nep-gth New Economics Papers
on Game Theory
Issue of 2013‒08‒05
eleven papers chosen by
Laszlo A. Koczy
Hungarian Academy of Sciences and Obuda University

  1. Rule Rationality By Heller, Yuval; Winter, Eyal
  2. The lattice structure of the strong Lorenz-core By Vincent Iehlé
  3. Manipulation of Stable Matchings using Minimal Blacklists By Yannai A. Gonczarowski
  4. Stability and trembles in extensive-form games By Heller, Yuval
  5. Minimum cost spanning tree problems with indifferent agents By Christian Trudeau
  6. House Allocation via Deferred-Acceptance By Lars Ehlers; Bettina Klaus
  7. Who knows It is a game? On rule understanding, strategic awareness and cognitive ability By Fehr, Dietmar; Huck, Steffen
  8. Egalitarian Equivalence And Strategyproofness In The Queueing Problem By Youngsub Chun; Manipushpak Mitra; Suresh Mutuswami
  9. Cupid's Invisible Hand: Social Surplus and Identification in Matching Models By Bernard Salanié; Alfred Galichon
  10. Reordering an existing queue By Youngsub Chun; Manipushpak Mitra; Suresh Mutuswami
  11. Leadership, Information, and Risk Attitude: A Game Theoretic Approach By John T. Kulas; Mana Komai; Saint Cloud State University; Philip J. Grossman

  1. By: Heller, Yuval; Winter, Eyal
    Abstract: We study the strategic advantages of following rules of thumb that bundle different games together (called rule rationality) when this may be observed by one's opponent. We present a model in which the strategic environment determines which kind of rule rationality is adopted by the players. We apply the model to characterize the induced rules and outcomes in various interesting environments. Finally, we show the close relations between act rationality and “Stackelberg stability” (no player can earn from playing first).
    Keywords: Bounded Rationality, Commitments, Categorization, Value of information.
    JEL: C72 D82
    Date: 2013–07–31
  2. By: Vincent Iehlé (LEDa - Laboratoire d'Economie de Dauphine - Université Paris IX - Paris Dauphine, CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - CNRS : UMR7534 - Université Paris IX - Paris Dauphine)
    Abstract: The strong Lorenz-core of a transferable utility game has a join-lattice structure on every rank-preserving region of the payoff set. The result unveils new properties on the arrangement of strong Lorenz-core allocations. As immediate corollaries we obtain complementary results to some findings of Dutta and Ray, {\it Games Econ. Behav.}, 3(4) p.403-422 (1991), on constrained egalitarian allocations.
    Keywords: Lorenz criterion; Lorenz-core; cooperative game; constrained egalitarian allocation; lattice
    Date: 2013–07–01
  3. By: Yannai A. Gonczarowski
    Abstract: Gale and Sotomayor (1985) have noted that if women can benefit from manipulating the men-proposing Gale-Shapley matching algorithm (1962), then they can optimally do so by truncating their preference lists. (I.e. by blacklisting a possibly-long suffix of their preference lists and leaving the prefix as is.) As Gusfield and Irving have already noted in 1989, there are no systematic results regarding the possibility of women manipulating the algorithm in any other manner, e.g. by permuting their preference lists. In this paper, we address Gusfield and Irving's open question by providing tight upper bounds on the amount and combined size of the blacklists required by the women if they wish to force a matching as the M-optimal stable matching, or, more generally, as the single stable matching. Our results show that the coalition of all women may strategically force any matching as the unique stable matching, using preference lists in which at most half of the women have nonempty blacklists, and in which the average blacklist size is less than 1, allowing them to manipulate the market in a manner that is far more inconspicuous, in a sense, than previously realized (and even more so in implementations that require the specification of preference lists of at most a certain length). When there are less women than men, we show that in the absence of blacklists for men, the women can force any matching as the unique stable matching without blacklisting anyone, while when there are more women than men, each to-be-unmatched woman may have to blacklist as many as all men. Together, these results shed light on the question of how much, if at all, do given preferences for one side a priori impose limitations on the set of stable matchings under various conditions. All the results in this paper are constructive, providing efficient algorithms for calculating the desired strategies.
