|
on Game Theory |
Issue of 2012‒01‒03
twenty-six papers chosen by Laszlo A. Koczy Hungarian Academy of Sciences and Obuda University |
By: | Barlo, Mehmet; Carmona, Guilherme |
Abstract: | In order to remedy the possible loss of strategic interaction in non-atomic games with a societal choice, this study proposes a refinement of Nash equilibrium, strategic equilibrium. Given a non-atomic game, its perturbed game is one in which every player believes that he alone has a small, but positive, impact on the societal choice; and a distribution is a strategic equilibrium if it is a limit point of a sequence of Nash equilibrium distributions of games in which each player's belief about his impact on the societal choice goes to zero. After proving the existence of strategic equilibria, we show that all of them must be Nash. Moreover, it is displayed that in many economic applications, the set of strategic equilibria coincides with that of Nash equilibria of large finite games. |
Keywords: | Strategic equilibrium; Games with a continuum of players; Equilibrium distributions |
JEL: | C72 |
Date: | 2011–12–13 |
URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:35549&r=gth |
By: | Kris De Jaegher; Robert van Rooij |
Abstract: | This paper combines a literature overview of existing literature in game-theoretic pragmatics, with new models that fill some voids in the literature. We start with an overview of signaling games with a conflict of interest between sender and receiver, and show that the literature on such games can be classified into models with direct, costly, noisy and imprecise signals. We then argue that this same subdivision can be used to classify signaling games with common interests, where we fill some voids in the literature. For each of the signaling games treated, we show how equilibrium- refinement arguments and evolutionary arguments can be interpreted in the light of pragmatic inference. |
Keywords: | Signaling games, pragmatics, equilibrium refinements, evolutionary game theory |
JEL: | D82 D83 |
Date: | 2011–12 |
URL: | http://d.repec.org/n?u=RePEc:use:tkiwps:1125&r=gth |
By: | Gonzalez-Alcon, C.; Borm, P.E.M.; Hendrickx, R.L.P. (Tilburg University, Center for Economic Research) |
Abstract: | This paper introduces the class of 2 × 2 × 2 trimatrix games with identical anonymous best-replies. For this class a complete classification on the basis of the Nash equilibrium set is provided. |
Keywords: | trimatrix games;Nash equilibrium;best-reply correspondences;symmetric games. |
JEL: | C72 |
Date: | 2011 |
URL: | http://d.repec.org/n?u=RePEc:dgr:kubcen:2011138&r=gth |
By: | A.W. Beggs |
Abstract: | This paper defines regular and weakly regular equilibria for monotone Bayesian games with one-dimensional actions and types. It proves an index theorem and provides applications to uniqueness of equilibrium. It also provides analyses of stability with respect to perturbations and dynamic stability. |
Keywords: | Bayesian games, Monotone strategies, Index theory, Stability, Uniqueness, Regularity |
JEL: | C72 D83 |
Date: | 2011 |
URL: | http://d.repec.org/n?u=RePEc:oxf:wpaper:587&r=gth |
By: | Giuseppe Russo (University of Salerno and CSEF) |
Abstract: | Decisions on joint funding of continuous public goods between two agents often involve heterogeneous targets. We introduce loss functions in a contribution game in order to study the effect of this conflict. Unlike Varian (1994), joint contribution occurs only if the players’ targets are sufficiently close and the sequential game reduces free riding problems, while total contribution is higher in the simultaneous game. |
Keywords: | Public Goods, Intergovernmental Relations |
JEL: | H41 H77 |
Date: | 2011–12–20 |
URL: | http://d.repec.org/n?u=RePEc:sef:csefwp:302&r=gth |
By: | Berninghaus, Siegfried K.; Todorova, Lora; Vogt, Bodo |
Abstract: | This paper presents results from an experiment designed to study the effect of self reporting risk preferences on strategy choices made in a subsequently played 2x2 coordination game. The main finding is that the act of answering a questionnaire about one's own risk preferences significantly alters strategic behavior. 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 induces an increase in subjects' risk aversion while keeping their beliefs unchanged. Our findings raise some questions about the stability of strategy choices in coordination games. -- |
