nep-gth New Economics Papers
on Game Theory
Issue of 2012‒03‒14
sixteen papers chosen by
Laszlo A. Koczy
Hungarian Academy of Sciences and Obuda University

  1. Rock-Paper-Scissors and Cycle-Based Games By Eric Bahel
  2. An Experiment on Prisoner’s Dilemma with Confirmed Proposals By Attanasi, Giuseppe; Garcia-Gallego, Aurora; Georgantzis, Nikolaos; Montesano, Aldo
  3. Entropic selection of Nash equilibrium By Alioğulları, Zeynel Harun; Barlo, Mehmet
  4. Coarse Correlated Equilibria and Sunspots By Indrajit Ray; Sonali Sen Gupta
  5. Stability of Coalitional Equilibria within Repeated Tax Competition By Sonja Brangewitz; Sarah Brockhoff
  6. How responsive are people to changes in their bargaining position? Earned bargaining power and the 50–50 norm By Nejat Anbarci; Nick Feltovich
  7. Delayed-Response Strategies in Repeated Games with Observation Lags By Drew Fudenberg; Yuhta Ishii; Scott Duke Kominers
  8. To Err is Human: Implementation in Quantal Response Equilibria By Norovsambuu Tumennasan
  9. Fixed Water Sharing Agreements Sustainable to Drought By Ambec, Stefan; Dinar, Ariel; McKinney, Daene
  10. Social interactions and complex networks By Opolot, Daniel
  11. Asymmetric Cournot duopoly: game complete analysis By Carfì, David; Perrone, Emanuele
  12. Endogenous Timing in Quality Investments and Price Competition By L. Lambertini; A. Tampieri
  13. Asymmetric R&D alliances and coopetitive games By Carfì, David; Bagileri, Daniela; Dagnino, Gianbattista
  14. A coopetitive approach to financial markets stabilization and risk management By Carfì, David; Musolino, Francesco
  15. Optimal Tariffs on Exhaustible Resources: The Case of Quantity Setting By Kenji Fujiwara; Ngo Van Long
  16. Asymmetric Competition among Nation States: A Differential Game Approach By Yutao Han; Patrice Pieretti; Skerdilajda Zanaj; Benteng Zou

  1. By: Eric Bahel
    Abstract: The present work characterizes the unique Nash equilibrium for games that are based on a cyclic preference relation. In the Nash equilibrium of these games, each player randomizes between three specific actions. In particular, an alternative way of deriving the unique Nash equilibrium of the Rock-Paper-Scissors game is proposed.
    Keywords: cycle, Nash equilibrium, prudent strategy
    Date: 2011
  2. By: Attanasi, Giuseppe; Garcia-Gallego, Aurora; Georgantzis, Nikolaos; Montesano, Aldo
    Abstract: We apply an alternating proposals protocol with a confirmation stage as a way of solving a Prisoner’s Dilemma game. We interpret players’ proposals and (no) confirmation of outcomes of the game as a tacit communication device. The protocol leads to unprecedented high levels of cooperation in the laboratory. Assigning the power of confirmation to one of the two players alone, rather than alternating the role of a leader significantly increases the probability of signing a cooperative agreement in the first bargaining period. We interpret pre-agreement strategies as tacit messages on players’ willingness to cooperate and on their beliefs about the others’ type.
    Keywords: Prisoner’s Dilemma; Bargaining; Confirmed Proposals; Confirmed Agreement; Tacit Communication.
    JEL: C72 C91 C92
    Date: 2011–12
  3. By: Alioğulları, Zeynel Harun; Barlo, Mehmet
    Abstract: This study argues that Nash equilibria with less variations in players' best responses are more appealing. To that regard, a notion measuring such variations, the entropic selection of Nash equilibrium, is presented: For any given Nash equilibrium, we consider the cardinality of the support of a player's best response against others' strategies that are sufficiently close to the behavior specified. These cardinalities across players are then aggregated with a real-valued function on whose form we impose no restrictions apart from the natural limitation to nondecreasingness in order to obtain equilibria with less variations. We prove that the entropic selection of Nash equilibrium is non-empty and admit desirable properties. Some well-known games, each of which display important insights about virtues / problems of various equilibrium notions, are considered; and, in all of these games our notion displays none of the criticisms associated with these examples. These examples also show that our notion does not have any containment relations with other associated and well-known refinements, perfection, properness and persistence.
