nep-gth New Economics Papers
on Game Theory
Issue of 2012‒11‒24
nine papers chosen by
Laszlo A. Koczy
Hungarian Academy of Sciences and Obuda University

  1. Group Size and Cooperation among Strangers By John Duffy; Huan Xie
  2. Pyramidal values By Ramón Jesús Flores Díaz; Elisenda Molina; Juan Tejada
  3. Are Behavioral Choices in the Ultimatum and Investment Games Strategic? By Lora R. Todorova; Bodo Vogt
  4. Correlation of Types in Bayesian Games By Luciano De Castro
  5. How Sensitive is Strategy Selection in Coordination Games? By Siegfried K. Berninghaus; Lora R. Todorova; Bodo Vogt
  6. Values for Markovian coalition processes By Ulrich Faigle; Michel Grabisch
  7. Free disposal, monotonicity and equilibrium By Yang, Yi-You
  8. Evolution of Social networks By Christoph Kuzmics; Mathias Staudigl; Brian W. Rogers
  9. Formal and informal markets: A strategic and evolutionary perspective By Anbarci, Nejat; Gomis-Porqueras, Pedro; Marcus, Pivato

  1. By: John Duffy (University of Pittsburgh); Huan Xie (Concordia University)
    Abstract: We study how group size affects cooperation in an infinitely repeated n-player Prisoner's Dilemma (PD) game. In each repetition of the game, groups of size n less than or equal to M are randomly and anonymously matched from a fixed population of size M to play the n-player PD stage game. We provide conditions for which the contagious strategy (Kandori, 1992) sustains a social norm of cooperation among all M players. Our main finding is that if agents are sufficiently patient, a social norm of society-wide cooperation becomes easier to sustain under the contagious strategy as n converges to M.
    Keywords: Cooperation, Social Norms, Group Size, Repeated Games, Random Matching, Prisoner's Dilemma
    JEL: C72 C73 C78 Z13
    Date: 2012–09–12
  2. By: Ramón Jesús Flores Díaz; Elisenda Molina; Juan Tejada
    Abstract: We propose a new type of values for cooperative TU-games, which we call pyramidal values. Assuming that the grand coalition is sequentially formed, and all orderings are equally likely, we define a pyramidal value to be any expected payoff in which the entrant player receives a salary and the right to get part of the benefits derived from subsequent incorporations to the just formed coalition, whereas the remaining benefit is distributed among the incumbent players. To be specific, we consider some parametric families of pyramidal values: the egalitarian pyramidal family, which coincides with the a-consensus value family introduced by Ju et al. in (2007), the proportional pyramidal family, and the weighted pyramidal family, which in turn includes the other two families as special cases. We also analyze the properties of these families, as well as their relationships with other previously defined values.
    Keywords: Game theory, TU games, Pyramidal values, Consensus values
    Date: 2012–10
  3. By: Lora R. Todorova (Faculty of Economics and Management, Otto-von-Guericke University Magdeburg); Bodo Vogt (Faculty of Economics and Management, Otto-von-Guericke University Magdeburg)
    Abstract: This paper experimentally examines the relationship between self-reporting risk preferences and behavioral choices in the subsequently played dictator, ultimatum and investment games. The results from these experiments are used to discern the motivational bases of behavioral choices in the ultimatum and investment games. The focus is on investigating whether strategic considerations are important for strategy selection in the two games. We find that self-reporting risk preferences does not alter the dictators' offers and trusters' investments, while it significantly decreases the proposers' offers and leads to a substantial decrease in the amount trustees give back to their partners. We interpret these results as evidence that the decisions of proposers in the ultimatum game and trustees in the investment game are strategic.
    Keywords: coordination game, dictator game, ultimatum game, investment game, questionnaire, risk scale, risk preferences
    JEL: C7 C91 D8
    Date: 2012–09
  4. By: Luciano De Castro
    Abstract: Despite their importance, games with incomplete information and dependent types are poorly understood; only special cases have been considered and a general approach is not yet available. In this paper, we propose a new condition (named richness) for correlation of types in (asymmetric) Bayesian games. Richness is related to the idea that “beliefs do not determine preferences” and that types should be modeled with two explicit parts: one for payoffs and another for beliefs. With this condition, we are able to provide the first pure strategy equilibrium existence result for a general model of multi-unit auctions with correlated types. We then focus on a special case of richness, called “grid distributions,” and establish necessary and sufficient conditions for the existence of a symmetric monotonic pure strategy equilibrium in first-price auctions with general levels of correlation. We also provide a polynomial-time algorithm to verify this existence and suggest, using simulations, that the revenue superiority of English auctions may not hold for positively correlated types in general. JEL Classification Numbers: C62, C72, D44, D82
    Date: 2012–01–12
  5. By: Siegfried K. Berninghaus (Institute for Economic Theory and Statistics, Karlsruhe Institute of Technology); Lora R. Todorova (Faculty of Economics and Management, Otto-von-Guericke University Magdeburg); Bodo Vogt (Faculty of Economics and Management, Otto-von-Guericke University Magdeburg)