Keywords: | coordination game,questionnaire,risk preferences,beliefs,best response correspondence |
JEL: | D81 C91 C72 |
Date: | 2011 |
URL: | http://d.repec.org/n?u=RePEc:zbw:kitwps:37&r=gth |
By: | 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: | The core of a cooperative game on a set of players $N$ is one of the most popular concepts of solution. When cooperation is restricted (feasible coalitions form a subcollection $\cF$ of $2^N$), the core may become unbounded, which makes its usage questionable in practice. Our proposal is to make the core bounded by turning some of the inequalities defining the core into equalities (additional efficiency constraints). We address the following mathematical problem: can we find a minimal set of inequalities in the core such that, if turned into equalities, the core becomes bounded? The new core obtained is called the restricted core. We completely solve the question when $\cF$ is a distributive lattice, introducing also the notion of restricted Weber set. We show that the case of regular set systems amounts more or less to the case of distributive lattices. We also study the case of weakly union-closed systems and give some results for the general case. |
Date: | 2011 |
URL: | http://d.repec.org/n?u=RePEc:hal:cesptp:hal-00650964&r=gth |
By: | Matthias Kräkel |
Abstract: | Participants of dynamic competition games may prefer to play with the rules of the game by systematically withholding e¤ort in the beginning. Such behavior is referred to as sandbagging. I consider a two-period con- test between heterogeneous players and analyze potential sandbagging of high-ability participants in the first period. Such sandbagging can be ben- eficial to avoid second-period matches against other high-ability opponents. I characterize the conditions under which sandbagging leads to a coordina- tion problem, similar to that of the battle-of-the sexes game. Moreover, if players' abilities have a stronger impact on the outcome of the first-period contest than e¤ort choices, mutual sandbagging by all high-ability players can arise. |
Keywords: | ecoordination problem, dynamic contest, heterogeneous contestants, withholding e¤ort |
JEL: | C72 D72 |
Date: | 2011–11 |
URL: | http://d.repec.org/n?u=RePEc:bon:bonedp:bgse12_2012&r=gth |
By: | Katerina Sherstyuk (Department of Economics, University of Hawaii at Manoa); Nori Tarui (Department of Economics, University of Hawaii at Manoa); Tatsuyoshi Saijo (Department of Economics, Osaka University) |
Abstract: | We consider payment schemes in experiments that model innite-horizon games by using random termination. We compare paying subjects cumulatively for all periods of the game; with paying subjects for the last period only; with paying for one of the periods, chosen randomly. Theoretically, assuming expected utility maximization and risk neutrality, both the Cumulative and the Last period payment schemes induce preferences that are equivalent to maximizing the discounted sum of utilities. The Last-period payment is also robust under dierent attitudes towards risk. In comparison, paying subjects for one of the periods chosen randomly creates a present period bias. We further provide experimental evidence from innitely repeated Prisoners' Dilemma games that supports the above theoretical predictions. |
Keywords: | economic experiments, infinite-horizon games, random termination |
JEL: | C90 C73 |
Date: | 2011–12–01 |
URL: | http://d.repec.org/n?u=RePEc:hai:wpaper:201118&r=gth |
By: | Bonanno, Giacomo (University of CA, Davis) |
Abstract: | We discuss a number of conceptual issues that arise in attempting to capture, in dynamic games, the notion that there is "common understanding" among the players that they are all rational. |
Date: | 2011–11 |
URL: | http://d.repec.org/n?u=RePEc:ecl:ucdeco:11-11&r=gth |
By: | Pierpaolo Battigalli; Simone Cerreia-Vioglio; Fabio Maccheroni; Massimo Marinacci |
