nep-gth New Economics Papers
on Game Theory
Issue of 2019‒11‒25
twenty-two papers chosen by
Sylvain Béal
Université de Franche-Comté

  1. Conventions and Coalitions in Repeated Games By Liu, Ce; Ali, S. Nageeb
  2. A Class of N-player Colonel Blotto games with multidimensional private information By Christian Ewerhart; Dan Kovenock
  3. Stability in Repeated Matching Markets By Liu, Ce
  4. Investment without Coordination Failures By Brian C. Albrecht
  5. Can market competition reduce anomalous behaviours By Choo, Lawrence; Zhou, Xiaoyu
  6. Asymmetric majority pillage games By Manfred Kerber; Colin Rowat; Naoki Yoshihara
  7. A two-player price impact game By Moritz Vo{\ss}
  8. The optimal size of a political party based on the Shapley-Shubik Power Index By Maruyama, Yuuki
  9. Interdependent Value Auctions with Insider Information: Theory and Experiment By Syngjoo Choi; Jos¢¥e-Alberto Guerra; Jinwoo Kim
  10. Strongly Budget Balanced Auctions for Multi-Sided Markets By Rica Gonen; Erel Segal-Halevi
  11. Interaction indices for multichoice games By Mustapha Ridaoui; Michel Grabisch; Christophe Labreuche
  12. Contests with sequential moves: An experimental study By Arthur B. Nelson; Dmitry Ryvkin
  13. A solution to the two-person implementation problem By Jean-François Laslier; Matias Nunez; M Remzi Sanver
  14. Analytical solution of $k$th price auction By Martin Mihelich; Yan Shu
  15. Network Formation in Large Groups By Syngjoo Choi; Sanjeev Goyal; Fr¢¥ed¢¥eric Moisan
  16. Cost additive rules in minimum cost spanning tree problems with multiple sources By Bergantiños, Gustavo; Lorenzo, Leticia
  17. Price disclosure by two-sided platforms By BELLEFLAMME Paul,; PEITZ Martin,
  18. Sequential bankruptcy problems By Arantza Estévez-Fernández; José Manuel Giménez-Gómez; María José Solís-Baltadano
  19. The Behavioral Economics of Artificial Intelligence: Lessons from Experiments with Computer Players By Christoph March
  20. Dynamic Influence on Replicator Evolution for the Propagation of Competing Technologies By Elijah D. Bolluyt; Cristina Comaniciu
  21. Double overreaction in beauty-contests with information acquisition: theory and experiment By Romain Baeriswyl; Kene Boun My; Camille Cornand
  22. Behavioral Equivalence of Extensive Game Structures By Pierpaolo Battigalli; Paolo Leonetti; Fabio Maccheroni

  1. By: Liu, Ce (Michigan State University, Department of Economics); Ali, S. Nageeb (Pennsylvania State University)
    Abstract: We develop a theory of repeated interaction for coalitional behavior. We consider stage games where both individuals and coalitions may deviate. However, coalition members cannot commit to long-run behavior (on and off the path), and anticipate that today’s actions influence tomorrow’s behavior. We evaluate the degree to which history-dependence can ward off coalitional deviations. If monitoring is perfect, every feasible and strictly individually rational payoff can be supported by history-dependent conventions. By contrast, if players can make secret side-payments to each other, every coalition achieves a coalitional minmax value, reducing the set of supportable payoffs to the core of the stage game.
    Keywords: cooperative games; core; repeated games; secrecy
    JEL: C71 C72 C73 D71
    Date: 2019–06–02
  2. By: Christian Ewerhart; Dan Kovenock
    Abstract: We consider a class of incomplete-information Colonel Blotto games in which N ≥ 2 agents are engaged in (N + 1) battlefields. An agent's vector of battlefield valuations is drawn from a generalized sphere in Lp-space. We identify a Bayes-Nash equilibrium in which any agent's resource allocation to a given battlefield is strictly monotone in the agent's valuation of that battlefield. In contrast to the single-unit case, however, agents never enjoy any information rent. We also outline an extension to networks of Blotto games.
    Keywords: Colonel Blotto games, private information, Bayes-Nash equilibrium, information rents, networks
    JEL: C72 D72 D82
    Date: 2019–11
  3. By: Liu, Ce (Michigan State University, Department of Economics)
    Abstract: I develop a framework for studying repeated matching markets, where in every period, a new generation of short-lived agents on one side of the market is matched to a fixed set of long-lived institutions on the other. Within this framework, I characterize self-enforcing arrangements for two types of environments. When wages are rigid, as in the matching market for hospitals and medical residents, players can be partitioned into two sets: regardless of patience level, some players can be assigned only according to a static stable matching; when institutions are patient, the other players can be assigned in ways that are unstable in one-shot interactions. I discuss these results’ implications for allocating residents to rural hospitals. When wages can be flexibly adjusted, I show that with flexible wages, repeated interaction resolves well-known non-existence issues: while static stable matchings may fail to exist with complementarities and/or peer effects, self-enforcing matching processes always exist if institutions are sufficiently patient.