    Keywords: Entropic Selection of Nash Equilibrium; Refinements of Nash Equilibrium
    JEL: C72
    Date: 2012–02–29
  4. By: Indrajit Ray; Sonali Sen Gupta
    Abstract: For duopoly models, we analyse the concept of coarse correlated equilibrium using simple symmetric devices that the players choose to commit to in equilibrium. In a linear duopoly game, we provice that Nash-centric devices, involving a sunspot structure, are simple symmetric coarse correlated equilibria. Any small unilaterial perturbation from such a structure fails to be equilibrium.
    Keywords: Duopoly, Coarse correlation, Simple devices, Sunspots
    JEL: C72
    Date: 2012–02
  5. By: Sonja Brangewitz (Institute of Mathematical Economics, Bielefeld University); Sarah Brockhoff (Department of Business Administration and Economics, Bielefeld University)
    Abstract: This paper analyzes the stability of capital tax harmonization agreements in a stylized model where countries have formed coalitions which set a common tax rate in order to avoid the inefficient fully non-cooperative Nash equilibrium. In particular, for a given coalition structure we study to what extend the stability of tax agreements is affected by the coalitions that have formed. In our set-up, countries are symmetric, but coalitions can be of arbitrary size. We analyze stability by means of a repeated game setting employing simple trigger strategies and we allow a sub-coalition to deviate from the coalitional equilibrium. For a given form of punishment we are able to rank the stability of different coalition structures as long as the size of the largest coalition does not change. Our main results are: (1) singleton regions have the largest incentives to deviate, (2) the stability of cooperation depends on the degree of cooperative behavior ex-ante.
    Keywords: capital tax competition, tax coordination, coalitional equilibria, repeated game
    JEL: C71 C72 H71 H77
    Date: 2012–02
  6. By: Nejat Anbarci; Nick Feltovich
    Abstract: Previous research has shown that individuals do not respond to changes in their bargaining position to the extent predicted by standard bargaining theories. Most of these results come from experiments with bargaining power allocated exogenously, so that individuals may perceive it as having been “unearned” and thus be reluctant to exploit it. Typically these experiments also allowed equal splits of the “cake” (the amount bargained over) as equilibrium outcomes, leading to a powerful tendency toward 50-50 splits. We conduct a bargaining experiment in which subjects earn their bargaining power through a real–effort task. Treatments are based on the Nash demand game (NDG) and an unstructured bargaining game (UBG). Subjects bargain over a fixed amount of money, with disagreement payments determined entirely by the number of units of the real–effort task successfully completed. Task parameters are set to allow disagreement payoffs above half the cake size, in which case 50–50 splits are not individually rational, and thus not consistent with equilibrium. We find that subjects are least responsive to changes in own and opponent disagreement payoffs in the NDG with both disagreement payments below half the cake size. Responsiveness is higher in the UBG, and in the NDG when one disagreement payment is more than half the cake size, but in both cases it is still less than predicted. It is only in the UBG when a disagreement payment is more than half the cake size that responsiveness to disagreement payoffs reaches the predicted level. Our results imply that even when real–life bargaining position is determined by past behaviour rather than luck, the extent to which actual bargaining corresponds to theoretical predictions will depend on (1) the institutions within which bargaining takes place, and (2) the distribution of bargaining power; in particular, whether the 50–50 norm is a viable outcome.
    Keywords: Nash demand game, unstructured bargaining, real effort, disagreement, experiment
    JEL: C78 C72 D81
    Date: 2012–03–07
  7. By: Drew Fudenberg; Yuhta Ishii; Scott Duke Kominers
    Date: 2012–03–02
  8. By: Norovsambuu Tumennasan (Department of Economics and Business, Aarhus University, Denmark)
    Abstract: We study the classical implementation problem when players are prone to make mis- takes. To capture the idea of mistakes, Logit Quantal Response Equilibrium (LQRE) is used, and we consider a case in which players are almost rational, i.e., the sophisti- cation level of players, delta, approaches infinity. We show that quasimonotonicity, a small variation of Maskin Monotonicity, and no worst alternative conditions are necessary for restricted Limiting LQRE (LLQRE) implementation. Moreover, these conditions are sufficient for both restricted and unrestricted LLQRE implementations if there are at least three players and each player's worst alternative set is constant over all states.