Abstract: | We propose to bring together two conceptually complementary ideas: (1) selfconfi?rming equilibrium (SCE): at a rest point of learning dynamics in a game played recurrently, agents best respond to confi?rmed beliefs, i.e. beliefs consistent with the evidence they accumulate, and (2) ambiguity aversion: agents, coeteris paribus, prefer to bet on events with known rather than unknown probabilities, more generally, agents distinguish objective from subjective uncertainty, which is captured by their ambiguity attitudes. Using as a workhorse the ?smooth ambiguity model of Klibanoff, Marinacci and Mukerji (2005), we provide a de?nition of "smooth SCE" which generalizes the traditional concept of Fudenberg and Levine (1993a,b), called Bayesian SCE, and admits Waldean (maxmin) SCE as a limit case. We show that the set of equilibria expands as ambiguity aversion increases. The intuition is simple: by playing the same "status-quo" strategy in a stable state an agent learns the implied objective probabilities of payoffs, but alternative strategies yield payoffs with unknown probabilities; keeping beliefs ?fixed, increased aversion to ambiguity makes such strategies less appealing. We rely on this core intuition to show that different notions of equilibrium are nested in a simple way, from ?ner to coarser: Nash, Bayesian SCE, Smooth SCE and Waldean SCE. We also prove some equivalence results, under special assumptions about the information structure. |
Date: | 2011 |
URL: | http://d.repec.org/n?u=RePEc:igi:igierp:428&r=gth |
By: | Flesch J.; Kuipers J.; Schoenmakers G.; Vrieze K. (METEOR) |
Abstract: | We prove the existence of a subgame-perfect epsilon-equilibrium, for every epsilon> 0, in a classof multi-player games with perfect information, which we call free transition games. The noveltyis that a non-trivial class of perfect information games is solved for subgame-perfection, withmultiple non-terminating actions, in which the payoff structure is generally not semi-continuous.Due to the lack of semi-continuity, there is no general rule of comparison between the payoffsthat a player can obtain by deviating a large but finite number of times or, respectively,infinitely many times. We introduce new techniques to overcome this difficulty. Our constructionrelies on an iterative scheme which is independent of epsilon and terminates in polynomial timewith the following output: for all possible histories h, a pure action a(1,h) or in some cases twopure actions a(2,h) and b(2,h) for the active player at h. The subgame-perfect epsilon-equilibriumthen prescribes for every history h that the active player plays a(1,h) with probability 1 orrespectively plays a(2,h) with probability 1-delta and b(2,h) with probability delta. Here, deltais arbitrary as long as it is positive and small compared to epsilon, so the strategies can bemade “almost” pure. |
Keywords: | mathematical economics; |
Date: | 2011 |
URL: | http://d.repec.org/n?u=RePEc:dgr:umamet:2011047&r=gth |
By: | Luigi Luini; Annmaria Nese; Patrizia Sbriglia |
Abstract: | Economists have often analysed the impact that the spread of beliefs and behaviors have on the equilibrium and performance of markets. Recent experimental studies on peer pressure in groups of agents interacting in investment and gift exchange games (Mittone and Ploner, 2011, Gachter et al. 2010) have proved that the imitation of partners’ behaviors can have substantial effects on reciprocity, thus confirming that the effects of information also need to be studied in games where social preferences play a fundamental role. The aim of this paper is to ascertain whether trust is affected by contagion and herding in small groups of trustors who can observe each other’s choices over time. We account for three important factors of trustors’ preferences,namely: risk attitude, generosity and expected trustworthiness. Using our data we test the basic hypothesis that an individual's propensity to trust recipients in the Trust Game can be affected by the observed behavior of other trustors. Our results confirm that trust is affected by contagion effects. Furthermore, we find that specific types of agents (generous or untrusting) more often imitate the same type, when positioned in the same group. Finally, we find that untrusting individuals are less affected by their peers compared to generous individuals, and they imitate less even when positioned in groups of agents who have the same characteristics. |
Keywords: | trust game, experiments, social influence, imitation |
JEL: | C72 C91 |
Date: | 2011–11 |
URL: | http://d.repec.org/n?u=RePEc:usi:wpaper:626&r=gth |
