
on Microeconomics 
By:  Anton Kolotilin (School of Economics, UNSW); Roberto Corrao (Department of Economics, MIT); Alexander Wolitzky (Department of Economics, MIT) 
Abstract:  In persuasion problems where the receiver’s utility is singlepeaked in a onedimensional action, optimal signals are characterized by duality, based on a firstorder approach to the receiver’s problem. A signal that pools at most two states in each realization is always optimal, and such pairwise signals are the only solutions under a nonsingularity condition on utilities (the twist condition). Our core results provide conditions under which higher actions are induced at more or less extreme pairs of states, so that the induced action is singledipped or singlepeaked on each set of nested pairs of states. We also provide conditions for the optimality of either full disclosure or negative assortative disclosure, where signal realizations can be ordered from least to most extreme. Methodologically, our proofs rely on a novel complementary slackness theorem for persuasion problems. 
Keywords:  persuasion, information design, duality, optimal transport, firstorder approach, pairwise signals, twist condition, singledipped disclosure, negative assortative disclosure, complementary slackness 
JEL:  C78 D82 D83 
Date:  2023–02 
URL:  http://d.repec.org/n?u=RePEc:swe:wpaper:202307&r=mic 
By:  Anton Kolotilin (School of Economics, UNSW); Roberto Corrao (Department of Economics, MIT); Alexander Wolitzky (Department of Economics, MIT) 
Abstract:  We consider general Bayesian persuasion problems where the receiver’s utility is singlepeaked in a onedimensional action. We show that a signal that pools at most two states in each realization is always optimal, and that such pairwise signals are the only solutions under a nonsingularity condition (the twist condition). Our core results provide conditions under which riskier prospects induce higher or lower actions, so that the induced action is singledipped or singlepeaked on each set of nested prospects. We also provide conditions for the optimality of either full disclosure or negative assortative disclosure, where all prospects are nested. Methodologically, our results rely on novel duality and complementary slackness theorems. Our analysis extends to a general problem of assigning onedimensional inputs to productive units, which we call optimal productive transport. This problem covers additional applications including club economies (assigning workers to firms, or students to schools), robust option pricing (assigning future asset prices to price distributions), and partisan gerrymandering (assigning voters to districts). 
Keywords:  Bayesian persuasion, information design, firstorder approach, optimal transport, duality, complementary slackness, pairwise signal, singledipped signal, negative assortative disclosure, club economies, option pricing, gerrymandering 
JEL:  C78 D82 D83 
Date:  2023–10 
URL:  http://d.repec.org/n?u=RePEc:swe:wpaper:202312&r=mic 
By:  Masaki Miyashita; Takashi Ui 
Abstract:  A linearquadraticGaussian (LQG) game is an incomplete information game with quadratic payoff functions and Gaussian payoff states. This study addresses an information design problem to identify an information structure that maximizes a quadratic objective function. Gaussian information structures are found to be optimal among all information structures. Furthermore, the optimal Gaussian information structure can be determined by semidefinite programming, which is a natural extension of linear programming. This paper provides sufficient conditions for the optimality and suboptimality of both no and full information disclosure. In addition, we characterize optimal information structures in symmetric LQG games and optimal public information structures in asymmetric LQG games, with each structure presented in a closedform expression. 
Date:  2023–12 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2312.09479&r=mic 
By:  Anton Kolotilin (School of Economics, UNSW); Alexander Wolitzky (Department of Economics, MIT) 
Abstract:  We study the problem of a partisan gerrymanderer who assigns voters to equipopulous districts so as to maximize his party’s expected seat share. The designer faces both aggregate uncertainty (how many votes his party will receive) and idiosyncratic, voterlevel uncertainty (which voters will vote for his party). We argue that packandpair districting, where weaker districts are “packed” with a single type of voter, while stronger districts contain two voter types, is typically optimal for the gerrymanderer. The optimal form of packandpair districting depends on the relative amounts of aggregate and idiosyncratic uncertainty. When idiosyncratic uncertainty dominates, it is optimal to pack opposing voters and pair more favorable voters; this plan resembles traditional “packingandcracking.” When aggregate uncertainty dominates, it is optimal to pack moderate voters and pair extreme voters; this “matching slices” plan has received some attention in the literature. Estimating the model using precinctlevel returns from recent US House elections indicates that, in practice, idiosyncratic uncertainty dominates and packing opponents is optimal; moreover, traditional packandcrack districting is approximately optimal. We discuss implications for redistricting reform and political polarization. Methodologically, we exploit a formal connection between gerrymandering—partitioning voters into districts—and information design—partitioning states of the world into signals. 
