nep-gth New Economics Papers
on Game Theory
Issue of 2017‒09‒03
sixteen papers chosen by
László Á. Kóczy
Magyar Tudományos Akadémia

  1. Stabilization of an Uncertain Simple Fishery Management Game By Engwerda, Jacob
  2. Sharing Sequential Values in a Network By Juarez, Ruben; Ko, Chiu Yu; Xue, Jingyi
  3. Natural implementation with semi-responsible agents in pure exchange economies By Michele Lombardi; Naoki Yoshihara
  4. Treading a Â…fine line: (Im)possibilities for Nash implementation with partially-honest individuals By Michele Lombardi; Naoki Yoshihara
  5. Fair Division with Uncertain Needs By Xue, Jingyi
  6. A concept of sincerity for combinatorial voting By Francesco De Sinopoli; Claudia Meroni
  7. Partially-honest Nash implementation: a full characterization By Lombardi, Michele; Yoshihara, Naoki
  8. Stability, Fairness and Random Walks in the Bargaining Problem By Jakob Kapeller; Stefan Steinerberger
  9. Arranged Marriages under Transferable Utilities By Pauline Morault
  10. The structure of priority in the school choice problem By Duddy, Conal
  11. Return on trust is lower for immigrants By Cettolin, Elena; Suetens, Sigrid
  12. Adoption of a New Payment System: Theory and Experimental Evidence By Jasmina Arifovic; John Duffy; Janet Jiang
  13. Maintaing vs. Milking Good Reputation when Customer Feedback is Inaccurate By Behnud Djawadi; Rene Fahr; Claus-Jochen Haake; Sonja Recker
  14. Equitable rent division By Rodrigo A. Velez
  15. Marriage Strategy Among European Nobility By Stefania Marcassa; Jérôme Pouyet; Thomas Trégouët
  16. A Simple Algorithm for Solving Ramsey Optimal Policy with Exogenous Forcing Variables By Chatelain, Jean-Bernard; Ralf, Kirsten

  1. By: Engwerda, Jacob (Tilburg University, Center For Economic Research)
    Abstract: This note analyzes in a fishery management problem the effects of relaxing one of the usual assumptions in the literature of dynamic games. Specifically, the assumption that players restrict to strategies that stabilize the system. Previous works in the literature have shown that feedback Nash equilibria can exist in which a player can improve unilaterally by choosing a feedback control for which the closed-loop system is unstable. This paper considers in some more detail the implication this setting has in the framework of a simple fishery management. It is shown that if the fishermen are not short-sighted in their valuation of future profits, the considered approach implies a division of them into two groups. One group going for maximal profits and the other group taking care of the imposed stability constraint. To see how noise might impact these results we additionally consider a framework where fishermen take into account the possibility that the fish growth might be corrupted by external factors. We consider a deterministic approach of dealing with noise in this set-up. The model predicts that the more people are involved in the group taking care of the stabilization constraint, the less active they get. Furthermore it predicts that the natural reaction of any of these persons is to increase his activities if he expects more noise. But that this activity is reduced, and partly replaced by more active control policies by group members, if the size of the group increases. Activity of fishermen going for maximal profits is not affected by noise expectations.
    Keywords: fishery management; fishing strategies; linear quadratic differential games; feedback information structure; soft-constrained Nash equilibrium; infinte planning horizon
    JEL: Q22 Q28 Q56 C61 C72 C73
    Date: 2017
  2. By: Juarez, Ruben (Department of Economics, University of Hawaii); Ko, Chiu Yu (Department of Economics, National University of Singapore); Xue, Jingyi (School of Economics, Singapore Management University)
    Abstract: Consider a sequential process where agents have individual values at every possible step. A planner is in charge of selecting steps and distributing the accumulated aggregate values among agents. We model this process by a directed network where each edge is associated with a vector of individual values. This model applies to several new and existing problems, e.g., developing a connected public facility and distributing total values received by surrounding districts; selecting a long-term production plan and sharing final profits among partners of a firm; choosing a machine schedule to serve different tasks and distributing total outputs among task owners. Herein, we provide the first axiomatic study on path selection and value sharing in networks. We consider four sets of axioms from different perspectives, including those related to (1) the sequential consistency of assignments with respect to network decompositions; (2) the monotonicity of assignments with respect to network expansion; (3) the independence of assignments with respect to certain network transformations; and (4) implementation in the case where the planner has no information about the underlying network and individual values. Surprisingly, these four disparate sets of axioms characterize similar classes of solutions — selecting efficient path(s) and assigning to each agent a share of total values which is independent of their individual values. Furthermore, we characterize more general solutions that depend on individual values.
