nep-gth New Economics Papers
on Game Theory
Issue of 2011‒11‒07
eighteen papers chosen by
Laszlo A. Koczy
Hungarian Academy of Sciences and Obuda University

  1. Extremal Choice Equilibrium: Existence and Purification with Infinite-Dimensional Externalities By Paulo Barelli; John Duggan
  2. Collusion, symmetry, and the Banzhaf value By Casajus, André
  3. The Power of Sunspots: An Experimental Analysis By Dietmar Fehr; Frank Heinemann; Aniol Llorente-Saguer
  4. Coordination with Communication under Oath By Nicolas Jacquemet; Stephane Luchini; Jason Shogren; Adam Zylbersztejn
  5. Sharing profit in parallel and serial transport networks By Grahn-Voorneveld, Sofia
  6. Sharing costs in Swedish road ownership associations By Grahn-Voorneveld, Sofia
  7. Common assumption of rationality By Keisler, H. Jerome; Lee, Byung Soo
  8. Technology adoption in markets with network effects: Theory and experimental evidence By Keser, Claudia; Suleymanova, Irina; Wey, Christian
  9. Promoting School Competition Through School Choice: A Market Design Approach By John William Hatfield; Fuhito Kojima; Yusuke Narita
  10. Unawareness, Beliefs, and Speculative Trade By Aviad Heifetz; Martin Meier; Burkhard Schipper
  11. Behavioral biases and representative agent By Elyès Jouini; Clotilde Napp
  12. Matching & Information Provision by One-Sided and Two-Sided Platforms By Carlos Canon
  13. An experiment on experimental instructions By Maria Bigoni; Davide Dragone
  14. How Do Informal Agreements and Renegotiation Shape Contractual Reference Points? By Ernst Fehr; Oliver D. Hart; Christian Zehnder
  15. Efficient bargaining versus right to manage: a stability analysis with heterogeneous players in a duopoly with quantity competition and trade unions By Fanti, Luciano; Gori, Luca
  16. Group Size, Coordination, and the Effectiveness of the Punishment Mechanism in the VCM: An Experimental Investigation By Bin Xu; Bram Cadsby; Liangcong Fan; Fei Song
  17. The river sharing problem: A review of the technical literature for policy economists By Beard, Rodney
  18. A Dynamic Duopoly Investment Game without Commitment under Uncertain Market Expansion By Marcel Boyer; Pierre Lasserre; Michel Moreaux

  1. By: Paulo Barelli (University of Rochester); John Duggan (University of Rochester)
    Abstract: We prove existence and purification results for equilibria in which players choose extreme points of their feasible actions in a class of strategic environments exhibiting a product structure. We assume finite-dimensional action sets and allow for infinite-dimensional externalities. Applied to large games, we obtain existence of Nash equilibrium in pure strategies while allowing a continuum of groups and general dependence of payoffs on average actions across groups, without resorting to saturated measure spaces. Applied to games of incomplete information, we obtain a new purification result for Bayes-Nash equilibria that permits substantial correlation across types, without assuming conditional independence given the realization of a finite environmental state. We highlight our results in examples of industrial organization, auctions, and voting.