By: | Serra Garcia, M.; Damme, E.E.C. van; Potters, J.J.M. (Tilburg University, Center for Economic Research) |
Abstract: | We compare communication about private information to communication about actions in a one- shot 2-person public good game with private information. The informed player, who knows the exact return from contributing and whose contribution is unobserved, can send a message about the return or her contribution. Theoretically, messages can elicit the uninformed player's contribution, and allow the informed player to free-ride. The exact language used is not expected to matter. Experimentally, however, we find that free-riding depends on the language: the informed player free-rides less, and thereby lies less frequently, when she talks about her contribution than when she talks about the return. Further experimental evidence indicates that it is the promise component in messages about the contribution that leads to less free-riding and less lying. |
Keywords: | Information transmission;lying;communication;experiment. |
JEL: | C72 D82 D83 |
Date: | 2011 |
URL: | http://d.repec.org/n?u=RePEc:dgr:kubcen:2011139&r=gth |
By: | Fabrice Valognes (CREM - Centre de Recherche en Economie et Management - CNRS : UMR6211 - Université de Rennes 1 - Université de Caen); Hélène Ferrer (CREM - Centre de Recherche en Economie et Management - CNRS : UMR6211 - Université de Rennes 1 - Université de Caen); Guillermo Owen (Department of Applied Mathematics - Naval Postgraduate School) |
Abstract: | The purpose of this paper is to examine the incentive of a player to join a syndicate in an environment of team production and payoff distribution according to Shapley value. We consider an economy in which a single output is produced by an increasing returns to scale production function using two inputs: labor and capital. By assuming that syndicates of factor owners can form, we are interested in their stability, i.e., the willingness of the members of the syndicate to stay in the syndicate. Our analysis, based on the Shapley value, allows us to find a fair imputation of the gains of cooperation and the conditions under which syndicates are stable. |
Keywords: | Shapley Value; Syndicate; Coalition formation; Increasing return to scale. |
Date: | 2011–12–15 |
URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:halshs-00651185&r=gth |
By: | Wolfgang Buchholz; Josef Falkinger; Dirk Rübbelke |
Abstract: | In small groups, norm enforcement is achieved through mutual punishment and reward. In large societies, norms are enforced by specialists such as government officials. However, not every public cause is overseen by states, for instance those organized at the international level. This paper shows how non-governmental norm enforcement can emerge as a decentralized equilibrium. As a first stage, individuals voluntarily contribute to a non-governmental agency that produces an incentive system. The second stage is the provision of a public good on the basis of private contributions. The incentive system punishes and rewards deviations from the norm for contributions by means of public approval or disapproval of behavior. It is shown that, even in large populations, nongovernmental norm enforcement can be supported in a non-cooperative equilibrium of utility-maximizing individuals. |
JEL: | H41 K40 Z13 |
Date: | 2011–12 |
URL: | http://d.repec.org/n?u=RePEc:acb:cbeeco:2011-566&r=gth |
By: | Urs Fischbacher (Department of Economics, University of Konstanz, Konstanz, Germany; Thurgau Institute of Economics, Kreuzlingen, Switzerland); Werner Güth (Max Planck Institute of Economics, Strategic Interaction Group); M. Vittoria Levati (Max Planck Institute of Economics, Strategic Interaction Group; Department of Economics, University of Verona) |
Abstract: | Participants in a public goods experiment receive private or common signals regarding the so-called "point of no return", meaning that if the group's total contribution falls below this point, all payoffs are reduced. An individual faces the usual conflict between private and collective interests above the point of no return, while he incurs the risk of damaging everyone by not surpassing the point. Our data reveal that contributions are higher if the cost of not reaching the threshold is high. In particular if the signal is private, many subjects are not willing to provide the necessary contribution. |