    Keywords: Sequential Values; Sharing; Network; Redistribution
    JEL: C72 D44 D71 D82
    Date: 2016–12–11
  3. By: Michele Lombardi (Adam Smith Business School, University of Glasgow); Naoki Yoshihara (Department of Economics, University of Massachusetts Amherst)
    Abstract: We study Nash implementation by natural price-quantity mechanisms in pure exchange economies when agents have intrinsic preferences for responsibility. An agent has an intrinsic preference for responsibility if she cares about truth-telling that is in line with the goal of the mechanism designer besides her material well-being. A semi-responsible agent is an agent who, given what her opponents do, acts in an irresponsible manner when a responsible behavior poses obstacles to her material well-being. The class of efficient allocation rules that are Nash implementable is identified provided that there is at least one agent who is semi-responsible. The Walrasian rule is shown to belong to that class.
    Keywords: Nash equilibrium, Exchange economies, Intrinsic preferences for responsibility, Boundary problem, Price-quantity mechanism
    JEL: C72 D71
    Date: 2017–08
  4. By: Michele Lombardi (Adam Smith Business School, University of Glasgow); Naoki Yoshihara (Department of Economics, University of Massachusetts Amherst)
    Abstract: This paper investigates the robustness of Dutta and Sen’s (2012) Theorem 1 to weaker notions of truth-telling. An individual honesty standard is modeled as a subgroup of the society, including the individual herself, for which she feels truth-telling concerns. An individual i is honest when she states her true preferences as well as rankings (not necessarily complete) of outcomes that are consistent with the true preferences of individuals in her honesty standard. The paper o¤ers a necessary condition for Nash implementation, called partial-honesty monotonicity, and shows that in an independent domain of preferences that condition is equivalent to Maskin monotonicity.
    Keywords: Nash implementation, Partial-honesty, Non-connected honesty standards, Independent domain
    JEL: C72 D71 D82
    Date: 2017–08
  5. By: Xue, Jingyi (School of Economics, Singapore Management University)
    Abstract: Imagine that agents have uncertain needs and a resource must be divided before uncertainty resolves. In this situation, waste typically occurs when the assignment to an agent turns out to exceed his realized need. How should the resource be divided in the face of possible waste? This is a question out of the scope of the existing rationing literature. Our main axiom to address the issue is no domination. It requires that no agent receive more of the resource than another while producing a larger expected waste, unless the other agent has been fully compensated. Together with conditional strict endowment monotonicity, consistency, and strong upper composition, we characterize a class of rules which we call expected-waste constrained uniform gains rules. Such a rule is associated with a function that aggregates the two components of cost generated by an agent at an allocation: the amount of the resource assigned to him and the expected waste he generates. The rule selects the allocation that equalizes as much as possible the cost generated by each agent. Moreover, we characterize the subclasses of rules associated with homothetic and linear cost functions. Lastly, to appreciate the role of no domination, we establish all the characterizations with a decomposition of no domination into two axioms: risk aversion and no reversal. They respectively capture that a rule should not ignore the claim uncertainty, and neither should it be too sensitive to the claim uncertainty.
    Keywords: Claims Problems; Need Uncertainty; Fair Division; Waste; Expected-waste Constrained Uniform Gains Rule; Rationing; Bankruptcy
    JEL: C71 D63 D74 D81
    Date: 2017–01–03
  6. By: Francesco De Sinopoli (Department of Economics (University of Verona)); Claudia Meroni (Department of Economics (University of Verona))
    Abstract: A basic problem in voting theory is that all the strategy profiles in which nobody is pivotal are Nash equilibria. We study elections where voters decide simultaneously on several binary issues. We extend the concept of conditional sincerity introduced by Alesina and Rosenthal (1996) and propose an intuitive and simple criterion to refine equilibria in which players are not pivotal. This is shown to have a foundation in a refinement of perfection that takes into account the material voting procedure. We prove that in large elections the proposed solution is characterized through a weaker definition of Condorcet winner and always survives sophisticated voting.
    Keywords: Voting theory, multi-issue elections, strategic voting, perfect equilibrium.
    JEL: C72 D72
    Date: 2017–01
  7. By: Lombardi, Michele; Yoshihara, Naoki
    Abstract: A partially-honest individual is a person who follows the maxim, "Do not lie if you do not have to" to serve your material interest. By assuming that the mechanism designer knows that there is at least one partially-honest individual in a society of n ≥ 3 individuals, a social choice rule (SCR) that can be Nash implemented is termed partially-honestly Nash implementable. The paper offers a complete characterization of the n-person SCRs that are partially-honestly Nash implementable. It establishes a condition which is both necessary and sufficient for the partially-honest Nash implementation. If all individuals are partially-honest, then all SCRs that satisfy the property of unanimity are partially-honestly Nash implementable. The partially-honest Nash implementation of SCRs is examined in a variety of environments.