    Keywords: implementation, mechanisms, bounded rationalitym, quantal response equilibria
    JEL: C72 D70 D78
    Date: 2011–09–12
  9. By: Ambec, Stefan; Dinar, Ariel; McKinney, Daene
    Abstract: By signing a fixed water sharing agreement (FWSA), countries voluntarily commit to release a fixed amount of river water in exchange for an agreed compensation. We examine the vulnerability of such commitments to reduced water ows. Among all FWSAs that are acceptable to riparian countries, we find out the one which is sustainable to the most severe drought scenarios. The so-called upstream incremental FWSA assigns to each country its marginal contribution to its followers in the river. Its mirror image, the downstream incremental FWSA, is not sustainable to reduced ow at the source. We apply our analysis to the Aral Sea basin agreement.
    Keywords: international river treaty, water, stability, core, compliance, Aral sea.
    JEL: D74 Q25 Q28 Q54
    Date: 2011–10
  10. By: Opolot, Daniel (UNU-MERIT, University of Maastricht,)
    Abstract: This paper studies the impact of interaction topologies on individual and aggregate behavior in environments with social interactions. We study social interaction games of an infnitely large population with local and global externalities. Local externalities are limited within agents' ego-networks while the global externality is derived from aggregate distribution in a feedback manner. We consider two forms of heterogeneity, that due to individual intrinsic tastes and that due to ego-networks. The agents know the potential number of other agents they will interact with but do not posses complete information about their neighbors' types and strategies so they base their decisions on expectations and beliefs. We characterize the existence, uniqueness and multiplicity of equilibrium distribution of strategies. By considering arbitrary interaction topologies, we show that the interaction structure greatly determines the uniqueness and multiplicity of equilibrium outcomes, as well as the equilibrium aggregate distribution of strategies as measured by the mean strategy.
    Keywords: Complex networks, Partial information, Local externality, Global externality, Adoption
    JEL: C72 D82 D84
    Date: 2012
  11. By: Carfì, David; Perrone, Emanuele
    Abstract: In this paper we apply the Complete Analysis of Differentiable Games (introduced by D. Carfì in [3], [6], [8], [9]; already employed by himself and others in [4], [5], [7]) and some new algorithms using the software wxMaxima 11.04.0, in order to reach a total scenario knowledge (that is the total knowledge of the payoff space of the interaction) of the classic Cournot Duopoly (1838), viewed as a complex interaction between two competitive subjects, in a particularly interesting asymmetric case. The software wxMaxima is an interface for the computer algebra system Maxima. Maxima is a system for the manipulation of symbolic and numerical expressions, including differentiation, sets, vectors and matrices.
    Keywords: Asymmetric Cournot Duopoly; Normal-form Games; Software algorithms in Microeconomic Policy; Complete Analysis of a normal-form game; Pareto optima; valuation of Nash equilibriums; Bargaining solutions
    JEL: D2 C02 C7
    Date: 2012
  12. By: L. Lambertini; A. Tampieri
    Abstract: We modify the price-setting version of the vertically differentiated duopoly model by Aoki (2003) by introducing an extended game in which firms noncooperatively choose the timing of moves at the quality stage. Our results show that there are multiple equilibria in pure strategies, in which firms always select sequential play at the quality stage. We also investigate the mixed-strategy equilibrium, revealing that the probability of generating outcomes out of equilibrium is higher than its complement to one. In the alternative of full market coverage, we show that the quality stage is solved in dominant strategies and therefore the choice of roles becomes irrelevant as the Nash and Stackelberg solutions coincide.
    JEL: C73 L13
    Date: 2012–03
  13. By: Carfì, David; Bagileri, Daniela; Dagnino, Gianbattista
    Abstract: In this paper we show how the study of asymmetric R\&D alliances, that are those between young and small firms and large and MNEs firms for knowledge exploration and/or exploitation, requires the adoption of a coopetitive framework which consider both collaboration and competition. We draw upon the literature on asymmetric R&D collaboration and coopetition to propose a mathematical model for the coopetitive games which is particularly suitable for exploring asymmetric R&D alliances.
