nep-gth New Economics Papers
on Game Theory
Issue of 2021‒02‒01
twenty-two papers chosen by
Sylvain Béal
Université de Franche-Comté

  1. Large Games with Heterogeneous Players By Serrano-Padial, Ricardo
  2. Deegan-Packel & Johnston spatial power indices and characterizations By Arnold Cédrick SOH VOUTSA
  3. Evolutionarily Stable (Mis)specifications: Theory and Applications By Kevin He; Jonathan Libgober
  4. The worst-case payoff in games with stochastic revision opportunities By Yevgeny Tsodikovich
  5. The Public Good spatial power index in political games By Arnold Cédrick SOH VOUTSA
  6. A Model of Market Making and Price Impact By Angad Singh
  7. Limited tenure concessions for collective goods By Nicolas Quérou; Agnes Tomini; Christopher Costello
  8. The Complex Political Game of Government Formation: A Nash Non-Cooperative Game Perspective By melhem, daniel; Azar, Mike
  9. Information Design by an Informed Designer By Frédéric Koessler; Vasiliki Skreta
  10. Multi-Player Bayesian Learning with Misspecified Models By Takeshi Murooka; Yuichi Yamamoto
  11. Cooperative Game Theory and the Theory of the State By McCain, Roger
  12. Dynamic Price Competition, Learning-By-Doing and Strategic Buyers By Andrew Sweeting; Dun Jia; Shen Hui; Xinlu Yao
  13. Per Unit and Ad Valorem Royalties in a Patent Licensing Game By Marta Montinaro; Rupayan Pal; Marcella Scrimitore
  14. The Endogenous Formation of Common Pool Resource Coalitions By Carlos A. Chávez; James J. Murphy; Felipe J. Quezada; John K. Stranlund
  15. The Lottery Player’s Fallacy Why Labels Predict Strategic Choices By Irenaeus Wolff
  16. Game-Theoretic Analyses of US Settlement Allowing for Coercion By Pardini, Chelsea; Espinola-Arredondo, Ana
  17. Climate Change Adaptation under Heterogeneous Beliefs By Marcel Nutz; Florian Stebegg
  18. A Pairwise Strategic Network Formation Model with Group Heterogeneity: With an Application to International Travel By Tadao Hoshino
  19. Mixed Bundling in Oligopoly Markets By Jidong Zhou
  20. Rating the Competition: Seller Ratings and Intra-Platform Competition By Charlson, G.
  21. The size of the maximum antichains in products of linear orders By Denis Bouyssou; Thierry Marchant; Marc Pirlot
  22. Consumer Information and the Limits to Competition By Mark Armstrong; Jidong Zhou

  1. By: Serrano-Padial, Ricardo (School of Economics)
    Abstract: We study large games played by heterogeneous agents whose payoffs depend on the aggregate action and provide novel equilibrium selection and comparative statics results. We prove the equivalence between the global games selection and potential maximization in games with strategic complementarities, and characterize the selected equilibrium as the solution to maximizing the ex-ante expected payoffs of a player with pessimistic beliefs. To obtain our results we uncover two key properties. First, we show that potential games exhibit quasilinear payoffs, which include as examples Cournot competition, public goods and externalities, search models and coordination games. Second, we show that beliefs in the global game satisfy a generalized Laplacian property, which links average beliefs about the aggregate action to the uniform distribution. Our comparative statics results rely on average rather than pointwise conditions on payoffs and can be used to analyze both parameter changes and the impact of heterogeneity.
    Keywords: aggregative games; potential games; global games; comparative statics; noise-independent selection; Laplacian beliefs
    JEL: C72 D82 D83 D84
    Date: 2020–08–18
  2. By: Arnold Cédrick SOH VOUTSA (Université de Cergy-Pontoise, THEMA)
    Abstract: In this paper, we propose two spatial power indices in political games, taking into account ideological preferences of players. To do this, we develop an explanatory spatial model linked to the asymmetry Deegan-Pakel index introduced by Rapoport & Golan [Rapoport, A., Golan, E., 1985. Assessment of political power in the israeli knesset. American Political Science Review 79 (3), 673-692], which is the original Deegan-Packel index readjusted for measuring power according to the spatial preferences of players in real political games. In addition to extending such a readjustment for the original John- ston index | transforming it concomitantly into the Johnston spatial power index | this paper presents both the general versions of these two spatial indices, and their axiomatic characterizations through new axioms such as the vetoer property and others mainly in- spired from Lorenzo-Freire et al. [Lorenzo-Freire, S., Alonso-Meijide, J. M., Casas-Mendez, B., Fiestras-Janeiro, M. G., 2007. Characterizations of the Deegan-Packel and johnston power indices. European Journal of Operational Research 177 (1), 431-444].