    Keywords: two-sided matching; stability; repeated games; market design
    JEL: C71 C72 C73 D47
    Date: 2018–12–06
  4. By: Brian C. Albrecht
    Abstract: I study games in which agents must sink their investments before they can match into partnerships that generate value. I focus on competitive matching markets where there is a public price to join any match. Despite the First Welfare Theorem for competitive markets, inefficiencies can still arise that can be interpreted as coordination failures. Armen does not invest because Bengt does not invest, and vice versa. Multiple equilibria can exist, with both efficient investment and not. The standard, Nash solution concept in these games does not help in determining if they are equally robust or stable. I argue we should replace the Nash solution concept in this context with a mild, common refinement: trembling-hand perfection. The main theorem of the paper proves that in a general class of models with general heterogeneity of types, cost of investment, and matching surplus, every perfect equilibrium is efficient and coordination failures do not exist in equilibrium. That means that in the context of competitive markets, coordination failures are not robust; the possibility of small mistakes rules out coordination failures. Even when markets are incomplete, every robust equilibrium in competitive markets is efficient.
    JEL: D52 C78 D41
    Date: 2019–10–07
  5. By: Choo, Lawrence; Zhou, Xiaoyu
    Abstract: We use an experiment to study whether market competition can reduce anomalous behaviour in games. In different treatments, we employ two alternative mechanisms, the random mechanism and the auction mechanism, to allocate the participation rights to the red hat puzzle game, a well-known logical reasoning problem. Compared to the random mechanism, the auction mechanism significantly reduces deviations from the equilibrium play in the red hat puzzle game. Our findings show that under careful conditions, market competition can indeed reduce anomalous behaviour in games.
    Keywords: market competition,market selection hypothesis,auctions,bounded-rationality,red hat puzzle
    JEL: C70 C90 D44
    Date: 2019
  6. By: Manfred Kerber (University of Birmingham); Colin Rowat (University of Birmingham); Naoki Yoshihara (School of Economics and Management, Kochi University of Technology)
    Abstract: This paper studies pillage games (Jordan in J Econ Theory 131.1:26-44, 2006, “Pillage and property†), which are well suited to modelling unstructured power contests. To enable empirical test of pillage games’ predictions, it relaxes a symmetry assumption that agents’ intrinsic contributions to a coalition’s power is identical. In the three-agent game studied: (i) only eight configurations are possible for the core, which contains at most six allocations; (ii) for each core configuration, the stable set is either unique or fails to exist; (iii) the linear power function creates a tension between a stable set’s existence and the interiority of its allocations, so that only special cases contain strictly interior allocations. Our analysis suggests that non-linear power functions may o er better empirical tests of pillage game theory.
    Keywords: power contests, core, stable sets
    JEL: C71 D51 P14
    Date: 2019–11
  7. By: Moritz Vo{\ss}
    Abstract: We study the competition of two strategic agents for liquidity in the benchmark portfolio tracking setup of Bank, Soner, Voss (2017), both facing common aggregated temporary and permanent price impact \`a la Almgren and Chriss (2001). The resulting stochastic linear quadratic differential game with terminal state constraints allows for an explicitly available open-loop Nash equilibrium in feedback form. Our results reveal how the equilibrium strategies of the two players take into account the other agent's trading targets: either in an exploitative intent or by providing liquidity to the competitor, depending on the ratio between temporary and permanent price impact. As a consequence, different behavioral patterns can emerge as optimal in equilibrium. These insights complement existing studies in the literature on predatory trading models examined in the context of optimal portfolio liquidation problems.
    Date: 2019–11
  8. By: Maruyama, Yuuki
    Abstract: I define Shapley-Shubik Power Index per Person (SSPIPP) as the ratio of a political party's Shapley-Shubik Power Index in a parliament to the number of people who voted for the party. SSPIPP can be regarded as the political power each of them has. I calculate the optimal size of a political party that maximizes SSPIPP, and it shows that the more approval votes a parliament requires to pass bills, the smaller the optimal party size becomes. It also shows that in countries that require supermajority approval vote to pass bills, party system fragmentation tends to become permanent.
