
on Game Theory 
By:  Peter A. Streufert 
Abstract:  This paper introduces Gm, which is a category for extensiveform games. It also provides some applications. The category's objects are games, which are understood to be sets of nodes which have been endowed with edges, information sets, actions, players, and utility functions. Its arrows are functions from source nodes to target nodes that preserve the additional structure. For instance, a game's informationset collection is newly regarded as a topological basis for the game's decisionnode set, and thus a morphism's continuity serves to preserve information sets. Given these definitions, a game monomorphism is characterized by the property of not mapping two source runs (plays) to the same target run. Further, a game isomorphism is characterized as a bijection whose restriction to decision nodes is a homeomorphism, whose induced player transformation is injective, and which strictly preserves the ordinal content of the utility functions. The category is then applied to some gametheoretic concepts beyond the definition of a game. A Selten subgame is characterized as a special kind of categorical subgame, and game isomorphisms are shown to preserve strategy sets, Nash equilibria, Selten subgames, subgameperfect equilibria, perfectinformation, and noabsentmindedness. Further, it is shown that the full subcategory for distinguishedaction sequence games is essentially wide in the category of all games, and that the full subcategory of actionset games is essentially wide in the full subcategory for games with noabsentmindedness. 
Date:  2021–05 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2105.11398&r= 
By:  Dai Zusai 
Abstract:  We present a general framework of evolutionary dynamics under persistent heterogeneity in payoff functions and revision protocols, allowing continuously many types in a game with finitely many strategies. Unlike the preceding literature, we do not assume anonymity of the game or aggregability of the dynamic. The dynamic is rigorously formulated as a differential equation of a joint probability measure of types and strategies. To establish a foundation of this framework, we clarify regularity assumptions on the revision protocol, the game and the type distribution to guarantee the existence of a unique solution trajectory as well as those to guarantee the existence of an equilibrium in a heterogeneous population game. We further verify equilibrium stationarity in general and stability in potential games under admissible dynamics. Our framework exhibits a wide range of possible applications, including equilibrium selection in Bayesian games and spatial evolution. 
Date:  2021–05 
URL:  http://d.repec.org/n?u=RePEc:toh:tupdaa:2&r= 
By:  Noga Alon; Kirill Rudov; Leeat Yariv 
Abstract:  We study the effectiveness of iterated elimination of strictlydominated actions in random games. We show that dominance solvability of games is vanishingly small as the number of at least one player's actions grows. Furthermore, conditional on dominance solvability, the number of iterations required to converge to Nash equilibrium grows rapidly as action sets grow. Nonetheless, when games are highly imbalanced, iterated elimination simplifies the game substantially by ruling out a sizable fraction of actions. Technically, we illustrate the usefulness of recent combinatorial methods for the analysis of general games. 
Date:  2021–05 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2105.10743&r= 
By:  Ludovic A. Julien 
Abstract:  This paper deals with the existence of a noncooperative sequential equilibrium in interrelated markets with heterogeneous atomic traders. Since this model features a rich set of strategic interactions, there are two kinds of problems associated with the existence of equilibrium. First, existence and uniqueness of followers' strategies are not guaranteed. Second, the notrade equilibrium is always an equilibrium outcome. To overcome these two difficulties we consider a differentiable approach. We show that the set of equations which determines the strategies of followers is a variety with the required dimension, i.e. the vector mapping which defines this set is a local C²diffeomorphism. The continuous differentiability of followers' strategies is critical for the existence of an interior equilibrium. Unlike the simultaneous move games, exchange can take place in one subgame while autarky can hold in another subgame, in which case only leaders (followers) make trade. Some examples buttress the approach and discuss the assumptions made on the primitives. 