    Keywords: Game theory, Spatial voting games, Deegan-Packel spatial power index, Johnston spatial power index, Axiomatic characterizations, Political games.
    JEL: C71 D71
    Date: 2020
  3. By: Kevin He; Jonathan Libgober
    Abstract: We introduce an evolutionary framework to evaluate competing (mis)specifications in strategic situations, focusing on which misspecifications can persist over a correct specification. Agents with heterogeneous specifications coexist in a society and repeatedly match against random opponents to play a stage game. They draw Bayesian inferences about the environment based on personal experience, so their learning depends on the distribution of specifications and matching assortativity in the society. One specification is evolutionarily stable against another if, whenever sufficiently prevalent, its adherents obtain higher expected objective payoffs than their counterparts. The learning channel leads to novel stability phenomena compared to frameworks where the heritable unit of cultural transmission is a single belief instead of a specification (i.e., set of feasible beliefs). We apply the framework to linear-quadratic-normal games where players receive correlated signals but possibly misperceive the information structure. The correct specification is not evolutionarily stable against a correlational error, whose direction depends on matching assortativity. As another application, the framework also endogenizes coarse analogy classes in centipede games.
    Date: 2020–12
  4. By: Yevgeny Tsodikovich (AMSE - Aix-Marseille Sciences Economiques - EHESS - École des hautes études en sciences sociales - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique - AMU - Aix Marseille Université)
    Abstract: We study infinitely repeated games in which players are limited to subsets of their action space at each stage—a generalization of asynchronous games. This framework is broad enough to model many real-life repeated scenarios with restrictions, such as portfolio management, learning by doing and training. We present conditions under which rigidity in the choice of actions benefits all players in terms of worst-case equilibrium payoff and worst-case payoff. To provide structure, we exemplify our result in a model of a two-player repeated game, where we derive a formula for the worst-case payoff. Moreover, we show that in zero-sum games, lack of knowledge about the timing of the revision can compensate for inability to change the action.
    Keywords: asynchronous games,rational minimax,worst-case payoffs,commitment,exogenous timing
    Date: 2020
  5. By: Arnold Cédrick SOH VOUTSA (Université de Cergy-Pontoise, THEMA)
    Abstract: We propose a new spatial index called the Public Good spatial index, which is the spatial version of the standard Public Good index under independence behaviors (PGI). However, we show that the spatial model used, is not well suited for both, the standard Shapley Shubik index and the standard Public Good index under Ho- mogeneity behaviors (PGH); and consequently they do not have a consistent spatial version with respect to our model. By contrast, the same spatial model is appro- priated for the Banzhaf index and the aforementioned PGI index, concomitantly, allowing their spatial versions in political games. We also argue that those two well convenient spatial indices are only understandable under behavioral descriptions with independence assumptions on political issues. Finally, the paper details our findings by means of examples, comparisons, and it also provides relevant ways of computing spatial power indices in real case studies when it comes to lower dimensions.
    Keywords: political games, spatial power indices, Public Good index, Banzhaf index.
    JEL: C71 D71
    Date: 2021
  6. By: Angad Singh
    Abstract: Traders constantly consider the price impact associated with changing their positions. This paper seeks to understand how price impact emerges from the quoting strategies of market makers. To this end, market making is modeled as a dynamic auction using the mathematical framework of Stochastic Differential Games. In Nash Equilibrium, the market makers' quoting strategies generate a price impact function that is of the same form as the celebrated Almgren-Chriss model. The key insight is that price impact is the mechanism through which market makers earn profits while matching their books. As such, price impact is an essential feature of markets where flow is intermediated by market makers.
