
on Microeconomics 
By:  Federico Innocenti; Domenico Menicucci 
Abstract:  This paper examines the issue of product compatibility in an oligopoly with three multiproduct firms. Whereas most of the existing literature focuses on the extreme cases of full compatibility or full incompatibility, we look at asymmetric settings in which some firms make their products compatible with a standard technology and others do not. Our analysis reveals each firm’s individual incentive to adopt the standard, and allows to study a twostage game in which first each firm chooses its technological regime (compatibility or incompatibility), then price competition occurs given the regime each firm has selected at stage one. When firms are ex ante symmetric, we find that for each firm, compatibility weakly dominates incompatibility. In a setting in which a firm’s products have higher quality than its rivals’ products, individual incentives to make products incompatible emerge, first for the firm with higher quality products, then also for the other firms, as the quality difference increases. This paper sheds lights on markets in which some firms adopt the standard technology but other firms use proprietary systems. 
Keywords:  Compatibility, Spatial competition, Vertical differentiation, Asymmetric equilibrium, Competitive Bundling 
JEL:  D43 L13 
Date:  2021–03 
URL:  http://d.repec.org/n?u=RePEc:bon:boncrc:crctr224_2021_278&r=all 
By:  Brams, Steven J.; Ismail, Mehmet S. 
Abstract:  It is wellknown that Nash equilibria may not be Paretooptimal; worse, a unique Nash equilibrium may be Paretodominated, as in Prisoners’ Dilemma. By contrast, we prove a previously conjectured result: Every finite normalform game of complete information and common knowledge has at least one Paretooptimal nonmyopic equilibrium (NME) in pure strategies, which we define and illustrate. The outcome it gives, which depends on where play starts, may or may not coincide with that given by a Nash equilibrium. We use some simple examples to illustrate properties of NMEs—for instance, that NME outcomes are usually, though not always, maximin—and seem likely to foster cooperation in many games. Other approaches for analyzing farsighted strategic behavior in games are compared with the NME analysis. 
Keywords:  Game theory, theory of moves, twoperson games, cooperation 
JEL:  C70 D74 F50 
Date:  2021–03–21 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:106718&r=all 
By:  Le Van, Cuong; Pham, NgocSang 
Abstract:  We study the existence of equilibrium when agents’ preferences may not be convex. For some specific utility functions, we provide a necessary and sufficient condition under which there exists an equilibrium. The standard approach cannot be directly applied to our examples because the demand correspondence of some agents is neither single valued nor convex valued. 
Keywords:  Nonconvex preferences, general equilibrium. 
JEL:  D11 D51 
Date:  2021–03–13 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:106774&r=all 
By:  Françoise Forges (LEDa  Laboratoire d'Economie de Dauphine  IRD  Institut de Recherche pour le Développement  Université Paris DauphinePSL  PSL  Université Paris sciences et lettres  CNRS  Centre National de la Recherche Scientifique, Université Paris DauphinePSL  PSL  Université Paris sciences et lettres); Jérôme Renault (TSE  Toulouse School of Economics  UT1  Université Toulouse 1 Capitole  INRA  Institut National de la Recherche Agronomique  EHESS  École des hautes études en sciences sociales  CNRS  Centre National de la Recherche Scientifique, UT1  Université Toulouse 1 Capitole) 
Abstract:  We consider a senderreceiver game with an outside option for the sender. After the cheap talk phase, the receiver makes a proposal to the sender, which the latter can reject. We study situations in which the sender's approval is crucial to the receiver. We show that a partitional, (perfect Bayesian Nash) equilibrium exists if the sender has only two types or if the receiver's preferences over decisions do not depend on the type of the sender as long as the latter participates. The result does not extend: we construct a counterexample (with three types for the sender and typedependent affine utility functions) in which there is no mixed equilibrium. In the three type case, we provide a full characterization of (possibly mediated) equilibria. 
Date:  2021 
URL:  http://d.repec.org/n?u=RePEc:hal:journl:hal02440627&r=all 
By:  Michel Le Breton (TSE  Toulouse School of Economics  UT1  Université Toulouse 1 Capitole  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); Alexander Shapoval (Unknown); Shlomo Weber (Unknown) 
Abstract:  In this paper we examine a gametheoretical generalization of the landscape theory introduced by Axelrod and Bennett (1993). In their twobloc setting each player ranks the blocs on the basis of the sum of her individual evaluations of members of the group. We extend the Axelrod–Bennett setting by allowing an arbitrary number of blocs and expanding the set of possible deviations to include multicountry gradual deviations. We show that a Pareto optimal landscape equilibrium which is immune to profitable gradual deviations always exists. We also indicate that while a landscape equilibrium is a stronger concept than Nash equilibrium in pure strategies, it is weaker than strong Nash equilibrium. 