    Date: 2011–10
  2. By: Casajus, André
    Abstract: We resolve redundancies in the characterizations of the Banzhaf value suggested by Haller (1994, Int J Game Theory 23, 261-281) and Malawski (2002, Int J Game Theory 31:47-67). In particular, we show that the collusion properties employed by them are equivalent. Combined with the dummy player axiom, any of the collusion properties has strong symmetry implications whenever the cardinality of the player set exceeds two. Finally, we establish that the Banzhaf value is non-redundantly characterized by the dummy player axiom and any of the collusion properties, provided that the player set is as above. --
    Keywords: Banzhaf value,symmetry,collusion,proxy,association,distrust
    JEL: C71
    Date: 2011
  3. By: Dietmar Fehr; Frank Heinemann; Aniol Llorente-Saguer
    Abstract: We present an experiment in which extrinsic information (signals) may generate sunspot equilibria. The underlying coordination game has a unique symmetric non-sunspot equilibrium, which is also risk-dominant. Other equilibria can be ordered according to risk dominance. We compare treatments with different salient, but extrinsic signals. By increasing the precision of private signals, we manipulate the available public information, which allows us to measure the force of extrinsic signals. We also vary the number of signals and combine public and private signals, allowing us to see how subjects aggregate available (and possibly irrelevant) information. Results indicate that sunspot equilibria emerge naturally if there are salient (but extrinsic) public signals. However, salient private signals of high precision may also cause sunspot-driven behavior, even though this is no equilibrium. The higher the precision of signals and the easier they can be aggregated, the more powerful they are in dragging behavior away from the risk-dominant to risk-dominated strategies. Sunspot-driven behavior may lead to welfare losses and exert negative externalities on agents, who do not receive extrinsic signals.
    Keywords: coordination games, strategic uncertainty, sunspot equilibria, irrelevant information
    JEL: C72 C92 D84
    Date: 2011–10
  4. By: Nicolas Jacquemet (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I, EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics - Ecole d'Économie de Paris); Stephane Luchini (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - Université de la Méditerranée - Aix-Marseille II - Université Paul Cézanne - Aix-Marseille III - Ecole des Hautes Etudes en Sciences Sociales (EHESS) - CNRS : UMR6579); Jason Shogren (Departement of Economics and Finance, University of Wyoming - University of Wyoming); Adam Zylbersztejn (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I)
    Abstract: We study the simultaneous move version of a coordination game in which failures arise due to the use (and fear) of weakly dominated strategies. Existing evidence shows neither cheap talk communication between players nor historical information on past decisions nor even repetition-based learning are able to implement the efficient outcome. We study the effect of one addition to the design: subjects sign a truth-telling oath before participating to the game with cheap-talk communication. We find oath significantly improves the truthfulness of messages sent, as well as helps eliminating weakly dominated actions. This change however has very few consequences on coordination, because receivers do not adjust their own strategies for this change.
    Keywords: Coordination game; Cheap talk communication; Oath
    Date: 2011–10–26
  5. By: Grahn-Voorneveld, Sofia (VTI)
    Abstract: This paper studies the incentives for different countries to cooperate concerning pricing in transport systems, and how to handle the profit from such cooperation. Two types of simple networks with congestion are considered; one with parallel links, and one serial network with a number of consecutive links. The owner of each link tolls the traffic using the link. First the incentives for cooperative behavior among the countries are studied, and shown to be considerable. This is done by using non-cooperative game theory. Second, cooperative game theory is used to analyse solution concepts for allocating the resources raised from cooperation.
    Keywords: Transport networks; game theory; cooperative game theory
    JEL: C71 C72 H71 L92 R41
    Date: 2011–11–02
  6. By: Grahn-Voorneveld, Sofia (VTI)
    Abstract: Usually transport systems, and roads in particular, are viewed as public goods. However, this is not always the case. In Sweden a large part of the road system is privately owned. Most of these privately owned roads are rural roads used by farmers and summer cottage owners, or used for forest transport. The roads are mainly provided by ownership associations. The motivation of this paper is the practical problem of how such an ownership association can dicide the costs for the road netword among the members in a "fair" way. The problem is treated from a game theoretical point of view, making use of the Shapley value. This means that the problem is associated with a game – a mathematical representation of the conflict situation. The Shapley value is a very important solution concept for cooperative games, like tha game in this case. For games corresponding to this specific type of problems, it is shown that the Shapley value has excellent properties, such as being an element of the core, and being very easy to compute.