    Keywords: Nash implementation, pure strategy Nash equilibrium, partial-honesty, Condition μ*
    JEL: C72 D71
    Date: 2017–08
  8. By: Jakob Kapeller; Stefan Steinerberger
    Abstract: We study the classical bargaining problem and its two canonical solutions, (Nash and Kalai-Smorodinsky), from a novel point of view: we ask for stability of the solution if both players are able distort the underlying bargaining process by reference to a third party (e.g. a court). By exploring the simplest case, where decisions of the third party are made randomly we obtain a stable solution, where players do not have any incentive to refer to such a third party. While neither the Nash nor the Kalai-Smorodinsky solution are able to ensure stability in case reference to a third party is possible, we found that the Kalai-Smorodinsky solution seems to always dominate the stable allocation which constitutes novel support in favor of the latter.
    Date: 2017–08
  9. By: Pauline Morault (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - CNRS - Centre National de la Recherche Scientifique - ECM - Ecole Centrale de Marseille, Sciences Po Paris, Department of Economics)
    Abstract: In many societies, marriage is a decision taken at the familial level. Arranged marriages are documented from Renaissance Europe to contemporary rural Kenya, and are still prevalent in many parts of the developing world. However, this family dimension has essentially been neglected by the existing matching literature on marriages. The objective of this paper is to introduce family considerations into the assignment game. We explore how shifting decision-making to the family level affects matching on the marriage market. We introduce a new concept of familial stability and find that it is weaker than individual stability. The introduction of families into the marriage market generates coordination problems, so the central result of the transferable utility framework no longer holds: a matching can be family-stable even if it does not maximize the sum of total marital surpluses. Interestingly, even when the stable matching is efficient, family decision-making drastically modifies how the surplus is shared-out. These results may have fundamental implications for pre-marital investments. We find that stable matchings depend on the type of family partitioning. Notably, when each family contains one son and one daughter, familial and individual stability are equivalent.
    Keywords: marriage,family,matching,transferable utility
    Date: 2017–06
  10. By: Duddy, Conal
    Abstract: In a school choice problem each school has a priority ordering over the set of students. These priority orderings depend on criteria such as whether a student lives within walking distance or has a sibling already at the school. I argue that by including just the priority orderings in the problem, and not the criteria themselves, we lose important information. More particularly, the priority orderings fail to capture important aspects of the information from which they are derived when a student may satisfy a given criterion across multiple schools. This loss of information results in mechanisms that discriminate between students in ways that are not easy to justify. I propose an extended formulation of the school choice problem wherein a “priority matrix”, indicating which criteria are satisfied by each student-school pair, replaces the usual profile of priority orderings.
    Keywords: school choice; matching; priority ordering; deferred acceptance
    JEL: C78 H40 I28
    Date: 2017–05–24
  11. By: Cettolin, Elena; Suetens, Sigrid
    Abstract: Trustworthiness is key for successful economic and social interactions. We conduct an experiment with a representative sample of the Dutch population to study whether trustworthiness depends on the ethnicity of the interaction partner. Native Dutch trustees play trust games with an anonymous other, who is either another native Dutch or an immigrant from non-Western descent. We find that the trustees reciprocate trust up to 13% less frequently if the trustor is a non-Western immigrant than if he/she is native Dutch. This percentage increases up to 23% for trustees who report disliking ethnic diversity in society in a survey that took place one year before the experiment. Since the decision to reciprocate does not involve behavioral risk, we take our results as evidence of taste-based discrimination. The implication is that the return on trust is lower for immigrants from non-Western descent than for native Dutch.
    Keywords: ethnic diversity; representative sample; taste-based discrimination; trust game; trustworthiness
    JEL: C72 C9 D01 J15
    Date: 2017–08
  12. By: Jasmina Arifovic (Simon Fraser University); John Duffy (Department of Economics, University of California-Irvine); Janet Jiang (Bank of Canada)
    Abstract: We model the introduction of a new payment method that competes with an existing payment method. Due to network adoption effects, there are two symmetric pure strategy equilibria in which only one of the two payment methods is used. The equilibrium where only the new payment method is used is socially optimal. In an experiment, we find that, depending on the fixed fee for acceptance of the new payment method and on the choices made by participants on both sides of the market, either equilibrium can be selected. An evolutionary learning model provides a good characterization of our experimental data.