    Abstract: This paper presents the results of an experiment designed to study the effect produced on strategy choices when a subject reports risk preferences on a risk scale before engaging in a 2x2 coordination game. The main finding is that the act of stating one's own risk preferences significantly alters strategic behavior. In particular, subjects tend to choose the risk dominant strategy more often when they have previously stated their attitudes to risk. Within a best-response correspondence framework, this result can be explained by a change in either risk preferences or beliefs. We find that self-reporting risk preferences does not induce a change in subjects' beliefs. We argue that the behavioral arguments of strategy selection, such as focal points, framing and uncertain preferences can explain our results.
    Keywords: coordination game, questionnaire, risk scale, risk preferences, beliefs, focal points, framing, uncertain preferences
    JEL: D81 C91 C72
    Date: 2012–09
  6. By: Ulrich Faigle (Zentrum für Angewandte Informatik Köln - Universität zu Köln); Michel Grabisch (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris I - Panthéon Sorbonne, EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics - Ecole d'Économie de Paris)
    Abstract: Time series of coalitions (so-called scenarios) are studied that describe processes of coalition formation where several players may enter or leave the current coalition at any point in (discrete) time and convergence to the grand coalition is not necessarily prescribed. Transitions from one coalition to the next are assumed to be random and to yield a Markov chain. Three examples of such processes (the Shapley-Weber process, the Metropolis process, and an example of a voting situation) and their properties are presented. A main contribution includes notions of value for such series, \emph{i.e.}, schemes for the evaluation of the expected contribution of a player to the coalition process relative to a given cooperative game. Particular processes permit to recover the classical Shapley value. This methodology's power is illustrated with well-known examples from exchange economies due to Shafer (1980) and Scafuri and Yannelis (1984), where the classical Shapley value leads to counterintuitive allocations. The Markovian process value avoids these drawbacks and provides plausible results.
    Keywords: coalitional game; coalition formation process; exchange economy; Markov chain; Shapley value
    Date: 2012
  7. By: Yang, Yi-You
    Abstract: This paper studies the effect of free disposal on the existence of Walrasian equilibrium for exchange economies with indivisible objects. It is shown that allowing an agent to enjoy free disposal has the same effect for generating an equilibrium (or eliminating existing equilibria) as allowing every agent to enjoy free disposal. A new equilibrium existence theorem is given to show how this observation can enhance the existence results by Kelso and Crawford (1982) and Sun and Yang (2006).
    Keywords: Indivisibility; equilibrium; free disposal; monotonic cover
    JEL: D5 D51
    Date: 2012–11–13
  8. By: Christoph Kuzmics (Bielefeld University); Mathias Staudigl (Bielefeld University); Brian W. Rogers
    Abstract: Modeling the evolution of networks is central to our understanding of modern large communication systems, such as theWorld-Wide-Web, as well as economic and social networks. The research on social and economic networks is truly interdisciplinary and the number of modeling strategies and concepts is enormous. In this survey we present some modeling approaches, covering classical random graph models and game-theoretic models, which may be used to provide a unified framework to model and analyze the evolution of networks.
    Date: 2012–10
  9. By: Anbarci, Nejat; Gomis-Porqueras, Pedro; Marcus, Pivato
    Abstract: We investigate the coexistence of formal and informal markets. In formal markets, we assume sellers can publicly advertise their prices and locations, whereas in informal markets, sellers need to trade through bilateral bargaining so as to remain anonymous from the taxing authority. We consider two models. As a benchmark, we first only allow sellers to switch between markets, which enables us to derive some analytical results that show the existence of a stable equilibrium where formal and informal markets coexist. We also establish that some sellers will migrate from the formal market to the informal market if the formal market's advantage in quality assurance erodes, or the government imposes higher taxes and regulations in the formal market, or the risk of crime and/or confiscation decreases in the informal market, or the number of buyers in the informal market increases. Some sellers will migrate from the informal market to the formal market whenever the opposite changes occur. We then allow both sellers and buyers to switch between markets. In this model, we illustrate that if the net costs of trading for sellers in the formal sector and buyers in the informal sector have opposite signs, then there is a unique locally stable equilibrium where formal and informal markets coexist.
    Keywords: informal markets; bilateral bargaining; directed search; taxation
    JEL: C78 E26
    Date: 2012–11–07

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