    Date: 2019–10–17
  9. By: Syngjoo Choi; Jos¢¥e-Alberto Guerra; Jinwoo Kim
    Abstract: We develop a model of interdependent value auctions in which two types of bidders compete: insiders, who are perfectly informed about their value, and outsiders, who are informed only about the private component of their value. Because of the mismatch of bidding strategies between insiders and outsiders, the second-price auc- tion is inefficient. The English auction has an equilibrium in which the information outsiders infer from the history of drop-out prices enables them to bid toward attaining ecffiency. The presence of insiders has positive impacts on the seller¡¯s revenue. A laboratory experiment confirms key theoretical predictions, despite evidence of naive bidding.
    Keywords: Interdependent value auctions; asymmetric information structure; second- price auction; English auction, experiment
    JEL: C92 D44 D82
    Date: 2018–09
  10. By: Rica Gonen; Erel Segal-Halevi
    Abstract: In two-sided markets, Myerson and Satterthwaite's impossibility theorem states that one can not maximize the gain-from-trade while also satisfying truthfulness, individual-rationality and no deficit. Attempts have been made to circumvent Myerson and Satterthwaite's result by attaining approximately-maximum gain-from-trade: the double-sided auctions of McAfee (1992) is truthful and has no deficit, and the one by Segal-Halevi et al. (2016) additionally has no surplus --- it is strongly-budget-balanced. They consider two categories of agents --- buyers and sellers, where each trade set is composed of a single buyer and a single seller. The practical complexity of applications such as supply chain require one to look beyond two-sided markets. Common requirements are for: buyers trading with multiple sellers of different or identical items, buyers trading with sellers through transporters and mediators, and sellers trading with multiple buyers. We attempt to address these settings. We generalize Segal-Halevi et al. (2016)'s strongly-budget-balanced double-sided auction setting to a multilateral market where each trade set is composed of any number of agent categories. Our generalization refines the notion of competition in multi-sided auctions by introducing the concepts of external competition and trade reduction. We also show an obviously-truthful implementation of our auction using multiple ascending prices.
    Date: 2019–11
  11. By: Mustapha Ridaoui (CES - Centre d'économie de la Sorbonne - CNRS - Centre National de la Recherche Scientifique - UP1 - Université Panthéon-Sorbonne, PSE - Paris School of Economics); Michel Grabisch (CES - Centre d'économie de la Sorbonne - CNRS - Centre National de la Recherche Scientifique - UP1 - Université Panthéon-Sorbonne, UP1 - Université Panthéon-Sorbonne, PSE - Paris School of Economics); Christophe Labreuche (Thales Research and Technology [Palaiseau] - THALES)
    Abstract: Models in Multicriteria Decision Analysis (MCDA) can be analyzed by means of an importance index and an interaction index for every group of criteria. We consider first discrete models in MCDA, without further restriction, which amounts to considering multichoice games, that is, cooperative games with several levels of participation. We propose and axiomatize two interaction indices for multichoice games: the signed interaction index and the absolute interaction index. In a second part, we consider the continuous case, supposing that the continuous model is obtained from a discrete one y means of the Choquet integral. We show that, as in the case of classical games, the interaction index defined for continuous aggregation functions coincides with the (signed) interaction index, up to a normalizing coefficient.
    Abstract: Les modèles en décision multicritère (MCDA) peuvent être analysés au moyen d'un indice d'importance et d'un indice d'interaction pour un groupe de critères. On considère premièrement des modèles discrets sans restriction, ce qui revient à considérer des jeux multichoix, i.e., des jeux coopératifs avec plusieurs niveaux de participation. Nous proposons et axiomatisons deux indices d'interaction pour les jeux multichoix : l'indice d'interaction signé et l'indice d'interaction absolu. Dans une deuxième partie, nous considérons le cas continu, en supposant que le modèle continu est obtenu à partir du modèle discret par l'intégrale de Choquet. Nous montrons que, comme dans le cas classique, l'index d'interaction défini pour les fonctions d'agrégation continues coïncide avec l'indice d'interaction (signé), à un coefficient près.
    Keywords: multicriteria decision analysis,interaction,multichoice game,Choquet integral,décision multicritère,jeu multichoix,intégrale de Choquet
    Date: 2019–07
  12. By: Arthur B. Nelson (Department of Economics, Florida State University); Dmitry Ryvkin (Department of Economics, Florida State University)
    Abstract: We study experimentally contests in which players make investment decisions sequentially, and information on prior investments is revealed between stages. Using a between-subject design, we consider all possible sequences in contests of three players and test two major comparative statics of the subgame-perfect Nash equilibrium: The positive effect of information disclosure on aggregate investment and earlier mover advantage. The former prediction is decidedly rejected, as we observe a reduction in aggregate investment when more information is sequentially disclosed. The evidence on earlier mover advantage is mixed but mostly does not support theory as well. Both predictions rely critically on forward-looking, sophisticated decision-making, which is not typical for our subjects.