    Date: 2021–01
  7. By: Nicolas Quérou (CEE-M - Centre d'Economie de l'Environnement - Montpellier - FRE2010 - UM - Université de Montpellier - CNRS - Centre National de la Recherche Scientifique - Montpellier SupAgro - Institut national d’études supérieures agronomiques de Montpellier - Institut Agro - Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement); Agnes Tomini (AMSE - Aix-Marseille Sciences Economiques - EHESS - École des hautes études en sciences sociales - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique - AMU - Aix Marseille Université); Christopher Costello (UCSB - University of California [Santa Barbara] - University of California)
    Abstract: This paper proposes and analyzes the consequences of a widely-used, but little-studied institution, limited-tenure concessions, for governing club goods and common-pool resources. We first show in a simple repeated game setting that such a system can incentivize socially-efficient provision of club goods. We then extend the model to account for spatially-connected resources, an arbitrary number of heterogeneous agents, and natural resource dynamics, and show that the basic ability of limited-tenure concessions to incentivize the first best private provision is preserved in this rich setting that is more representative of natural resources such as fish, water, and game. The duration of tenure and the dispersal of the resource then play pivotal roles in whether this limited-duration concession achieves the socially optimal outcome. Finally, in a setting with costly monitoring, we discuss the features of a concession contract that ensure first-best behavior, but at least cost to the implementing agency.
    Keywords: Concessions,club goods,cooperation,natural resources,spatial externalities,dynamic games
    Date: 2020–10–19
  8. By: melhem, daniel; Azar, Mike
    Abstract: We use the Nash Equilibrium to solve the complex Lebanese political game of forming a government. We solve for a probable and logical outcome given each player’s priority issues relative to each other player’s priority issues. The results indicate that there is a global best response equilibrium between Hizballah/Amal (“H/A”), Other National Parties (all major parties, including Patriarch) (“ONP”), and France. The equilibrium requires a cooperative approach between H/A and ONP to find a solution that satisfies both, particularly in respect of control over the Ministry of Finance (“MOF”), which represents an important executive position in the country’s domestic political system. For example, H/A (given its relatively higher utility for this variable) maintains nominal control over MOF while ONP shares in some manner in the nomination. This would ensure stability of the political regime (another priority parameter for H/A, ONP, and France), which could then facilitate at least some economic reforms (a priority parameter for France for reasons discussed in this paper). Under this scenario, France is the biggest winner in respect of its regional interests as the success or failure of its initiative in Lebanon may have significant consequences on its credibility in the East Mediterranean region. However, this equilibrium is sensitive to national and regional variables. Further analysis of the statistics indicates that France, in this game, is not the primary player, as the USA has the capability to sway the game in its favor. The results further indicate a clear conflict between the regional interests of France and the USA. The USA’s payoff function was not clear vis-a-vis the other players and their preferential interests. This may be due to the USA’s main interests residing in other national and regional considerations not considered in this game. Therefore, a more expansive game that integrates additional national and regional preferential interests and players may be needed to fully assess the role and the contribution of the USA in the dilemma that is the Lebanese government formation.
    Keywords: Nash Equilibrium, Best Response, Lebanese complex political Game, International Relations, Conflicts, F-score, Z-score
    JEL: F0
    Date: 2020–12–08
  9. By: Frédéric Koessler (PSE - Paris School of Economics - ENPC - École des Ponts ParisTech - ENS Paris - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique - EHESS - École des hautes études en sciences sociales - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, PJSE - Paris Jourdan Sciences Economiques - UP1 - Université Panthéon-Sorbonne - ENS Paris - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement); Vasiliki Skreta (CEPR - Center for Economic Policy Research - CEPR, University of Texas at Austin [Austin], UCL - University College of London [London])
    Abstract: A designer is privately informed about the state and chooses an information disclosure mechanism to influence the decisions of multiple agents playing a game. We define an intuitive class of incentive compatible information disclosure mechanisms which we coin interim optimal mechanisms. We prove that an interim optimal mechanism exists, and that it is an equilibrium outcome of the interim information design game. An ex-ante optimal mechanism may not be interim optimal, but it is whenever it is ex-post optimal. In addition, in leading settings in which action sets are binary, every ex-ante optimal mechanism is interim optimal. We relate interim optimal mechanisms to other solutions of informed principal problems.
