
on Game Theory 
By:  Maria Montero (University of Nottingham) 
Abstract:  This paper studies an extensive form game of coalition formation with random proposers in games with externalities. It is shown that an agreement will be reached without delay if any set of coalitions profits from merging. Even under this strong condition, the equilibrium coalition structure is not necessarily efficient. There may be multiple equilibria even in the absence of externalities, and symmetric players are not necessarily treated symmetrically in equilibrium. If the grand coalition forms without delay in equilibrium, expected payoffs must be in the core of the characteristic function game that assigns to each coalition its equilibrium payoff. Compared with the rule of order process of Ray and Vohra (1999), the bargaining procedure with random proposers tends to give a large advantage to the proposer, whereas the bargaining procedure with a rule of order tends to favor the responders. The equilibria of the two procedures cannot be ranked in general in terms of efficiency. 
Keywords:  coalition formation, externalities, partition function, random proposers, core, multiple equilibria 
Date:  2021–05 
URL:  http://d.repec.org/n?u=RePEc:not:notcdx:202105&r= 
By:  Ratul Lahkar (Ashoka University); Vinay Ramani (Indian Institute of Management, Vishakhapatnam) 
Abstract:  We consider a large population of firms in a market environment. The firms are divided into a finite set of types, with each type being characterized by a distinct private cost function. Moreover, the firms generate an external cost like pollution in the production process. As a result, the Nash equilibrium outcome is not socially optimal. We propose an evolutionary implementation mechanism to achieve the socially optimal outcome. In contrast to the classical Pigouvian pricing and the VCG mechanism, evolutionarily implementation does not require the planner to know or elicit any private information from firms. Hence, it is informationally parsimonious. By imposing a tax equal to the current external damage being imposed by a firm, the planner can guide the evolution of the society towards the social optimum. The imposition of the tax generates a potential game whose potential function is the social welfare function of the model. Evolutionary dynamics converge to the maximizer of this function thereby evolutionarily implementing the social welfare maximizer. 
Keywords:  Evolutionary Implementation; Negative Externality; Potential Games; Pigouvian Tax; Dominant Strategy Implementation 
Date:  2021–10 
URL:  http://d.repec.org/n?u=RePEc:ash:wpaper:68&r= 
By:  Lu Dong (Nanjing Audit University); Lingbo Huang (Nanjing Audit University); Jaimie W. Lien (Chinese University of Hong Kong); Jie Zheng (Tsinghua University) 
Abstract:  In a social network in which friendly and rival bilateral links can be formed, how do alliances between decisionmakers form, and what determines whether a conflict will arise? We study a network formation game between exante symmetric players in the laboratory to examine the dynamics of alliance formation and conflict evolution. A peaceful equilibrium yields the greatest social welfare, while a successful bullying attack transfers the victimized playerâ€™s resources evenly to the attackers at a cost. Consistently with the theoretical model predictions, peaceful and bullying outcomes are prevalent among the randomly rematched experimental groups, based on the cost of attack. We further examine the dynamics leading to the final network and find that groups tend to coordinate quickly on a first target for attack, while the first attacker entails a nonnegligible risk of successful counterattack by initiating the coordination. These findings provide insights for understanding social dynamics in group coordination. 
Keywords:  network formation, conflict, alliance, bully, peace 
Date:  2021–04 
URL:  http://d.repec.org/n?u=RePEc:not:notcdx:202104&r= 
By:  Masaaki Fujii (Quantitative Finance Course, Graduate School of Economics, The University of Tokyo); Akihiko Takahashi (Quantitative Finance Course, Graduate School of Economics, The University of Tokyo) 
Abstract:  In this work, we study an equilibriumbased continuous asset pricing problem which seeks to form a price process endogenously by requiring it to balance the flow of saleandpurchase orders in the exchange market, where a large number of agents 1 â‰¤ i â‰¤ N are interacting through the market price. Adopting a mean field game (MFG) approach, we find a special form of forwardbackward stochastic differential equations of McKeanVlasov type with common noise whose solution provides an approximate of the market price. We show the convergence of the net order flow to zero in the large Nlimit and get the order of convergence in N under some conditions. An extension of the model to a setup with multiple populations, where the agents within each population share the same cost and coefficient functions but they can be different population by population, is also discussed. 
Date:  2021–09 
URL:  http://d.repec.org/n?u=RePEc:cfi:fseres:cf521&r= 
By:  Wolfgang Buchholz; Keisuke Hattori 
Abstract:  This paper considers endogenous coalition formations and endogenous technology choices in a model of private provision of global public goods. We show that the possibility of future interstate (partial) coordination may hinder the current adoption of better technology by a country outside the cooperation, which may exacerbate an existing underprovision problem. In particular, in the subgame perfect equilibrium of a threestage game, we find two paradoxical results: prohibition of the formation of future partial coalitions encourages the country outside the cooperation to adopt better technology, which could lead to an increase in the total public good supply and an improvement of global welfare. The results have an important policy implication: in the context of the Paris Agreement, for example, a large country announces lower nationally determined contributions by a strategic incentive to adopt lower technology to motivate coalition building by other nations, which in the end may lead to lower aggregate publicgood supply and global welfare. 