Keywords: | Public goods, provision point mechanism, experiments, reduction factor, signal |
JEL: | H41 C92 C72 |
Date: | 2011–12–16 |
URL: | http://d.repec.org/n?u=RePEc:jrp:jrpwrp:2011-059&r=gth |
By: | Heinrich H. Nax; Thomas W.L. Norman |
Abstract: | The World’s nations have yet to reach a truly effective treaty to control the emission of greenhouse gases. The importance of compatibility with private incentives of individual countries has been acknowledged (at least by game theorists) in designing climate policies for the post-Kyoto world. Individually incentive-compatible agreements, however, may still be spoilt if coalitional incentives to deviate as a group exist. As a first step toward understanding these incentives from a game-theoretic perspective, we propose a hybrid noncooperative-cooperative game theory model of coalition formation in technology collaboration. Serious coalitional instabilities inherent to the existing climate policy architectures are revealed. It turns out that coalitionally stable agreements are achieved via intermediate self-selecting subcoalitions. The sequence of coalitions forming and the size of the direct and spillover effects of R&D collaboration on countries’ individual production technologies determine the effectiveness of the agreements to reduce carbon emissions. These coalitional group motives are already becoming important in the practice of climate change negotiations. |
Keywords: | Climate change policy, Coalitions, Cooperative game theory, Environmental agreements, Externalities, Mechanism design, Noncooperative game theory, R&D |
JEL: | C71 C73 D62 D86 F53 H87 Q54 |
Date: | 2011 |
URL: | http://d.repec.org/n?u=RePEc:oxf:wpaper:585&r=gth |
By: | Matthew O. Jackson (Department of Economics, Stanford University, Santa Fe Institute, and CIFAR); Dunia López Pintado (Department of Economics, Universidad Pablo de Olavide) |
Abstract: | We study how a behavior (an idea, buying a product, having a disease, adopting a cultural fad or a technology) spreads among agents in an a social network that exhibits segregation or homophily (the tendency of agents to associate with others similar to themselves). Individuals are distinguished by their types (e.g., race, gender, age, wealth, religion, profession, etc.) which, together with biased interaction patterns, induce heterogeneous rates of adoption. We identify the conditions under which a behavior diffuses and becomes persistent in the population. These conditions relate to the level of homophily in a society, the underlying proclivities of various types for adoption or infection, as well as how each type interacts with its own type. In particular, we show that homophily can facilitate diffusion from a small initial seed of adopters. |
Keywords: | Diffusion, Homophily, Segregation, Social Networks |
JEL: | D85 D83 C70 C73 L15 C45 |
Date: | 2011–12 |
URL: | http://d.repec.org/n?u=RePEc:pab:wpaper:11.14&r=gth |
By: | Cabrales, Antonio; Charness, Gary |
Abstract: | We devise an experiment to explore optimal contracts in a hidden-information context. A principal offers one of three possible contract menus to a team of two agents of unknown skill levels, with both agents’ participation needed for production. We observe numerous rejections of the more lopsided menus, and principals respond by offering more favorable menus. Apart from rejections,wesee almost complete separation in agent choices according to the agent types. Behavior converges towards a consensus in which one of the more equitable menus is proposed and agents accept a contract. The consensus menu differs across two treatments in which we vary the payoffs resulting from a rejection. We find strong evidence of social learning by low-skill agents (but only for low-skilled agents), in that a low-skill agent is more likely to reject a contract menu if her teammate rejected a contract menu in the previous period. In addition, low-skilled agents have a particularly adverse reaction to reduced wage offers. |
Keywords: | Experiment; Hidden information; Optimal contract; Production team; Wage rigidity; |
JEL: | A13 B49 C91 C92 D21 J41 |
Date: | 2011 |
URL: | http://d.repec.org/n?u=RePEc:ner:carlos:info:hdl:10016/12809&r=gth |
By: | Tan, Fangfang; Xiao, Erte |