    Date: 2013–07
  4. By: Heller, Yuval
    Abstract: A leading solution concept in the evolutionary study of extensive-form games is Selten's (1983) (selten1983evolutionary) notion of limit ESS. We demonstrate that a limit ESS does not imply neutral stability, and that it may be dynamically unstable (almost any small perturbation takes the population away). These problems arise due to an implicit assumption that “mutants” are arbitrarily rare relative to “trembling” incumbents. Finally, we present a novel definition that solves this issue and has appealing properties.
    Keywords: Limit ESS, evolutionary stability, extensive-form games.
    JEL: C73
    Date: 2013–07–09
  5. By: Christian Trudeau (Department of Economics, University of Windsor)
    Abstract: We consider an extension of minimum cost spanning tree (mcst) problems where some agents do not need to be connected to the source, but might reduce the cost of others to do so. Even if the cost usually cannot be computed in polynomial time, we extend the characterization of the Kar solution (Kar (2002, GEB)) for classic mcst problems. It is obtained by adapting the Equal treatment property: if the cost of the edge between two agents changes, their cost shares are a¤ected in the same manner if they have the same demand. If not, their changes are proportional to each other. We obtain three variations on the Kar solution, that are di¤erentiated and characterized using stability, fairness and manipulation-proofness properties.
    Keywords: Minimum cost spanning tree; Steiner tree; cost sharing; Shapley value.
    JEL: C71 D63
    Date: 2013–08
  6. By: Lars Ehlers; Bettina Klaus
    Abstract: We study the simple model of assigning indivisible and heterogenous objects (e.g., houses, jobs, offices, etc.) to agents. Each agent receives at most one object and monetary compensations are not possible. For this model, known as the house allocation model, we characterize the class of rules satisfying unavailable object invariance, individual rationality, weak non-wastefulness, resource-monotonicity, truncation invariance, and strategy-proofness: any rule with these properties must allocate objects based on (implicitly induced) objects' priorities over agents and the agent-proposing deferred-acceptance-algorithm.
    Keywords: deferred-acceptance-algorith; indivisible objects allocation; resource-monotonicity; strategy-proofness
    JEL: D63 D70
    Date: 2013–07
  7. By: Fehr, Dietmar; Huck, Steffen
    Abstract: We introduce the notion of strategic awareness in experimental games which captures the idea that subjects realize they are playing a game and thus have to form beliefs about others' actions in order to play well. The concept differs from both, rule understanding and rationality. We then turn to experimental evidence from a beauty contest game where we elicit measures of cognitive ability and beliefs about others' cognitive ability. We show that the effect of cognitive ability is highly non-linear. Subjects' behavior below a certain threshold is indistinguishable from uniform random play and does not correlate with beliefs about others ability. In contrast, choices of subjects who exceed the threshold avoid dominated choices and react very sensitively to beliefs about others cognitive ability. -- In vielen Situationen spielt das Bewusstsein über strategische Komponenten eine wichtige Rolle. In diesem kurzen Artikel führen wir das Konzept von strategic awareness in Experimenten ein. Dieses neue Konzept beschreibt die Fähigkeit von Experimentteilnehmer, strategische Situationen zu erkennen und daher Erwartungen über das Verhalten von anderen zu bilden. Das Konzept unterscheidet sich sowohl von Rationalität als auch vom bloßen Verstehen von den Regeln eines Experiments. Wir demonstrieren das Konzept empirisch mit Hilfe von Daten eines Beauty Contest Games, in dem wir die kognitiven Fähigkeiten der Teilnehmer und ihre Einschätzungen über die kognitiven Fähigkeiten der anderen Teilnehmer erheben. Die Resultate zeigen, dass kognitive Fähigkeiten einen starken nichtlinearen Effekt auf die Entscheidungen in dem Beauty Contest Game haben. Das Verhalten von Experimentteilnehmer, die unter einer bestimmten Schwelle liegen, kann nicht von zufälligen Entscheidungen unterschieden werden und korreliert auch nicht mit deren Einschätzung über die kognitiven Fähigkeiten der anderen Teilnehmer. Im Gegensatz dazu vermeiden Teilnehmer, die über dieser Schwelle liegen, dominierte Entscheidungen und basieren ihre Entscheidungen auf ihrer Einschätzung über die kognitiven Fähigkeiten der anderen Teilnehmer.