Keywords:  coalition formation, public goods, endogenous technology, environmental agreements 
JEL:  H41 F53 Q54 Q55 
Date:  2021 
URL:  http://d.repec.org/n?u=RePEc:ces:ceswps:_9354&r= 
By:  Renato Soeiro; Alberto Pinto 
Abstract:  The partition of society into groups, polarization, and social networks are part of most conversations today. How do they influence price competition? We discuss Bertrand duopoly equilibria with demand subject to network effects. Contrary to models where network effects depend on one aggregate variable (demand for each choice), partitioning the dependence into groups creates a wealth of pure price equilibria with profit for both price setters, even if positive network effects are the dominant element of the game. If there is some asymmetry in how groups interact, two groups are sufficient. If network effects are based on undirected and unweighted graphs, at least five groups are required but, without other differentiation, outcomes are symmetric. 
Date:  2021–10 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2110.05891&r= 
By:  Sosung Baik; SungHa Hwang 
Abstract:  We study the optimal auction design problem when bidders' preferences follow the maxmin expected utility model. We suppose that each bidder's set of priors consists of beliefs close to the seller's belief, where "closeness" is defined by a divergence. For a given allocation rule, we identify a class of optimal transfer candidates, named the winlose dependent transfers, with the following property: each type of bidder's transfer conditional on winning or losing is independent of the competitor's type report. Our result reduces the infinitedimensional optimal transfer problem to a twodimensional optimization problem. By solving the reduced problem, we find that: (i) among efficient mechanisms with no premiums for losers, the firstprice auction is optimal; and, (ii) among efficient winnerfavored mechanisms where each bidder pays smaller amounts when she wins than loses: the allpay auction is optimal. Under a simplifying assumption, these two auctions remain optimal under the endogenous allocation rule. 
Date:  2021–10 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2110.08563&r= 
By:  ShihTang Su; Vijay G. Subramanian; Grant Schoenebeck 
Abstract:  We consider a Bayesian persuasion or information design problem where the sender tries to persuade the receiver to take a particular action via a sequence of signals. This we model by considering multiphase trials with different experiments conducted based on the outcomes of prior experiments. In contrast to most of the literature, we consider the problem with constraints on signals imposed on the sender. This we achieve by fixing some of the experiments in an exogenous manner; these are called determined experiments. This modeling helps us understand realworld situations where this occurs: e.g., multiphase drug trials where the FDA determines some of the experiments, funding of a startup by a venture capital firm, startup acquisition by big firms where latestage assessments are determined by the potential acquirer, multiround job interviews where the candidates signal initially by presenting their qualifications but the rest of the screening procedures are determined by the interviewer. The nondetermined experiments (signals) in the multiphase trial are to be chosen by the sender in order to persuade the receiver best. With a binary state of the world, we start by deriving the optimal signaling policy in the only nontrivial configuration of a twophase trial with binaryoutcome experiments. We then generalize to multiphase trials with binaryoutcome experiments where the determined experiments can be placed at any chosen node in the trial tree. Here we present a dynamic programming algorithm to derive the optimal signaling policy that uses the twophase trial solution's structural insights. We also contrast the optimal signaling policy structure with classical Bayesian persuasion strategies to highlight the impact of the signaling constraints on the sender. 
Date:  2021–10 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2110.09594&r= 
By:  Sylvain Béal (CRESE EA3190, Univ. Bourgogne FrancheComté, F25000 Besançon, France); Sylvain Ferrières (Université de SaintEtienne, CNRS UMR 5824 GATE Lyon SaintEtienne, France); Philippe Solal (Université de SaintEtienne, CNRS UMR 5824 GATE Lyon SaintEtienne, France) 
Abstract:  A coalitional ranking problem is described by a weak order on the set of nonempty coalitions of a given agent set. A social ranking is a weak order on the set of agents. We consider social rankings that are consistent with stable/core partitions. A partition is stable if there is no coalition better ranked in the coalitional ranking than the rank of the cell of each of its members in the partition. The corepartition social ranking solution assigns to each coalitional ranking problem the set of social rankings such that there is a corepartition satisfying the following condition: a first agent gets a higer rank than a second agent if and only if the cell to which the first agent belongs is better ranked in the coalitional ranking than the cell to which the second agent belongs in the partition. We provide an axiomatic characterization of the corepartition social ranking and an algorithm to compute the associated social rankings. 