Keywords:  Gerrymandering, packandcrack, matching slices, packandpair, information design 
JEL:  C78 D72 D82 
Date:  2023–04 
URL:  http://d.repec.org/n?u=RePEc:swe:wpaper:202306&r=mic 
By:  Ratul Lahkar (Ashoka University); Saptarshi Mukherjee (Indian Institute of Technology Delhi) 
Abstract:  We consider large population Tullock contests in which agents are divided into different types according to their strategy cost function. A planner assigns type specific bias parameters to affect the likelihood of success with the objective of maximizing the Nash equilibrium level of aggregate strategy. We characterize such optimal bias parameters and identify conditions under which those parameters are increasing or decreasing according to the cost parameters. The parameters are biased in favor of high cost agents if the cost functions are strictly convex and the likelihood of success is sufficiently responsive to strategy. We also identify conditions under which a planner can truthfully implement the optimal parameters under incomplete information. In fact, under such conditions, dominant strategy implementation is equivalent to Nash implementation in our model. Hence, our mechanism double implements the optimal bias parameters. 
Date:  2022–07–20 
URL:  http://d.repec.org/n?u=RePEc:ash:wpaper:82&r=mic 
By:  Thomas Mariotti (TSER  Toulouse School of Economics  UT Capitole  Université Toulouse Capitole  UT  Université de Toulouse  EHESS  École des hautes études en sciences sociales  CNRS  Centre National de la Recherche Scientifique  INRAE  Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement); Nikolaus Schweizer (Tilburg University [Netherlands]); Nora Szech (KIT  Karlsruher Institut für Technologie); Jonas von Wangenheim (Universität Bonn = University of Bonn) 
Abstract:  We study the optimal design of information nudges for presentbiased consumers who make sequential consumption decisions without exact prior knowledge of their longterm consequences. For any distribution of risks, there exists a consumeroptimal information nudge that is of cutoff type, recommending abstinence if riskiness is high enough. Depending on the distribution of risks, more or less consumers may have to be sacriced in that they cannot be warned even though they would like to be. Under a stronger bias for the present, the target group receiving a credible warning to abstain must be tightened, but this need not increase the probability of harmful consumption. If some consumers are more strongly presentbiased than others, trafficlight nudges turn out to be optimal and, when subgroups of consumers differ sufficiently, the optimal trafficlight nudge is also subgroupoptimal. We finally compare the consumeroptimal nudge with those a health authority or a lobbyist would favor. 
Keywords:  Nudges, Information Design, PresentBiased Preferences, SelfControl 
Date:  2023 
URL:  http://d.repec.org/n?u=RePEc:hal:journl:hal04198487&r=mic 
By:  Tiziano De Angelis; Fabien Gensbittel; St\'ephane Villeneuve 
Abstract:  We construct a Nash equilibrium in feedback form for a class of twoperson stochastic games with absorption arising from corporate finance. More precisely, the paper focusses on a strategic dynamic game in which two financiallyconstrained firms operate in the same market. The firms distribute dividends and are faced with default risk. The strategic interaction arises from the fact that if one firm defaults, the other one becomes a monopolist and increases its profitability. To determine a Nash equilibrium in feedback form, we develop two different concepts depending on the initial endowment of each firm. If one firm is richer than the other one, then we use a notion of control vs.\ strategy equilibrium. If the two firms have the same initial endowment (hence they are symmetric in our setup) then we need mixed strategies in order to construct a symmetric equilibrium. 
Date:  2023–12 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2312.07703&r=mic 
By:  Mehmet S. Ismail; Ronald Peeters 
Abstract:  It is well known that ex ante social preferences and expected utility are not always compatible. In this note, we introduce a novel framework that naturally separates social preferences from selfish preferences to answer the following question: What specific forms of social preferences can be accommodated within the expected utility paradigm? In a departure from existing frameworks, our framework reveals that ex ante social preferences are not inherently in conflict with expected utility in games, provided a decisionmaker's aversion to randomization in selfish utility "counterbalances" her social preference for randomization. We also show that when a player's preferences in both the game (against another player) and the associated decision problem (against Nature) conform to expected utility axioms, the permissible range of social preferences becomes notably restricted. Only under this condition do we reaffirm the existing literature's key insight regarding the incompatibility of ex ante inequality aversion with expected utility. 
