these sets are nested. We exhibit two distinct sets of sufficient conditions. The ï¬ rst set of conditions weakens the monotonicity requirement of types and virtual values but maintains a regularity assumption, i.e., that the productbyproduct revenue curves are singlepeaked. The second set of conditions establishes the optimality of upgrade pricing for type spaces with monotone marginal rates of substitution (MRS)â€”the relative preference ratios for any two products are monotone across types. The monotone MRS condition allows us to relax the earlier regularity assumption. Under both sets of conditions, we fully characterize the product bundles and prices that form the optimal upgrade pricing menu. Finally, we show that, if the consumerâ€™s types are monotone, the seller can equivalently post a vector of singleitem prices: upgrade pricing and separate pricing are equivalent. 
Keywords:  Revenue Maximization, Mechanism design, Strong duality, Upgrade pricing 
JEL:  D42 D82 
Date:  2021–07 
URL:  http://d.repec.org/n?u=RePEc:cwl:cwldpp:2290r&r= 
By:  Mira Frick (Cowles Foundation, Yale University); Ryota Iijima (Cowles Foundation, Yale University); Yuhta Ishii (Department of Economics at Pennsylvania State University) 
Abstract:  We present an approach to analyze learning outcomes in a broad class of misspecified environments, spanning both singleagent and social learning. We introduce a novel "prediction accuracy" order over subjective models, and observe that this makes it possible to partially restore standard martingale convergence arguments that apply under correctly specified learning. Based on this, we derive general conditions to determine when beliefs in a given environment converge to some longrun belief either locally or globally (i.e., from some or all initial beliefs). We show that these conditions can be applied, first, to unify and generalize various convergence results in previously studied settings. Second, they enable us to analyze environments where learning is "slow," such as costly information acquisition and sequential social learning. In such environments, we illustrate that even if agents learn the truth when they are correctly specified, vanishingly small amounts of misspecification can generate extreme failures of learning. 
Keywords:  Misspecified learning, Stability, Robustness, BerkNash equilibrium 
Date:  2020–05 
URL:  http://d.repec.org/n?u=RePEc:cwl:cwldpp:2235r2&r= 
By:  Norio Takeoka (Department of Economics, Hitotsubashi University); Takashi Ui (Department of Economics, Hitotsubashi University) 
Abstract:  A decision problem under uncertainty is often given with a piece of objective but imprecise information about the states of the world such as in the Ellsberg urn. By incorporating such information into the smooth ambiguity model of Seo (2009), we characterize a class of smooth ambiguity representations whose secondorder beliefs are consistent with the objective information. As a corollary, we provide an axiomatization for the secondorder expected utility, which has been studied by Nau (2001), Neilson (2009), Grant, Polak, and Strzalecki (2009), Strzalecki (2011), and Ghirardato and Pennesi (2019). In our model, attitude toward uncertainty can be disentangled from a perception about uncertainty and connected with attitude toward reduction of compound lotteries. 
Date:  2021–12 
URL:  http://d.repec.org/n?u=RePEc:upd:utmpwp:037&r= 
By:  Marek Pycia (University of Zurich); M. Utku Ünver (Boston College) 
Abstract:  We study mechanism design and preference aggregation in environments in which the space of social alternatives is discrete and the preference domain is rich, as in standard models of social choice and socalled allocation without transfers. We show that a mechanism (or aggregation rule) selects the best outcome with respect to some resolute Arrovian social welfare function if, and only if, it is Pareto efficient and auditable. We further show that auditability implies nonbossiness and is implied by the conjunction of nonbossiness and individual strategyproofness, and that the later conjunction is equivalent to group strategyproofness as well as to Maskin monotonicity. As applications, we derive new characterizations in voting and allocation domains. 