    Keywords: Transport networks; cooperative game theory
    JEL: H71 L91
    Date: 2011–11–02
  7. By: Keisler, H. Jerome; Lee, Byung Soo
    Abstract: In this paper, we provide an epistemic characterization of iterated admissibility (IA), i.e., iterated elimination of weakly dominated strategies. We show that rationality and common assumption of rationality (RCAR) in complete lexicographic type structures implies IA, and that there exist such structures in which RCAR can be satisfied. Our result is unexpected in light of a negative result in Brandenburger, Friedenberg, and Keisler (2008) (BFK) that shows the impossibility of RCAR in complete continuous structures. We also show that every complete structure with RCAR has the same types and beliefs as some complete continuous structure. This enables us to reconcile and interpret the difference between our results and BFK’s. Finally, we extend BFK’s framework to obtain a single structure that contains a complete structure with an RCAR state for every game. This gives a game-independent epistemic condition for IA.
    Keywords: Epistemic game theory; rationality; admissibility; iterated weak dominance; assumption; completeness; Borel Isomorphism Theorem; o-minimality
    JEL: D80 C72
    Date: 2011–09–08
  8. By: Keser, Claudia; Suleymanova, Irina; Wey, Christian
    Abstract: We examine a technology adoption game with network effects in which coordination on technology A and technology B constitute a Nash equilibrium. Coordination on technology B is assumed to be payoff-dominant. We define a technology's critical mass as the minimum share of users necessary to make the choice of this technology a best response for any remaining user. We show that the technology with a lower critical mass is risk-dominant and is chosen by the maximin criterion. We present experimental evidence that both pay-off dominance and risk dominance explain participants' choices. The relative riskiness of a technology can be proxied using technologies' critical masses or stand-alone values. --
    Keywords: Network Effects,Critical Mass,Coordination,Riskiness
    JEL: C72 C91 D81
    Date: 2011
  9. By: John William Hatfield (Graduate School of Business, Stanford University); Fuhito Kojima (Department of Economics, Stanford University); Yusuke Narita (Department of Economics, MIT)
    Abstract: We study the effect of different school choice mechanisms on schools' incentives for quality improvement. To do so, we introduce the following criterion: A mechanism respects improvements of school quality if each school becomes weakly better off whenever that school becomes more preferred by students. We first show that no stable mechanism, or mechanism that is Pareto efficient for students (such as the Boston and top trading cycles mechanisms), respects improvements of school quality. Nevertheless, for large school districts, we demonstrate that any stable mechanism approximately respects improvements of school quality; by contrast, the Boston and top trading cycles mechanisms fail to do so. Thus a stable mechanism may provide better incentives for schools to improve themselves than the Boston and top trading cycles mechanisms.
    Keywords: Matching; School Choice; School Competition; Stability; Efficiency
    JEL: C78 D78 H75 I21
    Date: 2011–09
  10. By: Aviad Heifetz; Martin Meier; Burkhard Schipper
    Abstract: We define a generalized state-space model with interactive unawareness and probabilistic beliefs. Such models are desirable for potential applications of asymmetric unawareness. Applying our unawareness belief structures, we show that the common prior assumption is too weak to rule out speculative trade in all states. Yet, we prove a generalized "No-speculative-trade" theorem according to which there can not be common certainty of strict preference to trade. Moreover, we prove a generalization of the "No-agreeing-to-disagree" theorem. Finally, we show the existence of a universal unawareness belief type space.
    Keywords: Unawareness, awareness, common prior, agreement, speculative trade, universal type-space, interactive epistemology, inattention
    JEL: C70 C72 D53 D80 D82
  11. By: Elyès Jouini (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - CNRS : UMR7534 - Université Paris Dauphine - Paris IX); Clotilde Napp (CREST - Centre de Recherche en Économie et Statistique - INSEE - École Nationale de la Statistique et de l'Administration Économique, DRM - Dauphine Recherches en Management - CNRS : UMR7088 - Université Paris Dauphine - Paris IX)
    Abstract: In this paper, we show that behavioral features can be obtained at a group level when the individuals of the group are heterogeneous enough. Starting from a standard model of Pareto optimal allocations, with expected utility maximizers but allowing for heterogeneity among individual beliefs, we show that the representative agent has an inverse S-shaped probability distortion function. As an application of this result, we show that an agent with a probability weighting function as in Cumulative Prospect Theory may be represented as a collection of agents with noisy beliefs.