    Keywords: Payment methods; Network effects; E-money; Experimental economics.
    JEL: E41 C35 C83 C92
    Date: 2017–08
  13. By: Behnud Djawadi (Paderborn University); Rene Fahr (Paderborn University); Claus-Jochen Haake (Paderborn University); Sonja Recker (Paderborn University)
    Abstract: In Internet transactions, customers and service providers often interact once and anonymously. To prevent deceptive behavior a reputation system is particularly important to reduce information asymmetries about the quality of the o?ered product or service. In this study we examine the e?ectiveness of a reputation system to reduce information asymmetries when customers may make mistakes in judging the provided service quality. In our model, a service provider makes strategic quality choices and short-lived customers are asked to evaluate the observed quality by providing ratings to a reputation system. The customer is not able to always evaluate the service quality correctly and possibly submits an erroneous rating according to a prede?ned probability. Considering reputation pro?les of the last three sales, within the theoretical model we derive that the service provider’s dichotomous quality decisions are independent of the reputation pro?le and depend only on the probabilities of receiving positive and negative ratings when providing low or high quality. Thus, a service provider optimally either maintains a good reputation or completely refrains from any reputation building process. However, when mapping our theoretical model to an experimental design we ?nd that a signi?cant share of subjects in the role of the service provider deviates from optimal behavior and chooses actions which are conditional on the current reputation pro?le. With respect to these individual quality choices we see that subjects use milking strategies which means that they exploit a good reputation. In particular, if the sales price is high, low quality is delivered until the price drops below a certain threshold, and then high quality is chosen until the price increases again.
    Keywords: Service Quality, Reputation Systems, Online Markets, Experimental Economics, Markovian Decision Process
    JEL: C73 C91 L12 L15 L86
    Date: 2017–08
  14. By: Rodrigo A. Velez (Texas A&M University, Department of Economics)
    Abstract: How should a group of roommates allocate the rooms and contributions to rent in the house they lease? Economists have provided partial answers to this question in a literature that spans the least forty years. Unfortunately, these results were developed in a non-linear fashion, which obscures them to the non-specialist. Recently, computer scientists have developed an interest in this particular problem and have advanced from an algorithmic complexity perspective. Remarkably, an online application, (Goldman and Procaccia, 2014), has been deployed, gathering thousands of users around the world and sparking new questions about the optimal way to provide recommendations. With this new interest gaining traction in computer science, there is an evident need for a coherent development of the results in economics literature. This paper does so. In particular, we build connections among results that were seemingly unrelated and considerably simplify their development, fill in non-trivial gaps, and identify open questions. Our focus is on incentives issues, the area in which we believe economists have more to contribute in this discussion.
    Keywords: inequity aversion, general equilibrium
    JEL: C91 D63 C72
    Date: 2017–08–18
  15. By: Stefania Marcassa; Jérôme Pouyet; Thomas Trégouët (Université de Cergy-Pontoise, THEMA)
    Abstract: We use a unique dataset to analyze marriage and union patterns of European nobility from the 1500s to the 1800s. Our matching model predicts homophily in title, and that more stringent constraints on the dowries lead to a higher degree of homophily. Historical evidence supports both predictions: nobles tended to marry nobles with identical title; and, German marriages, whose dowry rules were more rigid, were characterized by a higher degree of homophiliy in titles than English marriages. Moreover, homophily in titles decreased over time for Germans, and remained constant for English nobles.
    Keywords: marriage, nobility, class, elite, history, assortative matching.
    JEL: C78 J12 J16 N34 Z1
    Date: 2017
  16. By: Chatelain, Jean-Bernard; Ralf, Kirsten
    Abstract: This algorithm extends Ljungqvist and Sargent (2012) algorithm of Stackelberg dynamic game to the case of dynamic stochastic general equilibrium models including exogenous forcing variables. It is based Anderson, Hansen, McGrattan, Sargent (1996) discounted augmented linear quadratic regulator. It adds an intermediate step in solving a Sylvester equation. Forward-looking variables are also optimally anchored on forcing variables. This simple algorithm calls for already programmed routines for Ricatti, Sylvester and Inverse matrix in Matlab and Scilab. A final step using a change of basis vector computes a vector auto regressive representation including Ramsey optimal policy rule function of lagged observable variables, when the exogenous forcing variables are not observable.
    Keywords: Ramsey optimal policy, Stackelberg dynamic game, algorithm, forcing variables, augmented linear quadratic regulator.
    JEL: C61 C62 C73 E47 E52 E61 E63
    Date: 2017–08–26

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