Date:  2023–12 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2312.06048&r=mic 
By:  Pierfrancesco Guarino 
Abstract:  Given a dynamic ordinal game, we deem a strategy sequentially rational if there exist a Bernoulli utility function and a conditional probability system with respect to which the strategy is a maximizer. We establish a complete class theorem by characterizing sequential rationality via the new Conditional BDominance. Building on this notion, we introduce Iterative Conditional BDominance, which is an iterative elimination procedure that characterizes the implications of forward induction in the class of games under scrutiny and selects the unique backward induction outcome in dynamic ordinal games with perfect information satisfying a genericity condition. Additionally, we show that Iterative Conditional BDominance, as a `forward induction reasoning' solution concept, captures: $(i)$ the unique backward induction outcome obtained via sophisticated voting in binary agendas with sequential majority voting; $(ii)$ farsightedness in dynamic ordinal games derived from social environments; $(iii)$ a unique outcome in ordinal MoneyBurning Games. 
Date:  2023–12 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2312.03536&r=mic 
By:  Bruno Jullien (TSER  TSER Toulouse School of Economics – Recherche  INRAE  Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement); Markus Reisinger (Frankfurt School of Finance and Management); Patrick Rey (TSER  TSER Toulouse School of Economics – Recherche  INRAE  Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement) 
Abstract:  The availability of consumer data is inducing a growing number of firms to adopt more personalized pricing policies. This affects both the performance of, and the competition between, alternative distribution channels, which in turn has implications for firms' distribution strategies. We develop a formal model to examine a brand manufacturer's choice between mono distribution (selling only through its own direct channel) or dual distribution (selling through an independent retailer as well). We consider different demand patterns, covering both horizontal and vertical differentiation and different pricing regimes, with the manufacturer and retailer each charging personalized prices or a uniform price. We show that dual distribution is optimal for a large number of cases. In particular, this is always the case when the channels are horizontally differentiated, regardless of the pricing regime; moreover, if both firms charge personalized prices, a welldesigned wholesale tariff allows them to extract the entire consumer surplus. These insights obtained here for the case of intrabrand competition between vertically related firms are thus in stark contrast to those obtained for interbrand competition, where personalized pricing dissipates industry profit. With vertical differentiation, dual distribution remains optimal if the manufacturer charges a uniform price. By contrast, under personalized pricing, mono distribution can be optimal when the retailer does not expand demand sufficiently. Interestingly, the industry profit may be largest in a hybrid pricing regime, in which the manufacturer forgoes the use of personalized pricing and only the retailer charges personalized prices. This paper was accepted by Joshua Gans, business strategy. Funding: The financial support of the European Research Council under the European Union's Horizon 2020 research and innovation programme [Grant Agreement 670494] and of the Agence nationale de la recherche (ANR) [Grant ANITI (ANR Grant 3IA)] and [Grant CHESS ANR17EURE0010] (Investissements d'Avenir program) is gratefully acknowledged. Supplemental Material: The online appendix is available at https://doi.org/10.1287/mnsc.2022.4437 . 
Keywords:  Personalized pricing, Distribution strategies, Vertical contracting, Downstream competition 
Date:  2023–03 
URL:  http://d.repec.org/n?u=RePEc:hal:journl:hal04282548&r=mic 
By:  Sven Neth 
Abstract:  How do we ascribe subjective probability? In decision theory, this question is often addressed by representation theorems, going back to Ramsey (1926), which tell us how to define or measure subjective probability by observable preferences. However, standard representation theorems make strong rationality assumptions, in particular expected utility maximization. How do we ascribe subjective probability to agents which do not satisfy these strong rationality assumptions? I present a representation theorem with weak rationality assumptions which can be used to define or measure subjective probability for partly irrational agents. 
Date:  2023–12 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2312.09796&r=mic 
By:  Ayush Pant (Ashoka University); Federico Trombetta (Universita Cattolica del Sacro Cuore) 
Abstract:  Conventional wisdom suggests that competition in the modern digital environment pushes media outlets toward the early release of less accurate information. We show that this is not necessarily the case. We argue that two opposing forces determine the resolution of the speedaccuracy tradeoff: preemption and reputation. More competitive environments may be more conducive to reputation building, which may lead to better reporting. However, the audience may be worse off due to the outlets' better initial information. Finally, we show how a source may exploit the speedaccuracy tradeoff to quickly get "unverified facts" out to the audience. 