Keywords:  Pure strategies, diffeomorphisms, StackelbergNash equilibrium 
JEL:  C72 D52 
Date:  2021 
URL:  http://d.repec.org/n?u=RePEc:drm:wpaper:202114&r= 
By:  Shinichi Ishihara (Toto Sugaku Kyoiku Kenkyusha, 121 Kudankita, Chiyodaku, Tokyo, Japan, 1020073); Junnosuke Shino (School of International Liberal Studies, Waseda University, 161 Nishiwaseda, Shinjukuku, Tokyo, Japan 1698050); Shimpei Yamauchi (University of Warwick, Faculty of Science) 
Abstract:  An interval game is an extension of the characteristic function form games, in which players are assumed to face payoff uncertainty. This characteristic function thus assigns a closed interval, instead of a real number. This paper proposes a new solution mapping of nperson interval games, called Shapley mapping and applies it to nperson interval games. It is shown that the Shapley mapping is the unique solution mapping that satisfies the axioms of (i) efficiency, (ii) symmetry, (iii) null player property and (iv) an interval game version of additivity. 
Keywords:  cooperative interval games; interval uncertainty; Shapley value; solution mapping; axiomatization 
Date:  2021–03 
URL:  http://d.repec.org/n?u=RePEc:wap:wpaper:2019&r= 
By:  Berliant, Marcus 
Abstract:  We examine the fine microstructure of commuting in a gametheoretic setting with a continuum of commuters. Commuters' home and work locations can be heterogeneous. A commuter transport network is exogenous. Traffic speed is determined by link capacity and by local congestion at a time and place along a link, where local congestion at a time and place is endogenous. The model can be reinterpreted to apply to congestion on the internet. We find sufficient conditions for existence of equilibrium, that multiple equilibria are ubiquitous, and that the welfare properties of morning and evening commute equilibria differ on a generalization of a directed tree. 
Keywords:  Commuting; Internet traffic; Congestion externality; Efficient Nash equilibrium 
JEL:  L86 R41 
Date:  2021–05–24 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:107937&r= 
By:  Stéphan Sémirat (GAEL  Laboratoire d'Economie Appliquée de Grenoble  INRAE  Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement  Grenoble INP  Institut polytechnique de Grenoble  Grenoble Institute of Technology  UGA  Université Grenoble Alpes  CNRS  Centre National de la Recherche Scientifique  UGA  Université Grenoble Alpes); Francoise Forges (CEREMADE  CEntre de REcherches en MAthématiques de la DEcision  CNRS  Centre National de la Recherche Scientifique  Université Paris DauphinePSL  PSL  Université Paris sciences et lettres) 
Abstract:  We consider a senderreceiver game, in which the sender has finitely many types and the receiver's decision is a real number. We assume that utility functions are concave, singlepeaked and singlecrossing. After the cheap talk phase, the receiver makes a decision, which requires the sender's approval to be implemented. Otherwise, the sender "exits". At a perfect Bayesian equilibrium without exit, the receiver must maximize his expected utility subject to the participation constraints of all positive probability types. This necessary condition may not hold at the receiver's prior belief, so that a nonrevealing equilibrium may fail to exist. Similarly, a fully revealing equilibrium may not exist either due to the sender's incentive compatibility conditions.We propose a constructive algorithm that always achieves a perfect Bayesian equilibrium without exit. 
Keywords:  Approval,cheap talk,senderreceiver game,participation constraints,singlecrossing 
Date:  2021–05 
URL:  http://d.repec.org/n?u=RePEc:hal:wpaper:hal03231673&r= 
By:  JeanFrançois Laslier (PSE  Paris School of Economics  ENPC  École des Ponts ParisTech  ENS Paris  École normale supérieure  Paris  PSL  Université Paris sciences et lettres  UP1  Université Paris 1 PanthéonSorbonne  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 Paris 1 PanthéonSorbonne  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) 
Abstract:  To any normal form game, we associate the symmetric twostage game in which, in a first stage, the roles to be played in the base game are randomly assigned. We show that any equilibrium of the κuniversalization of this extended game is an equilibrium of the base game played by altruistic players ("ex ante Homo Moralis is altruistic"), and that the converse is false. The paper presents the implications of this remark for the philosophical nature of ethical behavior (Kantianism behind the veil of ignorance implies but is stronger than altruism) and for its evolutionary foundations. 
Keywords:  ethics,games,evolution,altruism,universalization,Kant,Homo Moralis ethics,Homo Moralis 
Date:  2021–05 
URL:  http://d.repec.org/n?u=RePEc:hal:wpaper:halshs03227354&r= 
By:  Belleflamme, Paul; Peitz, Martin; Toulemonde, Eric 
Abstract:  We introduce asymmetries across platforms in the linear model of competing twosided platforms with singlehoming on both sides and fully characterize the price equilibrium. We identify market environments in which one platform has a larger market share on both sides while obtaining a lower profit than the other platform. This platform enjoys a competitive advantage on one or both sides. Our finding raises further doubts on using market shares as a measure of market power in platform markets. 