    Keywords: strategic awareness,cognitive ability,beauty contest
    JEL: C7 C9 D0
    Date: 2013
  8. By: Youngsub Chun; Manipushpak Mitra; Suresh Mutuswami
    Abstract: We investigate the implications of egalitarian equivalence (Pazner and Schmeidler [22]) together with queue efficiency and strategyproofness in the context of queueing problems. We completely characterize the class of mechanisms satisfying the three requirements. Though there is no mechanism in this class satisfying budget balance, feasible mechanisms exist. We also show that it is impossible to find a mechanism satisfying queue efficiency, egalitarian equivalence and a stronger notion of strategyproofness called weak group strategyproofness. In addition, we show that generically there is no mechanism satisfying two normative notions, egalitarian equivalence and no-envy, together.
    Keywords: Queueing problem, queue efficiency, strateyproofness, egalitarian equivalence, budget balance, feasibility, weak group strategyproofness, no-envy.
    JEL: C72 D63 D82
    Date: 2013–07
  9. By: Bernard Salanié; Alfred Galichon (Département d'économie)
    Abstract: We investigate a model of one-to-one matching with transferable utility when some of the characteristics of the players are unobservable to the analyst. We allow for a wide class of distributions of unobserved heterogeneity, subject only to a separability assumption that generalizes Choo and Siow (2006). We first show that the stable matching maximizes a social gain function that trades off the average surplus due to the observable characteristics and a generalized entropy term that reflects the impact of matching on unobserved characteristics. We use this result to derive simple closed-form formulæ that identify the joint surplus in every possible match and the equilibrium utilities of all participants, given any known distribution of unobserved heterogeneity. If transfers are observed, then the pre-transfer utilities of both partners are also identified. We also present a very fast algorithm that computes the optimal matching for any specification of the joint surplus. We conclude by discussing some empirical approaches suggested by these results.
    Date: 2013
  10. By: Youngsub Chun; Manipushpak Mitra; Suresh Mutuswami
    Abstract: We investigate the problem of reordering agents starting from an existing queue. First, we introduce four important axioms of the problem, budget balance (BB), outcome efficiency (OE), strategyproofness (SP), and individual rationality (IR). Unfortunately, it is easy to show that these four axioms are incompatible in the current setup. Given this negative result, we examine the consequences of relaxing BB, OE and SP, one at a time. Our results are as follows: (i) There is no mechanism satisfying OE, SP and IR which runs a nonnegative surplus at all profiles. (ii) When there are two agents, the only non-trivial mechanisms satisfying BB, SP and IR are Fixed price trading mechanisms but there are additional mechanisms when there are more than two agents. We identify an intuitive mechanism which we call the median price exchange mechanism and characterize its maximal level of inefficiency. (iii) By weakening SP to `one-sided' strategyproofness, we identify two mechanisms, the buyers' mechanism and the sellers' mech- anism, and characterize them on the basis of independence axioms.
    Keywords: Queueing problem with an initial order, budget balance, outcome efficiency, strateyproofness, individual rationality
    JEL: C72 D63 D82
    Date: 2013–07
  11. By: John T. Kulas; Mana Komai; Saint Cloud State University; Philip J. Grossman
    Abstract: This paper experimentally investigates how risk attitudes mitigate leadership effectiveness in a collective setting with projects that exhibit both free riding and coordination problems. We take two novel approaches: 1) the introduction of economic game theory to psychological studies of leadership, and 2) the application of the leadership ontology of Drath et al. (2008) as a crossdisciplinary integrative framework. Leadership here is focused on the presence or absence of direction, alignment, and commitment as well as antecedent beliefs and practices that are held within a collective (for us, our experimental participants). Our leadership context is stripped down to very minimal conditions: three group members, an investment decision, and the introduction of information regarding group members' attitudes toward risk. We find that the mere mention of risk attitude (whether risky or risk averse) undermines leadership effectiveness in mitigating free riding for our 420 experimental participants. Our study’s primary implications lie in the application of game theory methodology to the psychological study of leadership, the introduction of relevant individual difference constructs to economic studies of leadership, and the advocation of the Drath et al. (2008) framework as a helpful integrative mechanism for interdisciplinary leadership research.
    Keywords: game theory; risk attitude; interdisciplinary research; group dynamics
    Date: 2013–07

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