Keywords:  media competition; preemption; reputation 
Date:  2023–01–30 
URL:  http://d.repec.org/n?u=RePEc:ash:wpaper:92&r=mic 
By:  Abhinash Borah (Ashoka University); Raghvi Garg (Ashoka University) 
Abstract:  As is wellknown, choices of a decision maker (DM) who attempts selfcontrol in the face of temptation may exhibit menu effects and â€œnonstandardâ€ patterns. Existing models can accommodate some of these patterns but not others; e.g., they can explain selfcontrol undermining menu effects, but not selfcontrol enhancing ones. We introduce a model of selfcontrol with the goal of better understanding and accounting for such effects. The basic idea underlying our model is that the DM experiences a psychological cost if she succumbs to temptation and chooses in a manner that is totally antithetical to her commitment preferences. To mitigate such costs, in any menu, her expression of selfcontrol involves, first, eliminating a subset of alternatives that are worst according to her commitment preferences, with the elimination process being referencedependent. Then, amongst the remaining alternatives, she chooses the best one according to her temptation preferences. Besides studying menu effects, we characterize the model behaviorally based on a novel axiom called WARP with norms. We also show that the model is wellidentified. 
Keywords:  self control; temptation; normative elimination; reference dependence; menu effects 
Date:  2022–08–12 
URL:  http://d.repec.org/n?u=RePEc:ash:wpaper:83&r=mic 
By:  Ivan Conjeaud 
Abstract:  Most contributions in the algorithmic collusion literature only consider symmetric algorithms interacting with each other. We study a simple model of algorithmic collusion in which Qlearning algorithms repeatedly play a prisoner's dilemma and allow players to choose different exploration policies. We characterize behavior of such algorithms with asymmetric policies for extreme values and prove that any Nash equilibrium features some cooperative behavior. We further investigate the dynamics for general profiles of exploration policy by running extensive numerical simulations which indicate symmetry of equilibria, and give insight for their distribution. 
Date:  2023–12 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2312.02644&r=mic 
By:  Niccolò Lomys (CSEF and Università degli Studi di Napoli Federico II.); Emanuele Tarantino (Luiss University, EIEF, and CEPR) 
Abstract:  We theoretically study the problem of a researcher seeking to identify and estimate the search cost distribution when a share of agents in the population observes some peers’ choices. To begin with, we show that social information changes agents’ optimal search and, as a result, the distributions of observable outcomes identifying the search model. Consequently, neglecting social information leads to nonidentification of the search cost distribution. Whether, as a result, search frictions are under or overestimated depends on the dataset’s content. Next, we present empirical strategies that restore identification and correct estimation. First, we show how to recover robust bounds on the search cost distribution by imposing only minimal assumptions on agents’ social information. Second, we explore how leveraging additional data or stronger assumptions can help obtain more informative estimates. 
Keywords:  Search & Learning; Social Information; Identification; Networks; Robustness; Partial Identification. 
JEL:  C1 C5 C8 D1 D6 D8 
Date:  2023–11–24 
URL:  http://d.repec.org/n?u=RePEc:sef:csefwp:694&r=mic 
By:  Wesley H. Holliday; Eric Pacuit 
Abstract:  May's Theorem [K. O. May, Econometrica 20 (1952) 680684] characterizes majority voting on two alternatives as the unique preferential voting method satisfying several simple axioms. Here we show that by adding some desirable axioms to May's axioms, we can uniquely determine how to vote on three alternatives. In particular, we add two axioms stating that the voting method should mitigate spoiler effects and avoid the socalled strong no show paradox. We prove a theorem stating that any preferential voting method satisfying our enlarged set of axioms, which includes some weak homogeneity and preservation axioms, agrees with Minimax voting in all threealternative elections, except perhaps in some improbable knifeedged elections in which ties may arise and be broken in different ways. 
Date:  2023–12 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2312.14256&r=mic 
By:  Jan Christoph Schlegel 
Abstract:  We study equilibrium investment into bidding and latency reduction for different sequencing policies. For a batch auction design, we observe that bidders shade bids according to the likelihood that competing bidders land in the current batch. Moreover, in equilibrium, in the exante investment stage before the auction, bidders invest into latency until they make zero profit in expectation. We compare the batch auction design to continuous time bidding policies (time boost) and observe that (depending on the choice of parameters) they obtain similar revenue and welfare guarantees. 
Date:  2023–12 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2312.02055&r=mic 