Keywords:  Antitrust; market power; Market Share; network effects; oligopoly; Twosided platforms 
JEL:  D43 L13 L86 
Date:  2020–08 
URL:  http://d.repec.org/n?u=RePEc:cpr:ceprdp:15204&r= 
By:  Seungjin Han 
Abstract:  This paper proposes a general competing mechanism game of incomplete information where a mechanism allows its designer to send a message to himself at the same time agents send messages. This paper introduces a notion of robust equilibrium. If each agent’s payoff function is separable with respect to principals’ actions, they lead to the full characterization of equilibrium allocations in terms of incentive compatible direct mechanisms without reference to the set of arbitrary mechanisms allowed in the game. Szentes’ Critique (Szentes (2010)) on the standard competing mechanism game of complete information is also valid in a model with incomplete information. 
Keywords:  competing mechanisms; robust equations; general mechanisms; direct mechanisms 
JEL:  D82 D86 
Date:  2021–05 
URL:  http://d.repec.org/n?u=RePEc:mcm:deptwp:202107&r= 
By:  Gabriel Desgranges; Sayantan Ghosal 
Abstract:  When are heterogenous beliefs compatible with equilibrium and if not, which nonequilibrium outcomes do they lead to? In this paper, we examine the conditions under which heterogenous beliefs lead to approximately selffulfilling outcomes consistent with all that is commonly known by each agent via an iterative elimination process. We develop a formal definition of approximately selffulfilling outcomes, pconsensus, and an associated, continuous measure of the degree of stability of equilibrium, pstability. Applying our concepts to intertemporal trade in a two period economy, we examine how heterogenous beliefs and heterogenous preferences interact to create to asset price bubbles. 
Keywords:  pconsensus, pstability, equilibrium, rationalizability, heterogeneous, beliefs, preferences, games, markets 
JEL:  C70 D84 
Date:  2021–05 
URL:  http://d.repec.org/n?u=RePEc:gla:glaewp:2021_07&r= 
By:  Dworczak, Piotr; Pavan, Alessandro 
Abstract:  We propose a robust solution concept for Bayesian persuasion that accounts for the Sender's ambiguity over (i) the exogenous sources of information the Receivers may learn from, and (ii) the way the Receivers play (when multiple strategy profiles are consistent with the assumed solution concept and the available information). The Sender proceeds in two steps. First, she identifies all information structures that yield the largest payoff in the "worstcase scenario," i.e., when Nature provides information and coordinates the Receivers' play to minimize the Sender's payoff. Second, she picks an information structure that, in case Nature and the Receivers play favorably to her, maximizes her expected payoff over all information structures that are "worstcase optimal." We characterize properties of robust solutions, identify conditions under which robustness requires separation of certain states, and qualify in what sense robustness calls for more information disclosure than standard Bayesian persuasion. Finally, we discuss how some of the results in the Bayesian persuasion literature change once robustness is accounted for. 
Keywords:  information design; Persuasion; robustness; worstcase optimality 
JEL:  D82 
Date:  2020–07 
URL:  http://d.repec.org/n?u=RePEc:cpr:ceprdp:15017&r= 
By:  Bandyopadhyay, Siddhartha; Cabrales, Antonio 
Abstract:  We consider a model where agents differ in their 'types' which determines their voluntary contribution towards a public good. We analyze what the equilibrium composition of groups are under centralized and centralized choice. We show that there exists a topdown sorting equilibrium i.e. an equilibrium where there exists a set of prices which leads to groups that can be ordered by level of types, with the first k types in the group with the highest price and so on. This exists both under decentralized and centralized choosing. We also analyze the model with endogenous group size and examine under what conditions is topdown sorting socially ecient. We illustrate when integration (i.e. mixing types so that each group's average type if the same) is socially better than topdown sorting. Finally, we show that top down sorting is efficient even when groups compete among themselves. 