    Keywords: strong-neologism proofness,neutral optimum,informed principal,Bayesian persuasion,interim information design,core mechanism,verifiable types.
    Date: 2021–02
  10. By: Takeshi Murooka (Osaka School of International Public Policy (OSIPP), Osaka University); Yuichi Yamamoto (Institute of Economic Research, Hitotsubashi University)
    Abstract: We consider strategic players who may have a misspecified view about an environment, and investigate their long-run behavior. Each period, players simultaneously take actions, observe a public outcome, and then update own belief about an uncertain economic state by using Bayes' rule. We provide a condition under which players' beliefs and actions converge to a steady state, and then characterize how one's misspecification influences the long-run (steady-state) actions. When a player has a biased view about the physical environment (e.g., overconfidence on own capability or prejudice on an opponent's capability), the presence of strategic interaction influences the size of the impact of misspecification, but not the direction. In particular, when the game is symmetric, the presence of strategic interaction amplifies the deviation of the long-run actions from those in the correctly specified model. When a player misspecifies the opponent's view about the environment (e.g., the player is not aware of the opponent's bias), the strategic interaction generates a directional impact for the long-run actions. We extensively discuss implications to a variety of applications, such as Cournot duopoly, team production, tournaments, and discrimination.
    Keywords: model misspecification, learning, convergence, overconfidence, bias transmission
    JEL: C73 D83 D90 D91
    Date: 2021–01
  11. By: McCain, Roger (School of Economics LeBow College of Business Drexel University)
    Abstract: In Welfare Economics and the Theory of the State, Baumol (1952) argued that phenomena of the sort that came to be known as “market failures” (Bator 1958) marked out the domain of action of a liberal state in a predominantly market economy. More recently, as the influence of game theory on economics has become more important, economists have often made the contrast of cooperative and noncooperative solutions a basis for such a judgment, characterizing “market failures” as inefficient noncooperative outcomes and arguing that state action could be justified as realizing a cooperative solution. However, the development of cooperative game theory has made it difficult to formalize this informal argument. This paper revisits the issue, adapting ideas from effectivity theory in cooperative game theory for special cases in which limited money transfers are allowed. Representing the game in extensive form, money transfers are among the basic proper subgames of the underlying game. Because backward induction eliminates the transfers, transfers never occur in the noncooperative (subgame perfect Nash) equilibrium of the game. However, transfers may dominate non-transfer solutions and define the core of the cooperative game, in one or both of two senses. Examples are given in which cooperative solutions without transfers do not improve on the noncooperative equilibrium, but solutions in the effectivity cores with transfers provide plausible market and public policy solutions. For large-N games, following a tactic in The Theory of Games and Economic Behavior, the paper posits a fictitious N+1st player whose outcome set is null and whose only strategies are transfers. Since the N+1st player – “the state” – can be a member of any coalitions, some transfers may be available to any coalition. This model is used to characterize a Pigovian tax and to argue that the stability of the tax may depend on how the revenue from the tax is redistributed, suggesting a rationale for a proposal due to the Climate Leadership Council, a free-market conservative group.
    Keywords: cooperative; transfers; game theory; public policy
    JEL: C70 D70 H20
    Date: 2021–01–11
  12. By: Andrew Sweeting; Dun Jia; Shen Hui; Xinlu Yao
    Abstract: We generalize recent models of dynamic price competition where sellers benefit from learning-by-doing by allowing for long-lived strategic buyers, with a single parameter capturing the extent to which each buyer internalizes future buyer surplus. Many of the equilibria that exist when buyers are atomistic or myopic are eliminated when buyers internalize even a modest share of their effects on future surplus. The equilibria that survive tend to be those where long-run market competition is preserved.
    JEL: C73 D21 D43 L13 L41
    Date: 2020–12
  13. By: Marta Montinaro (University of Salento); Rupayan Pal (Indira Gandhi Institute of Development Research (IGIDR)); Marcella Scrimitore (University of Salento)
    Abstract: In a context of product innovation, we study two-part tariff licensing between a patentee and a potential rival which compete in a differentiated product market characterized by network externalities. The latter are shown to crucially affect the relative profitability of Cournot vs. Bertrand when a per unit royalty is applied. By contrast, we find that Cournot yields higher profits than Bertrand under ad valorem royalties, regardless of the strength of network effects.