    Keywords: contest, sequential moves, experiment
    JEL: C72 C99 D82 D91
    Date: 2019–11
  13. By: Jean-François Laslier (PJSE - Paris Jourdan Sciences Economiques - UP1 - Université Panthéon-Sorbonne - ENS Paris - École normale supérieure - Paris - INRA - Institut National de la Recherche Agronomique - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics); Matias Nunez (CECO - Laboratoire d'économétrie de l'École polytechnique - X - École polytechnique - CNRS - Centre National de la Recherche Scientifique, CREST - Centre de Recherche en Economie et Statistique [Bruz] - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz]); M Remzi Sanver (LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision - Université Paris-Dauphine - CNRS - Centre National de la Recherche Scientifique)
    Abstract: We propose a solution to the classical problem of Hurwicz and Schmeidler [1978] and Maskin [1999] according to which, in two-person societies, no Pareto efficient rule is Nash-implementable. To this end, we consider implementation through mechanisms that are deterministic-in-equilibrium while lotteries are allowed off-equilibrium. For strict preferences over alternatives and under a very weak condition for extending preferences over lotteries, we build simple veto mechanisms that Nash implement a class of Pareto efficient social choice rules called Pareto-and-veto rules. Moreover, under mild richness conditions on the domain of preferences over lotteries, any Pareto efficient Nashimplementable rule is a Pareto-and-veto rule and hence is implementable through one of our simple veto mechanisms.
    Date: 2019–11
  14. By: Martin Mihelich; Yan Shu
    Abstract: We provide an exact analytical solution of the Nash equilibrium for the $k$th price auction by using inverse of distribution functions. As applications, we identify the unique symmetric equilibrium where the valuations have polynomial distribution, fat tail distribution and exponential distributions.
    Date: 2019–11
  15. By: Syngjoo Choi; Sanjeev Goyal; Fr¢¥ed¢¥eric Moisan
    Abstract: We conduct an experiment to understand the principles that govern network formation. The design of the experiment builds on a model of linking and efforts taken from Galeotti and Goyal [2010]. In order to reduce cognitive complexity facing human subjects and facilitate learning, we develop a new experimental platform that integrates a network visualization tool using an algorithm of Barnes and Hut [1986] with an interactive tool of asynchronous choices in continuous time. Our experiment provides strong support for macroscopic predictions of the theory: there is specialization in linking and e?orts across all treatments. Moreover, and in line with the theory, the specialization is more pronounced in larger groups. Thus subjects abide by the law of the few. Information on payo?s provided to subjects a?ects their behavior and yields di?erential welfare consequences. In the treatment where subjects see only their own payo?s, in large groups, the most connected individuals compete ?ercely they exert large efforts and have small earnings. By contrast, when a subject sees everyone¡¯s payo?s, in large groups, the most connected individuals engage in less intense competition they exert little e?ort and have large earnings. The e?ects of information are much more muted in small groups.
    JEL: C92 D83 D85 Z13
    Date: 2019–03
  16. By: Bergantiños, Gustavo; Lorenzo, Leticia
    Abstract: In this paper, we introduce a family of rules in minimum cost spanning tree problems with multiple sources called Kruskal sharing rules. This family is characterized with cone wise additivity and independence of irrelevant trees . We also investigate some subsets of this family and provide their axiomatic characterizations. The first subset is obtained by adding core selection. The second one is obtained by adding core selection and equal treatment of source costs
    Keywords: minimum cost spanning tree problems, multiple sources, Kruskal sharing rules, axiomatic characterizations.
    JEL: C71
    Date: 2019–11–11
  17. By: BELLEFLAMME Paul, (CORE, UCLouvain); PEITZ Martin, (Universität Mannheim)
    Abstract: We consider two-sided platforms with the feature that some users on one or both sides of the market lack information about the price charged to participants on the other side of the market. With positive cross-group external effects, such lack of pricie information makes demand less elastic. A monopoly platform does not benefit from opaqueness and optimality reveals price information. By contrast, in a two-sided singlehoming duopoly, platforms benefit from opaqueness and, thus, do not have an incentive to disclose price information. In competitive bottleneck markets, results are more nuanced: if one side is fully informed (for exogenous reasons), plaltforms may decide to inform users on the other side either fully, partially or not at all, depending on the strength of cross-group external effects and hte degree of horizontal differentiation.