Keywords:  Groupformation; integration; Public Good; Segregation; Topdown sorting 
JEL:  D02 D64 D71 H41 
Date:  2020–08 
URL:  http://d.repec.org/n?u=RePEc:cpr:ceprdp:15137&r= 
By:  Timothy N. Cason; Alex Tabarrok; Robertas Zubrickas 
JEL:  C72 C92 H41 
Date:  2021–06 
URL:  http://d.repec.org/n?u=RePEc:pur:prukra:1326&r= 
By:  Hsieh, ChihSheng; König, Michael; Liu, Xiaodong; Zimmermann, Christian 
Abstract:  This paper studies the impact of collaboration on research output. First, we build a microfounded model for scientific knowledge production, where collaboration between researchers is represented by a bipartite network. The equilibrium of the game incorporates both the complementarity effect between collaborating researchers and the substitutability effect between concurrent projects of the same researcher. Next, we develop a Bayesian MCMC procedure to estimate the structural parameters, taking into account the endogenous matching of researchers and projects. Finally, we illustrate the empirical relevance of the model by analyzing the coauthorship network of economists registered in the RePEc Author Service. 
Keywords:  bipartite networks; coauthorship networks; economics of science; research collaboration; Spillovers 
JEL:  C31 C72 D85 L14 
Date:  2020–08 
URL:  http://d.repec.org/n?u=RePEc:cpr:ceprdp:15195&r= 
By:  Soumen Banerjee; YiChun Chen; Yifei Sun 
Abstract:  We study full implementation with hard evidence in a bounded environment. By invoking monetary transfers off the equilibrium, we show that a social choice function is Nash implementable in a direct revelation mechanism if and only if it satisfies the measurability condition proposed by BenPorath and Lipman (2012). Building on a novel classification of lies according to their refutability with evidence, the mechanism requires only two agents, accounts for mixedstrategy equilibria, accommodates evidentiary costs, and can also be modified to account for limited solvency of the agents. We also establish a necessary and sufficient condition on the evidence structure for renegotiationproof bilateral contracts, based on the classification of lies. 
Date:  2021–05 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2105.12298&r= 
By:  Mark Armstrong; John Vickers 
Abstract:  We explore patterns of price competition in an oligopoly where consumers vary in the set of firms they consider for their purchase and buy from the lowestpriced firm they consider. We study a pattern of consideration, termed "symmetric interactions", that generalises models used in existing work (duopoly, symmetric firms, and firms with independent reach). Within this class, equilibrium profits are proportional to a firm's reach, firms with a larger reach set higher average prices, and a reduction in the number of firms (either by exit or by merger) harms consumers. However, increased competition (either by entry of by increased consumer awareness) does not always benefit consumers. We go on to study patterns of consideration with asymmetric interactions. In situations with disjoint reach and with nested reach we find equilibria in which price competition is "duopolistic": only two firms compete within each price range. We characterize the contrasting equilibrium patterns of price competition for all patterns of consideration in the threefirm case. 
Keywords:  Price competition, consideration sets, price dispersion, entry and merger 
JEL:  C72 D43 D83 L13 
Date:  2021–05–06 
URL:  http://d.repec.org/n?u=RePEc:oxf:wpaper:936&r= 
By:  Nieves Montes 
Abstract:  The Institutional Analysis and Development (IAD) framework is a conceptual toolbox put forward by Elinor Ostrom and colleagues in an effort to identify and delineate the universal common variables that structure the immense variety of human interactions. The framework identifies rules as one of the core concepts to determine the structure of interactions, and acknowledges their potential to steer a community towards more beneficial and socially desirable outcomes. This work presents the first attempt to turn the IAD framework into a computational model to allow communities of agents to formally perform whatif analysis on a given rule configuration. To do so, we define the Action Situation Language  or ASL  whose syntax is hgighly tailored to the components of the IAD framework and that we use to write descriptions of social interactions. ASL is complemented by a game engine that generates its semantics as an extensiveform game. These models, then, can be analyzed with the standard tools of game theory to predict which outcomes are being most incentivized, and evaluated according to their socially relevant properties. 
Date:  2021–05 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2105.13151&r= 
By:  Borrero, Miguel Borrero; Rubio, Santiago J. 