Keywords:  Landscape theory,Landscape equilibrium,Blocs,Gradual deviation,Potential functions,Hedonic games 
Date:  2021–01 
URL:  http://d.repec.org/n?u=RePEc:hal:journl:hal03156677&r=all 
By:  Yuhki Hosoya; Chaowen Yu 
Abstract:  We consider a game in which the action set of each player is uncountable, and show that, from weak assumptions on the common prior, for any mixed strategy there exists a pure strategy that is approximately equivalent to it. The assumption of this result can be further weakened if we consider a purification of an Nash equilibrium. Combined with the existence theorem for a Nash equilibrium, we derive an existence theorem for pure strategy approximated Nash equilibrium under sufficiently weak assumptions. All pure strategies we derive in this paper can take a finite number of possible actions. 
Date:  2021–03 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2103.07736&r=all 
By:  Axel Anderson (Department of Economics, Georgetown University); Lones Smith (Department of Economics, University of Wisconsin) 
Abstract:  We create a general and tractable theory of increasing sorting in pairwise matching models with transferable utility — one that subsumes Becker (1973) as the extreme cases with most and least sorting. We first prove that the positive quadrant dependence order smartly measures increasing sorting, e.g. it rises in the correlation of matched partners. Our theory centers on synergy — the cross partial difference or derivative of match production. Notably, if synergy everywhere increases, sorting need not rise, but cannot fall. To rescue increasing sorting, we posit often met crosssectional restrictions on match synergy. Our theory illuminates top economics sorting papers, affording quick proofs of their results and new insights. Synergy reflects basic economic forces, such as diminishing returns, moral hazard, insurance, and learning dynamics. Our proof develops and exploits new monotone comparative statics methods. The main proof proceeds by induction with finitely many types, and secures the continum type results by taking limits. Classification C6, D2, D5, J1 
Keywords:  Sorting, comparative statics, matching, complementarity, single crossing aggregation, monotone methods 
Date:  2021–03–16 
URL:  http://d.repec.org/n?u=RePEc:geo:guwopa:gueconwpa~212106&r=all 
By:  Bloch, Francis (Universite Paris 1 and Paris School of Economics); Chatterjee, Kalyan (Pennsylvania State University); Dutta, Bhaskar (University of Warwick and Ashoka University) 
Abstract:  This paper studies a game of attack and interception in a network, where a single attacker chooses a target and a path, and each node chooses a level of protection. We show that the Nash equilibrium of the game exists and is unique. It involves a mixed strategy of the attacker except when one target has a very high value relative to others. We characterize equilibrium attack paths and attack distributions as a function of the underlying network and target values. We also show that adding a link or increasing the value of a target may harm the attacker  a comparative statics e ect which is reminiscent of Braess's paradox in transportation economics. Finally, we contrast the Nash equilibrium with the equilibria of two variations of the model : one where nodes make sequential protection decisions upon observing the arrival of a suspicious object, and one where all nodes cooperate in defense. 
Keywords:  Keywords: Network interdiction ; Networks ; Attack and defense ; Inspection 
Date:  2021 
URL:  http://d.repec.org/n?u=RePEc:wrk:warwec:1338&r=all 
By:  Toomas Hinnosaar 
Abstract:  Most products are produced and sold by supply chain networks, where an interconnected network of producers and intermediaries set prices to maximize their profits. I show that there exists a unique equilibrium in a pricesetting game on a network. The key distortion reducing both total profits and social welfare is multiplemarginalization, which is magnified by strategic interactions. Individual profits are proportional to influentiality, which is a new measure of network centrality defined by the equilibrium characterization. The results emphasize the importance of the network structure when considering policy questions such as mergers or trade tariffs. 
Keywords:  price setting, networks, sequential games, multiplemarginalization, supply chains, mergers, tariffs, trade, centrality. 
JEL:  C72 L14 D43 
Date:  2020 
URL:  http://d.repec.org/n?u=RePEc:cca:wpaper:618&r=all 
By:  Alessandro De Chiara (Universitat de Barcelona, BEAT); Marco A. Schwarz (University of Innsbruck, CESifo) 
Abstract:  Firms often try to influence individuals that, like regulators, are tasked with advising or deciding on behalf of a third party. In a dynamic regulatory setting, we show that a firm may prefer to capture regulators through the promise of a lucrative future job opportunity (i.e., the revolvingdoor channel) than through a hidden payment (i.e., a bribe). This is because the revolving door publicly signals the firm's eagerness and commitment to rewarding lenient regulators, which facilitates collusive equilibria. We find that opening the revolving door conditional on the regulator's report is usually more efficient than a blanket ban on postagency employment and may increase social welfare. This insight extends to a variety of applications and can also be used to determine the optimal length of coolingoff periods. 
