nep-gth New Economics Papers
on Game Theory
Issue of 2021‒10‒25
fourteen papers chosen by
Sylvain Béal
Université de Franche-Comté

  1. Coalition Formation in Games with Externalities By Maria Montero
  2. An Evolutionary Approach to Pollution Control in Competitive Markets By Ratul Lahkar; Vinay Ramani
  3. How Alliances Form and Conflict Ensues By Lu Dong; Lingbo Huang; Jaimie W. Lien; Jie Zheng
  4. A Mean Field Game Approach to Equilibrium Pricing with Market Clearing Condition By Masaaki Fujii; Akihiko Takahashi
  5. A Paradox of Coalition Building in Public Good Provision By Wolfgang Buchholz; Keisuke Hattori
  6. Group network effects in price competition By Renato Soeiro; Alberto Pinto
  7. Auction design with ambiguity: Optimality of the first-price and all-pay auctions By Sosung Baik; Sung-Ha Hwang
  8. Bayesian Persuasion in Sequential Trials By Shih-Tang Su; Vijay G. Subramanian; Grant Schoenebeck
  9. A Core-partition solution for coalitional rankings with a variable population domain By Sylvain Béal; Sylvain Ferrières; Philippe Solal
  10. Round-Robin Political Tournaments: Abstention, Truthful Equilibria, and Effective Power By Roland Pongou; Bertrand Tchantcho
  11. Volatility-reducing biodiversity conservation under strategic interactions By Emmanuelle Augeraud-Véron; Giorgio Fabbri; Katheline Schubert
  12. Persuasion by Dimension Reduction By Semyon Malamud; Andreas Schrimpf
  13. Strategic uncertainty and market size: An illustration on the Wright amendment By Philippe Gagnepain; Stéphane Gauthier
  14. Online Segregation By John Lynham; Philip R Neary

  1. 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
  2. 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
  3. 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 decision-makers form, and what determines whether a conflict will arise? We study a network formation game between ex-ante 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 player’s resources evenly to the attackers at a cost. Consistently with the theoretical model predictions, peaceful and bullying outcomes are prevalent among the randomly re-matched 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 non-negligible risk of successful counter-attack 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
  4. 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 equilibrium-based continuous asset pricing problem which seeks to form a price process endogenously by requiring it to balance the flow of sale-and-purchase orders in the exchange market, where a large number of agents 1 ≤ i ≤ N are interacting through the market price. Adopting a mean field game (MFG) approach, we find a special form of forward-backward stochastic differential equations of McKean-Vlasov 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 N-limit 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
  5. 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 three-stage 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 public-good supply and global welfare.
    Keywords: coalition formation, public goods, endogenous technology, environmental agreements
    JEL: H41 F53 Q54 Q55
    Date: 2021
  6. 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
  7. By: Sosung Baik; Sung-Ha 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 win-lose 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 infinite-dimensional optimal transfer problem to a two-dimensional optimization problem. By solving the reduced problem, we find that: (i) among efficient mechanisms with no premiums for losers, the first-price auction is optimal; and, (ii) among efficient winner-favored mechanisms where each bidder pays smaller amounts when she wins than loses: the all-pay auction is optimal. Under a simplifying assumption, these two auctions remain optimal under the endogenous allocation rule.
    Date: 2021–10
  8. By: Shih-Tang 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 multi-phase 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 real-world situations where this occurs: e.g., multi-phase drug trials where the FDA determines some of the experiments, funding of a startup by a venture capital firm, start-up acquisition by big firms where late-stage assessments are determined by the potential acquirer, multi-round job interviews where the candidates signal initially by presenting their qualifications but the rest of the screening procedures are determined by the interviewer. The non-determined experiments (signals) in the multi-phase 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 non-trivial configuration of a two-phase trial with binary-outcome experiments. We then generalize to multi-phase trials with binary-outcome 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 two-phase 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
  9. By: Sylvain Béal (CRESE EA3190, Univ. Bourgogne Franche-Comté, F-25000 Besançon, France); Sylvain Ferrières (Université de Saint-Etienne, CNRS UMR 5824 GATE Lyon Saint-Etienne, France); Philippe Solal (Université de Saint-Etienne, CNRS UMR 5824 GATE Lyon Saint-Etienne, 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 core-partition social ranking solution assigns to each coalitional ranking problem the set of social rankings such that there is a core-partition 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 core-partition 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
  10. 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 round-robin 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 truth-telling.
    Keywords: Round-robin Political Tournaments; Ranked Voting; Hyper-preferences; Truthful Equilibria; Effective Power; Psychology; Political Design.
    Date: 2021
  11. By: Emmanuelle Augeraud-Véron; 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
  12. By: Semyon Malamud; Andreas Schrimpf
    Abstract: How should an agent (the sender) observing multi-dimensional 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 (non-linear) dimension reduction by projecting the state vector onto a lower-dimensional 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 multi-dimensional Bayesian persuasion problems.
    Date: 2021–10
  13. 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 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 Paris 1 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); 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 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 Paris 1 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)
    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 Difference-inDifference 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
  14. 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

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