Abstract:  This paper studies how the investment in adaptation can influence the participation in an international environmental agreement (IEA) when countries decide in adaptation before they choose their levels of emissions. Two types of agreements are studied, a complete agreement for which countries coordinate their decisions on adaptation and emissions, and an adaptation agreement for which there is only coordination when countries decide their levels of adaptation. In both cases, we assume that the degree of effectiveness of adaptation is bounded from above, in order words, adaptation can alleviate the environmental problem, but it cannot solve it by itself leading the vulnerability of the country to almost zero. Our results show that the grand coalition could be stable for both types of agreement, but for extremely high degrees of effectiveness of adaptation. If this condition is not satisfied, the model predicts low levels of membership. The standard result of three countries for the complete agreement. For the adaptation agreement participation can be higher than three, but not higher than six countries. In any case, we can conclude that under reasonable values for the degree of effectiveness of adaptation, in our model adaptation does not promote participation in an IEA. 
Keywords:  Environmental Economics and Policy 
Date:  2021–05–24 
URL:  http://d.repec.org/n?u=RePEc:ags:feemwp:311055&r= 
By:  Bergemann, Dirk; Heumann, Tibor; Morris, Stephen 
Abstract:  We consider demand function competition with a finite number of agents and private information. We show that any degree of market power can arise in the unique equilibrium under an information structure that is arbitrarily close to complete information. Regardless of the number of agents and the correlation of payoÂ¤ shocks, market power may be arbitrarily close to zero (the competitive outcome) or arbitrarily large (so there is no trade). By contrast, price volatility is always lower than the variance of the aggregate shock across all information structures. Alternative trading mechanisms lead to very distinct bounds as a comparison with Cournot competition establishes. 
Keywords:  Cournot Competition; Demand function competition; incomplete information; market power; price impact; Price volatility; Supply function competition 
JEL:  C72 D43 D44 D83 G12 
Date:  2020–07 
URL:  http://d.repec.org/n?u=RePEc:cpr:ceprdp:15104&r= 
By:  Persichina, Marco (CERE  the Center for Environmental and Resource Economics) 
Abstract:  This work shows that defective behaviors from the cooperative equilibrium in the management of common resources can be fueled and triggered by the presence of agents with myopic behaviors. The behavior implemented by naïve agents, even if performed with cooperative intent, can activate a dynamic of cascading defections from the cooperative strategy within the harvesters’ group. This paper demonstrates and discusses that the apparent and detectable decay of the cooperative choices in the dilemmas of common resources is not an exclusive and indisputable signal of an escalation in freeriding intentions but also an outcome of the presentbiased preferences and myopic behaviors of the cooperative agents. Notably, within the context populated by conditional cooperators with a heterogeneous myopic discount factor, in the absence of information on agents’ intentions, the presentbiased preferences can trigger a strategy that directs the community to excessively increase its harvesting level, even in presence of the otherregarding motives. Therefore, lowering cooperative behaviors can also be the effect of the absence of coordination instruments in response to the cognitive bias that influences human behaviors. 
Keywords:  Present bias; Commons; Cooperation; Cascading Defections; Naïve Agent 
JEL:  C71 C73 D01 D90 D91 Q20 Q29 
Date:  2021–05–20 
URL:  http://d.repec.org/n?u=RePEc:hhs:slucer:2021_008&r= 
By:  Bergemann, Dirk; Strack, Philipp 
Abstract:  A single seller faces a sequence of buyers with unit demand. The buyers are forwardlooking and longlived but vanish (and are replaced) at a constant rate. The arrival time and the valuation is private information of each buyer and unobservable to the seller. Any incentive compatible mechanism has to induce truthtelling about the arrival time and the evolution of the valuation. We derive the optimal stationary mechanism in closed form and characterize its qualitative structure. As the arrival time is private information, the buyer can choose the time at which he reports his arrival. The truthtelling constraint regarding the arrival time can be represented as an optimal stopping problem. The stopping time determines the time at which the buyer decides to participate in the mechanism. The resulting value function of each buyer cannot be too convex and must be continuously differentiable everywhere, reflecting the option value of delaying participation. The optimal mechanism thus induces progressive participation by each buyer: he participates either immediately or at a future random time. 