    Keywords: Licensing, Product Innovation, Bertrand, Cournot, Network Effects
    JEL: L13 L20 D43
    Date: 2020–10
  14. By: Carlos A. Chávez (Universidad de Talca); James J. Murphy (Department of Economics, University of Alaska Anchorage); Felipe J. Quezada (University of Massachusetts Amherst); John K. Stranlund (University of Massachusetts Amherst)
    Abstract: We develop a theoretical model of endogenous CPR coalition formation in which the resource is co-defended with costly monitoring by coalition members and sanctions for encroachment imposed by the government. We demonstrate that CPR coalitions can form even when monitoring is so costly that coalition members choose not to monitor for encroachment, but the coalitions will be relatively small. Larger coalitions will form if monitoring costs are low enough to yield effective deterrence. We tested the results of the model using lab-in-field experiments with fishers who were members of Chile’s territorial use rights fisheries (TURFs) and in the lab with Chilean university students. We find that fishers frequently formed CPR coalitions, even when they could not deter outsider poaching. Fishers usually formed the grand coalition when the monitoring cost was low, but they formed smaller coalitions when monitoring was more costly. Fishers invested in monitoring frequently and these investments reduced poaching. Relative to open access, when coalitions formed, total harvest effort was curtailed and earnings for coalition members generally increased. Students formed coalitions less frequently, these coalitions tended to be small, and they infrequently invested in monitoring, even when it was profitable to do so. Consequently, student coalition member earnings were not better off on average than under open access.
    Keywords: experimental economics, Common pool resources; enforcement; field experiments; poaching; territorial use rights fisheries; social dilemma; fisheries management; development economics; co-enforcement; coalition formation; encroachment
    JEL: C72 C90 C93 D70 K42 Q22 Q28 Q56 H40
    Date: 2021–01
  15. By: Irenaeus Wolff
    Abstract: This paper examines games with non-neutral option labels (such as “A†, “B†, “A†, “A†) and finds surprisingly invariant behaviour across games. The behaviour closely resembles the choices people make when they have to bet on one of the options in individual lotteries. An option’s ‘representativeness’ (lack of distinguishing features) and ‘reachability’ (physical centrality, salience, and va- lence) determine choice behaviour in both the lotteries and the highly strategic games. There is no evidence of people best-responding to others’ betting(-like) behaviour. This is in line with the idea that once people decide that strategic reasoning would not take them any further, they pick an alternative as if they were betting on one of their ‘current best-responses’. The ￿ndings explain the well-documented seeker advantage in hide-and-seek games, as well as why par- ticipants often display behaviour that could be exploited by others. On top, they help understand why in national lotteries, people also tend to bet on identical subsets of the available numbers.
    Keywords: Bounded Rationality, Level-k, Salience, Strategic Behaviour, Hide & Seek, Discoordination, Rock-Paper-Scissors, Representativeness.
    Date: 2021
  16. By: Pardini, Chelsea (Washington State University); Espinola-Arredondo, Ana (Washington State University)
    Abstract: Previous game-theoretic analyses of the settlement of the United States assume that Indigenous peoples and settler colonizers either engaged in free exchange or total war for land. We reframe the model to consider that violence, including coercion, was present in most of their interactions; that is, we allow for the settler colonizer to engage in coercion to strategically lower their appropriation costs for Indigenous peoples' lands. We find that the ettler strategically uses violence to pay less in exchanges for Indigenous peoples' lands. In addition, we examine how uncertainty, about whether an agreement can ensure the avoidance of all-out conflict, affects initial violence and resistance. We find that the likelihood of all out-conflict affects settler violence and it critically depends on whether the Indigenous people can seek compensation.
    Keywords: Settler colonialism; coercion; violence; game theory
    JEL: C78 D63 D74 K10 N41
    Date: 2020–10–20
  17. By: Marcel Nutz; Florian Stebegg
    Abstract: We study strategic interactions between firms with heterogeneous beliefs about future climate impacts. To that end, we propose a Cournot-type equilibrium model where firms choose mitigation efforts and production quantities such as to maximize the expected profits under their subjective beliefs. It is shown that optimal mitigation efforts are increased by the presence of uncertainty and act as substitutes; i.e., one firm's lack of mitigation incentivizes others to act more decidedly, and vice versa.