Keywords:  Strategyproofness, Pareto efficiency, Arrovian preference aggregation, auditability, nonbossiness, voting, house allocation 
JEL:  C78 D78 
Date:  2021–11–15 
URL:  http://d.repec.org/n?u=RePEc:boc:bocoec:1044&r= 
By:  Herings, P. JeanJacques (RS: GSBE Theme DataDriven DecisionMaking, RS: GSBE Theme Conflict & Cooperation, Microeconomics & Public Economics); Mauleon, Ana; Vannetelbosch, Vincent 
Abstract:  We propose a solution concept for social environments called social rationalizability with mediation that identifies the consequences of common knowledge of rationality and farsightedness. In a social environment several coalitions may and could be willing to move at the same time. Individuals not only hold conjectures about the behaviors of other individuals but also about how a mediator is going to solve conflicts of interest. The set of socially rationalizable outcomes with mediation is shown to be nonempty for all social environments and it can be computed by an iterative reduction procedure. We show that social rationalizability with mediation does not necessarily satisfy coalitional rationality when the number of coalition members is greater than two. 
JEL:  C70 C72 C78 
Date:  2021–12–02 
URL:  http://d.repec.org/n?u=RePEc:unm:umagsb:2021019&r= 
By:  Hamed Hamze Bajgiran; Houman Owhadi 
Abstract:  A natural notion of rationality/consistency for aggregating models is that, for all (possibly aggregated) models $A$ and $B$, if the output of model $A$ is $f(A)$ and if the output model $B$ is $f(B)$, then the output of the model obtained by aggregating $A$ and $B$ must be a weighted average of $f(A)$ and $f(B)$. Similarly, a natural notion of rationality for aggregating preferences of ensembles of experts is that, for all (possibly aggregated) experts $A$ and $B$, and all possible choices $x$ and $y$, if both $A$ and $B$ prefer $x$ over $y$, then the expert obtained by aggregating $A$ and $B$ must also prefer $x$ over $y$. Rational aggregation is an important element of uncertainty quantification, and it lies behind many seemingly different results in economic theory: spanning social choice, belief formation, and individual decision making. Three examples of rational aggregation rules are as follows. (1) Give each individual model (expert) a weight (a score) and use weighted averaging to aggregate individual or finite ensembles of models (experts). (2) Order/rank individual model (expert) and let the aggregation of a finite ensemble of individual models (experts) be the highestranked individual model (expert) in that ensemble. (3) Give each individual model (expert) a weight, introduce a weak order/ranking over the set of models/experts, aggregate $A$ and $B$ as the weighted average of the highestranked models (experts) in $A$ or $B$. Note that (1) and (2) are particular cases of (3). In this paper, we show that all rational aggregation rules are of the form (3). This result unifies aggregation procedures across different economic environments. Following the main representation, we show applications and extensions of our representation in various separated economics topics such as belief formation, choice theory, and social welfare economics. 
Date:  2021–11 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2111.11630&r= 
By:  Hattori, Keisuke 
Abstract:  This paper compares the profitability and sustainability between profitsharing collusion with side payments and pricefixing collusion without side payments in a twofirm repeated Bertrand game when firms differ in both cost and discount factor. Although profitsharing collusion yields larger joint profits, bargaining over collusive agreements makes heterogeneous firms prefer different types of collusion: a lowcost (high cost) firm is more likely to adhere to profitsharing (pricefixing) collusion. If both firms have the same discount factor, profitsharing collusion is more sustainable. However, pricefixing collusion can be the only sustainable collusion if the efficient firm is more patient than the inefficient firm. Furthermore, we extend profitsharing collusion by incorporating side payments with different enforcement procedures (i.e., different timing of side payments) and different purposes: to reach agreement and to make the agreement sustainable. Our results provide a theoretical rationale for why firms fail or succeed at reaching and sustaining some forms of collusion. 
Keywords:  Collusion; Asymmetric costs; Asymmetric discount factors; Side payments; Repeated game 
JEL:  C73 C78 L13 L41 
Date:  2021–11–23 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:110800&r= 