    Keywords: Behavioral agent; probability weighting function; representative agent
    Date: 2012
  12. By: Carlos Canon (Toulouse School of Economics)
    Abstract: This paper studies a "market creating" firm (platform) that offers a matching environment by charging an access fee to a population of high and low type users who wish to form a match. We focus on an environment where users only observe a signal of their randomly assigned partner's type and where the informativeness of the signal is controlled by the firm. We study how both tools, access fee and signal informativeness, can be used to screen particular segments of the population. We finish by characterizing the set of optimal menus. The paper proposes three results. We show that information provision has a screening role when network effects are heterogeneous because a platform cannot induce every level of participation using only the access fee. Secondly, any platform will optimally offer a menu such that only high types participate, or where every user participates. In the former the signal is perfectly informative; in the latter it is partially informative. Lastly, the profit maximizing firm will over-provide information in relation to the surplus maximizing firm, and the higher the heterogeneity in the population, the higher the chance of the optimal menu excluding low type users.
    Keywords: Pricing; Market Design; Matching; Information Provision; Heterogeneous Network Effects
    JEL: L11 L15 D42 D83
    Date: 2011–09
  13. By: Maria Bigoni (Dipartimento di Scienze Economiche, Universita di Bologna); Davide Dragone (Dipartimento di Scienze Economiche, Universita di Bologna and Max Plank Institute of Economics, Jena)
    Abstract: In this paper we treat instructions as an experimental variable. Using a public good game, we study how the instructions' format affects the participants' understanding of the experiment, their speed of play and their experimental behavior. We show that longer instructions do not significantly improve the subjects' understanding of the experiment; on-screen instructions shorten average decision times with respect to on-paper instructions, and requiring forced inputs reduces waiting times, in particular for the slowest subjects. Consistent with cognitive load theory, we find that short, on-screen instructions which require forced inputs improve on subjects' comprehension and familiarity with the experimental task, and they contribute to reduce both decision and waiting times without affecting the overall pattern of contributions.
    Keywords: Cognitive load theory, Comprehension, Distraction, Experimental instructions
    JEL: C72 C90 H41
    Date: 2011–11–03
  14. By: Ernst Fehr; Oliver D. Hart; Christian Zehnder
    Abstract: Previous experimental work provides encouraging support for some of the central assumptions underlying Hart and Moore (2008)’s theory of contractual reference points. However, existing studies ignore realistic aspects of trading relationships such as informal agreements and ex post renegotiation. We investigate the relevance of these features experimentally. Our evidence indicates that the central behavioral mechanism underlying the concept of contractual reference points is robust to the presence of informal agreements and ex post renegotiation. However, our data also reveal new behavioral features that suggest refinements of the theory. In particular, we find that the availability of informal agreements and ex post renegotiation changes how trading parties evaluate ex post outcomes. Interestingly, the availability of these additional options affects ex post evaluations even in situations in which the parties do not use them.
    JEL: C91 D86 J41
    Date: 2011–10
  15. By: Fanti, Luciano; Gori, Luca
    Abstract: The present study considers a unionised duopoly with the two most popular labour market institutions, i.e. efficient bargaining (EB) and right to manage (RTM) unions and analyses product market stability under quantity competition. By focusing on the role played by labour market institutions on the market dynamics, we show that when the preference of unions towards wages is fairly low, (i) the stability region under RTM is higher than under EB, and (ii) a rise in the union power in the Nash bargaining monotonically increases (reduces) the parametric stability region under RTM (EB). In contrast, when the preference of unions towards wages becomes higher, an increase in the union’s bargaining power acts: (1) as an economic stabiliser when the union power is still low; (2) as an economic de-stabiliser when the union power is already high. These results shed some light on the effects of how labour market structures affect out-of equilibrium behaviours in a duopoly in addition to the many established results on how they affect equilibrium behaviours in such a context, and thus also constitute policy warnings for the design of the labour market institutions as regards the important issue of economic stability.