    Date: 2021–01
  18. By: Tadao Hoshino
    Abstract: In this study, we consider a pairwise network formation model in which each dyad of agents strategically determines the link status between them. Our model allows the agents to have latent group heterogeneity in the propensity of link formation. For the model estimation, we propose a three-step maximum likelihood (ML) method. First, we obtain consistent estimates for the heterogeneity parameters at individual level using the ML estimator. Second, we estimate the latent group structure using the binary segmentation algorithm based on the results obtained from the first step. Finally, based on the estimated group membership, we re-execute the ML estimation. Under certain regularity conditions, we show that the proposed estimator is asymptotically unbiased and distributed as normal at the parametric rate. As an empirical illustration, we focus on the network data of international visa-free travels. The results indicate the presence of significant strategic complementarity and a certain level of degree heterogeneity in the network formation behavior.
    Date: 2020–12
  19. By: Jidong Zhou (Cowles Foundation, Yale University)
    Abstract: This paper proposes a framework for studying competitive mixed bundling with an arbitrary number of ï¬ rms. We examine both a ï¬ rm’s incentive to introduce mixed bundling and equilibrium tariffs when all ï¬ rms adopt the mixed-bundling strategy. In the duopoly case, relative to separate sales, mixed bundling has ambiguous impacts on prices, proï¬ t and consumer surplus; with many ï¬ rms, however, mixed bundling typically lowers all prices, harms ï¬ rms and beneï¬ ts consumers.
    Keywords: Bundling, Multiproduct pricing, Price competition, Oligopoly
    JEL: D43 L13 L15
    Date: 2021–01
  20. By: Charlson, G.
    Abstract: Product ratings are commonplace on large online platforms, like Airbnb and Amazon Marketplace. One use for these ratings is to order search results. Platform owners are able to choose the extent to which ratings can be used to determine the probability a given seller is observed by a sets of buyers. Since demand is higher for high quality products, there is an incentive to increase the probability that highly-rated sellers are observed by biasing search results towards them. However, biasing search results in this way results in competition being more concentrated, reducing prices. The extent to which it is profitable to use ratings as a means of ordering search results depends on the properties of the market(s) the platform operates in.
    Keywords: Networks, strategic interaction, network games, interventions, industrial organisation, platforms
    JEL: D40 L10 L40
    Date: 2021–01–14
  21. By: Denis Bouyssou (LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision - Université Paris Dauphine-PSL - PSL - Université Paris sciences et lettres - CNRS - Centre National de la Recherche Scientifique); Thierry Marchant (UGENT - Ghent University [Belgium]); Marc Pirlot (UMons - Université de Mons)
    Abstract: The size of maximum antichains in the product of n linear orders is known when the n linear orders have the same length. We present an exact expression for the size of maximum antichains when the linear orders have (possibly) different lengths. From this, we derive an exact expression for the size of maximum antichains in the product of n linear orders with the same length. This expression is equivalent to but different from the existing expression. It allows us to present an asymptotic result for the size of maximum antichains of n linear orders with the same length m going to infinity.
    Keywords: maximal antichain,Sperner,multichoice cooperative game,linear orders Mathematics Subject Classification (2010) 91B06
    Date: 2020
  22. By: Mark Armstrong (Department of Economics Oxford University); Jidong Zhou (Cowles Foundation, Yale University)
    Abstract: This paper studies competition between ï¬ rms when consumers observe a private signal of their preferences over products. Within the class of signal structures which induce pure-strategy pricing equilibria, we derive signal structures which are optimal for ï¬ rms and those which are optimal for consumers. The ï¬ rm-optimal policy ampliï¬ es underlying product differentiation, thereby relaxing competition, while ensuring consumers purchase their preferred product, thereby maximizing total welfare. The consumer-optimal policy dampens differentiation, which intensiï¬ es competition, but induces some consumers to buy their less-preferred product. Our analysis sheds light on the limits to competition when the information possessed by consumers can be designed flexibly.
    Keywords: Information design, Bertrand competition, Product differentiation, Online platforms
    JEL: D43 D83 L13
    Date: 2021–01

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