    Keywords: price transparency, two-sided markets, competitive bottleneck, platform competition, price information, strategic disclosure
    Date: 2019–06–18
  18. By: Arantza Estévez-Fernández (VU Amsterdam); José Manuel Giménez-Gómez (Universitat Rovira i Virgili); María José Solís-Baltadano (Universitat Rovira i Virgili)
    Abstract: In this paper, we analyze sequential bankruptcy problems, which generalize bankruptcy problems. They contain the problems of sharing water in a transboundary river and of allocating expedition rewards in projects. We provide three mechanisms for generalizing rules for bankruptcy problems to rules for sequential bankruptcy problems: the upwards, the downwards, and the two-steps mechanisms. Further, we characterize the upwards constrained equal awards, the upwards constrained equal losses, and the upwards proportional rules on the basis of upwards composition and upwards path independence. Moreover, we compare the three mechanisms based on inheritance of well-established properties for bankruptcy rules to the setting of sequential bankruptcy rules.
    Keywords: Sequential bankruptcy, upwards mechanism, downwards mechanism, twosteps mechanism, constrained equal awards rule, constrained equal losses rule, proportional rule
    JEL: D74 C79 D63
    Date: 2019–11–16
  19. By: Christoph March
    Abstract: Artificial intelligence (AI) is starting to pervade the economic and social life rendering strategic interactions with artificial agents more and more common. At the same time, experimental economic research has increasingly employed computer players to advance our understanding of strategic interaction in general. What can this strand of research teach us about an AI-shaped future? I review 90 experimental studies using computer players. I find that, in a nutshell, humans act more selfishly and more rational in the presence of computer players, and they are often able to exploit these players. Still, many open questions prevail.
    Keywords: experiment, robots, computer players, survey
    JEL: C90 C92 O33
    Date: 2019
  20. By: Elijah D. Bolluyt; Cristina Comaniciu
    Abstract: This work introduces a novel modified Replicator Dynamics model, which includes external influences on the population. This framework models a realistic market into which companies, the external dynamic influences, invest resources in order to bolster their product's standing and increase their market share. The dynamic influences change in each time step of the game, and directly modify the payoff matrix of the population's interactions. The model can learn from real data how each influence affects the market, and can be used to simulate and predict the outcome of a real system. We specifically analyze how a new technology can compete and attempt to unseat an entrenched technology as the market leader. We establish a relationship between the external influences and the population payoff matrix and show how the system can be implemented to predict outcomes in a real market by simulating the rise of the Android mobile operating system over its primary competition, the iPhone, from 2009 to 2017.
    Date: 2019–11
  21. By: Romain Baeriswyl (Swiss National Bank, Boersenstrasse 15, 8001 Zurich, Switzerland); Kene Boun My (BETA-Strasbourg University, 61 Avenue de la Forêt Noire - 67085 Strasbourg Cedex, France); Camille Cornand (Univ Lyon, CNRS, GATE L-SE UMR 5824, F-69130 Ecully, France)
    Abstract: Central banks' disclosures, such as forward guidance, have a weaker effect on the economy in reality than in theoretical models. The present paper contributes to understanding how people pay attention and react to various sources of information. In a beauty-contest with information acquisition, we show that strategic complementarities give rise to a double overreaction to public disclosures by increasing agents equilibrium attention, which, in turn, increases the weight assigned to them in equilibrium action. A laboratory experiment provides evidence that the effect of strategic complementarities on the realised attention and the realised action is qualitatively consistent with theoretical predictions, though quantitatively weaker. Both the lack of attention to public disclosures and a limited level of reasoning by economic agents account for the weaker realised reaction. This suggests that it is just as important for a central bank to control reaction to public disclosures by swaying information acquisition by recipients as it is by shaping information disclosures themselves.
    Keywords: beauty-contest, information acquisition, overreaction, central bank communication
    JEL: D82 E52 E58
    Date: 2019
  22. By: Pierpaolo Battigalli; Paolo Leonetti; Fabio Maccheroni
    Abstract: Two extensive game structures with imperfect information are said to be behaviorally equivalent if they share the same map (up to relabelings) from profiles of structurally reduced strategies to induced terminal paths. We show that this is the case if and only if one can be transformed into the other through a composition of two elementary transformations, commonly known as \textquotedblleft Interchanging of Simultaneous Moves\textquotedblright\ and \textquotedblleft Coalescing Moves/Sequential Agent Splitting.\textquotedblright
    Date: 2019–11

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