Keywords:  Coalitional ranking problem, social ranking, core partition, axiomatic characterization, hedonic games 
JEL:  C71 
Date:  2021–10 
URL:  http://d.repec.org/n?u=RePEc:crb:wpaper:202106&r= 
By:  Roland Pongou (Department of Economics, University of Ottawa, Ottawa, ON); Bertrand Tchantcho (Department of Mathematics, École Normale Supérieure, University of Yaoundé I, Cameroon; Université de Cergy Pontoise) 
Abstract:  A roundrobin political tournament is an election format where multiple candidates contest in pairs, and votes are aggregated using a general rule to form a social ranking. We formalize this tournament as a strategic form game and provide a necessary and sufficient condition under which truthful voting is a Nash equilibrium. Building on this analysis, we study the concept of effective power, defined as a voter's ability to bring about a social ranking that maximizes his preferences. We show that the classical theories of political power do not translate into effective power in general. We then provide a full characterization of the classes of political tournaments and utility metrics for which these theories capture effective power. We offer both structural and behavioral interpretations of the findings, and derive practical implications for the design of political tournaments that are compatible with truthtelling. 
Keywords:  Roundrobin Political Tournaments; Ranked Voting; Hyperpreferences; Truthful Equilibria; Effective Power; Psychology; Political Design. 
Date:  2021 
URL:  http://d.repec.org/n?u=RePEc:ott:wpaper:2110e&r= 
By:  Emmanuelle AugeraudVéron; Giorgio Fabbri (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); Katheline Schubert 
Abstract:  How can decentralized individual decisions inefficiently reduce the ability of biodiversity to mitigate ecological and environmental variability and then its "natural insurance" role? In this article we present a simple theoretical setup to address this question and to evaluate some policy options. We study a model of strategic competition among farmers for the conversion of a natural forest to agricultural land. Unconverted forest land allows to conserve biodiversity, which contributes to reducing the volatility of agricultural production. Agents' utility is given in terms of a Kreps Porteus stochastic differential utility capable of disentangling risk aversion and aversion to fluctuations. We characterize the land used by each farmer and her welfare at the Nash equilibrium, we evaluate the overexploitation of the land and the agents' welfare loss compared to the socially optimal solution and we study the drivers of the inefficiencies of the decentralized equilibrium. After characterizing the value of biodiversity in the model, we use it to obtain a decomposition which helps to study the policy implications of the model by identifying in which cases the allocation of property rights is preferable to the introduction of a tax on land conversion. Our results suggest that enforcing property rights is more relevant in case of stagnant economies while taxing land conversion may be more suited for rapidly developing economies. 
Date:  2021–08–25 
URL:  http://d.repec.org/n?u=RePEc:hal:journl:hal03369958&r= 
By:  Semyon Malamud; Andreas Schrimpf 
Abstract:  How should an agent (the sender) observing multidimensional data (the state vector) persuade another agent to take the desired action? We show that it is always optimal for the sender to perform a (nonlinear) dimension reduction by projecting the state vector onto a lowerdimensional object that we call the "optimal information manifold." We characterize geometric properties of this manifold and link them to the sender's preferences. Optimal policy splits information into "good" and "bad" components. When the sender's marginal utility is linear, revealing the full magnitude of good information is always optimal. In contrast, with concave marginal utility, optimal information design conceals the extreme realizations of good information and only reveals its direction (sign). We illustrate these effects by explicitly solving several multidimensional Bayesian persuasion problems. 
Date:  2021–10 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2110.08884&r= 
By:  Philippe Gagnepain (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); Stéphane Gauthier (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:  This paper exploits the repeal of the Wright amendment as a natural experiment in order to contribute to the ongoing discussion on how the enlargement of the relevant market affects the ability of firms to coordinate on a Nash equilibrium. Using data on the U.S. air transportation industry, we present a DifferenceinDifference procedure which sheds light on the significant loss of accuracy in airlines' predictions in markets originating in Dallas after the Love Field airport started operating long distance services in 2014. This suggests that competition authorities should be careful when they refer to the Nash equilibrium following market expansion reforms. 
Keywords:  Airline industry,Nash equilibrium,Market definition,Transportation 
Date:  2021–09 
URL:  http://d.repec.org/n?u=RePEc:hal:psewpa:halshs03359597&r= 
By:  John Lynham; Philip R Neary 
Abstract:  A large number of agents from two groups prefer to interact with their own types online and also have preferences over two online platforms. We find that an online platform can be tipped from integrated to segregated without any change in the ratio of the two groups interacting on the platform. Instead, segregation can be triggered by changes in the absolute numbers of both groups, holding the Schelling ratio fixed. In extreme cases, the flight of one group from a platform can be triggered by a change in the group ratio in favor of the group that ends up leaving. 
Date:  2021–10 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2110.05608&r= 