Keywords:  Corruption, dynamic games, regulatory capture, revolving door. 
JEL:  D73 D86 H11 J45 L51 
Date:  2021 
URL:  http://d.repec.org/n?u=RePEc:ewp:wpaper:410web&r=all 
By:  Loïc Berger (CNRS  Centre National de la Recherche Scientifique, IÉSEG School Of Management [Puteaux], EIEE  European Institute on Economics and the Environment, CMCC  Centro EuroMediterraneo per i Cambiamenti Climatici [Bologna]) 
Abstract:  This paper reflects on the notion of partial ambiguity. Using a framework decomposing ambiguity into distinct layers of analysis, among which are risk and model uncertainty, and allowing for different attitudes toward these layers, I show that partial ambiguity may prove less desirable than full ambiguity, even under ambiguity aversion. This observation poses difficulties for interpreting the notion of partial ambiguity in relation to the partial information available to determine the potential compositions of an ambiguous urn. Two Ellsbergstyle thought experiments are described to challenge the meaning of partial ambiguity further, and an alternative interpretation, based on a more ambiguous relation, is discussed. 
Keywords:  Ambiguity,model uncertainty,smooth ambiguity aversion,Ellsberg paradox 
Date:  2021 
URL:  http://d.repec.org/n?u=RePEc:hal:journl:hal03158580&r=all 
By:  Yun Kuen Cheung; Stefanos Leonardos; Georgios Piliouras 
Abstract:  We study learning dynamics in distributed production economies such as blockchain mining, peertopeer file sharing and crowdsourcing. These economies can be modelled as multiproduct Cournot competitions or allpay auctions (Tullock contests) when individual firms have market power, or as Fisher markets with quasilinear utilities when every firm has negligible influence on market outcomes. In the former case, we provide a formal proof that Gradient Ascent (GA) can be LiYorke chaotic for a step size as small as $\Theta(1/n)$, where $n$ is the number of firms. In stark contrast, for the Fisher market case, we derive a Proportional Response (PR) protocol that converges to market equilibrium. The positive results on the convergence of the PR dynamics are obtained in full generality, in the sense that they hold for Fisher markets with \emph{any} quasilinear utility functions. Conversely, the chaos results for the GA dynamics are established even in the simplest possible setting of two firms and one good, and they hold for a wide range of price functions with different demand elasticities. Our findings suggest that by considering multiagent interactions from a market rather than a gametheoretic perspective, we can formally derive natural learning protocols which are stable and converge to effective outcomes rather than being chaotic. 
Date:  2021–03 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2103.08529&r=all 
By:  Paula Onuchic 
Abstract:  A sender acquires a signal about an object's quality and commits to a rule to disclose its realizations to a receiver, who then chooses to buy the object or to keep an outside option of privately known value. Optimal disclosure rules typically conceal negative signal realizations when the object's sale is very profitable to the sender and positive signal realizations when the sale is less profitable. Using such disclosure rules, the advisor is able to steer sales from lower to higherprofitability objects. I show that, despite this strategic concealment of some signal realizations, the receiver may prefer being informed by a nontransparent sender, because the sender's hidden motives produce an additional incentive to invest in acquiring a precise signal of the object's quality. I use my model to evaluate policies commonly proposed in the context of financial advisors, such as mandatory disclosure of commissions and commission caps. 
Date:  2021–03 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2103.07446&r=all 
By:  Andrew Rhodes (TSE  Toulouse School of Economics  UT1  Université Toulouse 1 Capitole  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); Makoto Watanabe; Jidong Zhou 
Abstract:  This paper develops a new framework for studying multiproduct intermediaries when consumers demand multiple products and face search frictions. We show that a multiproduct intermediary is profitable even when it does not improve consumer search efficiency. The intermediary optimally stocks highvalue products exclusively to attract consumers to visit and then profits by selling nonexclusive products that are relatively cheap to buy from upstream suppliers. Relative to the social optimum, the intermediary tends to be too big and stock too many products exclusively. We use the framework to study the design of shopping malls and the impact of directtoconsumer sales by upstream suppliers on the retail market. 
Date:  2021–02 
URL:  http://d.repec.org/n?u=RePEc:hal:journl:hal03160803&r=all 