    Keywords: R&D alliances; coopetitive games
    JEL: D7 M1 D74 C7 O32 M54 O3 J5
    Date: 2012
  14. By: Carfì, David; Musolino, Francesco
    Abstract: The aim of this paper is to propose a methodology to stabilize the financial markets by adopting Game Theory, in particular, the Complete Study of a Differentiable Game and the new mathematical model of Coopetitive Game, proposed recently in the literature by D. Carfì. Specifically, we will focus on two economic operators: a real economic subject and a financial institute (a bank, for example) with a big economic availability. For this purpose we will discuss about an interaction between the two above economic subjects: the Enterprise, our first player, and the Financial Institute, our second player. The only solution which allows both players to win something, and therefore the only one collectively desirable, is represented by an agreement between the two subjects: the Enterprise artificially causes an inconsistency between spot and future markets, and the Financial Institute, who was unable to make arbitrages alone, because of the introduction by the normative authority of a tax on economic transactions (that we propose to stabilize the financial market, in order to protect it from speculations), takes the opportunity to win the maximum possible collective (social) sum, which later will be divided with the Enterprise by contract. We propose hereunder two kinds of agreement: a fair transferable utility agreement on the an initial natural interaction and a same type of compromise on a quite extended coopetitive context.
    Keywords: Financial Markets and Institutions; Financing Policy; Financial Risk; Financial Crises; Game Theory; Arbitrages; Coopetition
    JEL: D53 C7 E44 G32 G01
    Date: 2012
  15. By: Kenji Fujiwara; Ngo Van Long
    Abstract: Constructing a dynamic game model of trade of an exhaustible resource, this paper compares feedback Nash and Stackelberg equilibria when the exporting country sets quantity rather than price. We consider two different leadership scenarios: leadership by the importing country, and leadership by the exporting country. We numerically show that as compared to the Nash equilibrium, both countries are better off if the importing country is a leader, but that the follower is worse off if the exporting country is a leader. Consequently, the world welfare is highest under the importing country's leadership and lowest under the exporting country's leadership. <P>On construit un modèle d’un jeu dynamique d’échange en ressource non-renouvelable sous l’hypothèse que le pays exportateur détermine la quantité au lieu du prix. L’objectif est de comparer l’équilibre de Nash avec les équilibres de Stackelberg. Dans un premier temps, c’est le pays importateur qui est le leader. Dans un deuxième temps, le pays exportateur assume le leadership. On démontre numériquement que, par rapport à l’équilibre de Nash , le niveau de bien-être des deux pays est plus élevé sous l’équilibre de Stackelberg dans le cas où l’importateur est le leader. Dans le cas où le pays exportateur est le leader, le niveau de bien-être du pays importateur est moins élevé que celui de l’équilibre de Nash. Le bien-être du monde entier dans le cas du leadership du pays importateur est plus élevé que dans le cas opposé.
    Keywords: dynamic game, exhaustible resource, Stackelberg leadership., jeu dynamique, ressources non-renouvelables, leadership de Stackelberg.
    JEL: C73 L72 Q34 F18
    Date: 2012–01–01
  16. By: Yutao Han (CREA, Université du Luxembourg); Patrice Pieretti (CREA, Université du Luxembourg); Skerdilajda Zanaj (CREA, Université du Luxembourg); Benteng Zou (CREA, Université du Luxembourg)
    Abstract: This paper analyzes the impact of foreign investments on a small country's economy in the context of international competition. To that end, we model tax and infrastructure competition within a differential game framework between two unequally sized countries. The model accounts for the widely recognized characteristic that small states are more flexible in their political decision making than larger countries. However, we also acknowledge that small size is associated with limited institutional capacity in the provision of public goods. The model shows that the long-term outcome of international competition crucially depends on the degree of capital mobility. In particular, we show that flexibility mitigates against - but does not eliminate - the likelihood of collapse in a small economy. Finally, we note that the beneficial effect of flexibility in a small state increases with its inefficiency in providing public infrastructure and with the degree of international openness.
    Keywords: Tax/Infrastructure competition, Open-loop/Markovian strategies, Differential games
    JEL: H25 H73 O30 O43
    Date: 2012–02

This nep-gth issue is ©2012 by Laszlo A. Koczy. It is provided as is without any express or implied warranty. It may be freely redistributed in whole or in part for any purpose. If distributed in part, please include this notice.
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