    Keywords: Bifurcation; Cournot; Duopoly; Efficient bargaining; Right to manage
    JEL: J51 L13 D43 C62
    Date: 2011–11–01
  16. By: Bin Xu (Public Administration College, Zhejiang Gongshang University and Experimental Social Science Laboratory, Zhejiang University.); Bram Cadsby (Department of Economics, University of Guelph.); Liangcong Fan (College of Public Administration, Zhejiang University.); Fei Song (Ted Rogers School of Management, Ryerson University.)
    Abstract: In this study, we examine the effectiveness of the individual-punishment mechanism in larger groups, comparing groups of four to groups of 40 participants. We find that the individual punishment mechanism is remarkably robust when the MPCR is held constant despite the coordination problems inherent in an institution relying on decentralized individual punishment decisions in the context of a larger group. This reflects increased per-capita expenditures on punishment that offset the greater coordination difficulties in the larger group. However, if the marginal group return stays constant, resulting in an MPCR that shrinks with group size, no such offset occurs and punishment loses much but not all of its effectiveness at encouraging voluntary contributions to a public good.
    Keywords: Experiment, Public Good, Punishment, Large Groups
    JEL: C91 H41
    Date: 2011
  17. By: Beard, Rodney
    Abstract: Water is essential for life. However, the basic problem of water resource allocation has been that water tends to be over-allocated. Demand for water exceeds the available supply. Essentially, the water economy is bankrupt. Bankruptcy problems have been almost exhaustively studied in the literature on economic theory-primarily from the perspective of cooperative game theory. The main concern of this literature has been how to fairly divide up the assets of a bankrupt entity. In water resource economics cooperative game theory has often been employed as a means of analyzing water resource allocation. It was only recently that the problem of directional flow was incorporated into such analyses. This has come to be known as the “river sharing problem” in the theoretical literature. Accounting for the direction of flow in water resource allocation problems has profound implications for policies that wish to facilitate both fair and efficient water allocations. This is the case whether proposed policies are interventionist or market based in nature. There is now a considerable literature on the allocation and distribution of water resources characterized by unidirectional flow. In this paper I critically review and appraise this literature with a view to making it more accessible to applied and policy economists. A key feature of the paper is that the connection between the bankruptcy literature, which has recently also realized the importance of flow, and the river sharing literature is discussed. The current state of the art in game theoretic models of water resource allocation with directional flow is discussed and implications and consequences for water resource policy highlighted
    Keywords: River sharing problem; Bankruptcy; Cooperative game theory; Water resouyrce allocation; distributive justice
    JEL: D63 C71 B23 Q25
    Date: 2011–10–28
  18. By: Marcel Boyer; Pierre Lasserre; Michel Moreaux
    Abstract: We model capacity-building investments in a homogeneous product duopoly facing uncertain demand growth. Capacity building is achieved through the addition of production units that are durable and lumpy and whose cost is irreversible. While building their capacity over time, firms compete à la Cournot in the product market given their installed capacity. There is no exogenous order of moves, no commitment regarding future decisions, and no finite horizon. We investigate Markov Perfect Equilibrium (MPE) paths of the investment game, which may include episodes during which firms invest at different times, a preemption pattern, and episodes in which firms invest simultaneously, a tacit collusion pattern. These episodes may alternate and are typically several. When firms have yet to invest in capacity, the sole pattern that is MPE-compatible is a preemption episode: firms invest at different times but have equal value. The first such investment may occur earlier and therefore be riskier than socially optimal. When both firms hold capacity, tacit collusion episodes may be MPE-compatible: firms invest simultaneously at a postponed time (hence holding back production in the meantime), thereby generating an investment wave in the industry. Such investment episodes are more likely with higher demand volatility, faster market growth, and lower cost of capital (discount rate). <P>
    Keywords: Real Options; Dynamic Duopoly; Lumpy Investments; Preemption; Investment Waves; Tacit Collusion,
    JEL: C73 D43 D92 L13
    Date: 2011–10–01

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