Keywords:  Dynamic Mechanism Design; Interim Incentive Constraints; Interim Participation Constraints; Observable Arrival; Option value; Progressive Participation; Repeated Sales; Stopping Problem; Unobservable Arrival 
JEL:  D44 D82 D83 
Date:  2020–07 
URL:  http://d.repec.org/n?u=RePEc:cpr:ceprdp:15111&r= 
By:  Timothy N. Cason; Simanti Banerjee; Frans P. De Vries; Nick Hanley 
Abstract:  Classification 
Date:  2021–06 
URL:  http://d.repec.org/n?u=RePEc:pur:prukra:1327&r= 
By:  Foarta, Dana; Morelli, Massimo 
Abstract:  Decision makers called to evaluate and approve a reform, proposed by an interest group, a politician, or a bureaucracy, suffer from a double asymmetric information problem: about the competence of the proposer and the consequences of the proposal. Moreover, the ability of decision makers to evaluate proposals depends on the complexity of the legislative environment, itself a product of past reforms. We model the strategic interaction between reformers and decision makers as a function of legislative complexity, and study the dynamics of endogenous complexity and stability of reforms. Complexicationsimplication cycles can occur on the equilibrium path, and expected longrun complexity may be higher when competence of reform proposers is lower. The results apply to regulatory reforms, legislative politics, and institutional design. 
Keywords:  bureaucracy; Checks and balances; competence; Incremental Reforms; Information; interest groups; Politicians; Regulatory Complexity 
JEL:  D73 G28 H83 L51 
Date:  2020–08 
URL:  http://d.repec.org/n?u=RePEc:cpr:ceprdp:15136&r= 
By:  Dai Zusai 
Abstract:  We present a version of Lyapunov's direct method for stability of a set under a differential inclusion. We pay careful attention to the assumption of forward invariance of a basin of attraction, which is often overlooked when applying the method to local stability. Even if the value of a local Lyapunoov function monotonically changes in some neighborhood of the limit set, this alone does not prevent a trajectory from escaping from this particular neighborhood. In this note, we verify that we can construct a smaller but forward invariant neighborhood. As a corollary, we obtain a transitivity theorem on basins of attractions without requiring forward invariance. 
Date:  2021–05 
URL:  http://d.repec.org/n?u=RePEc:toh:tupdaa:3&r= 
By:  Harstad, Bård; Lancia, Francesco; Russo, Alessia 
Abstract:  We characterize the optimal policy and policy instruments for selfenforcing treaties when countries invest in green technology before they pollute. If the discount factor is too small to support the first best, then both emissions and investments will be larger than in the first best, when technology is expensive. When technology is inexpensive, countries must instead limit or tax green investment in order to make future punishment credible. We also uncover a novel advantage of price regulation over quantity regulation, namely that when regulation is sufficiently flexible to permit firms to react to noncompliance in another country, the temptation to defect is reduced. The model is tractable and allows for multiple extensions. 
Keywords:  climate change; compliance; environmental agreements; green technology; policy instruments; repeated games; selfenforcing treaties 
JEL:  D86 F53 H87 Q54 
Date:  2020–07 
URL:  http://d.repec.org/n?u=RePEc:cpr:ceprdp:15044&r= 
By:  Boucher, Vincent; Del Bello, Carlo; Panebianco, Fabrizio; Verdier, Thierry; Zenou, Yves 
Abstract:  We propose a model of intergenerational transmission of education wherein children belong to either higheducated or loweducated families. Children choose the intensity of their social activities, while parents decide how much educational effort to exert. We characterize the equilibrium and show the conditions under which cultural substitution or complementarity emerges. Using data on adolescents in the United States, we structurally estimate our model and find that, on average, children's homophily acts as a complement to the educational effort of higheducated parents but as a substitute for the educational effort of loweducated parents. We also perform some policy simulations. We find that policies that subsidize social interactions can backfire for loweducated students because they tend to increase their interactions with other loweducated students, which reduce the education effort of their parents and, thus, their chance of becoming educated. 
Keywords:  Education; Social Networks 
JEL:  D85 I21 Z13 
Date:  2020–07 
URL:  http://d.repec.org/n?u=RePEc:cpr:ceprdp:14997&r= 