Abstract: | This paper investigates how punishment promotes cooperation when the punishment enforcer is a third party independent of the implicated parties who propose the punishment. In a prisoner's dilemma experiment, we find an independent third party vetoes not only punishment to the cooperators but punishment to the defectors as well. Compared with the case when the implicated parties are allowed to punish each other, both the cooperation rate and the earnings are lower when the enforcement of punishment requires approval from an independent third party. |
Keywords: | Social dilemmas; third party; punishment; cooperation; experiment |
JEL: | D63 C92 C72 |
Date: | 2011–12–21 |
URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:35473&r=gth |
By: | Jeroen Hinloopen; Wieland Müller; Hans-Theo Normann |
Abstract: | We analyze the impact of product bundling in experimental markets. A firm has monopoly power in one market but faces competition by a second firm in another market. We compare treatments where the monopolist can bundle its two products to treatments where it cannot, and we contrast simultaneous and sequential order of moves. Our data indicate support for the theory of product bundling, even though substantial payoff differences between players exist. With bundling and simultaneous moves, the monopolist offers the predicted number of units. When the monopolist is the Stackelberg leader, the predicted equilibrium is better attained with bundling although in theory bundling should not make a difference here. In sum: bundling works as a commitment device that enables the transfer of market power from one market to another. |
JEL: | C92 D43 L11 L12 L41 |
Date: | 2011–12 |
URL: | http://d.repec.org/n?u=RePEc:vie:viennp:1112&r=gth |
By: | Bigoni, Maria (University of Bologna); Casari, Marco (University of Bologna); Skrzypacz, Andrzej (Stanford University); Spagnolo, Giancarlo (University of Rome "Tor Vergata" and Stockholm School of Economics) |
Abstract: | When subjects interact in continuous time, their ability to cooperate may dramatically increase. In an experiment, we study the impact of different time horizons on cooperation in (quasi) continuous time prisoner's dilemmas. We find that cooperation levels are similar or higher when the horizon is deterministic rather than stochastic. Moreover, a deterministic duration generates different aggregate patterns and individual strategies than a stochastic one. For instance, under a deterministic horizon subjects show high initial cooperation and a strong end-of-period reversal to defection. Moreover, they do not learn to apply backward induction but to postpone defection closer to the end. |
JEL: | C72 C73 C91 C92 D74 |
Date: | 2011–11 |
URL: | http://d.repec.org/n?u=RePEc:ecl:stabus:2088&r=gth |
By: | Juan D. Moreno-Ternero (Department of Economics, Universidad Pablo de Olavide; CORE, Université catholique de Louvain); John E. Roemer (Department of Political Science, Yale University) |
Abstract: | Resource egalitarianism and welfare egalitarianism are two focal conceptions of distributive justice. We show in this paper that they share a solid common ground. To do so, we analyze a simple model of resource allocation in which agents’ abilities (to transform the resource into an interpersonally comparable outcome) and starting points may differ. Both conceptions of egalitarianism are naturally modeled in this context as two allocation rules. The two rules are jointly characterized by the combination of three appealing axioms: priority, solidarity, and composition. |
Keywords: | Team production, budget constraints, efficiency, manipulability, impartiality; resource allocation, egalitarianism, welfare, priority, solidarity, composition |
JEL: | C70 D23 D78 D63 |
Date: | 2011–12 |
URL: | http://d.repec.org/n?u=RePEc:pab:wpaper:11.12&r=gth |
By: | Stolper, Anno |
Abstract: | It is often argued that certifiers have an incentive to offer inflated certificates, although they deny it. In this paper, we study a model in which a certifier is paid by sellers, and may offer them inflated certificates, but incurs costs if doing so. We find that the certifier may face a commitment problem: The certifier offers inflated certificates if the costs of offering the first inflated certificate are lower than the sellers' willingness-to-pay for it. However, in equilibrium, the buyers cannot be fooled. The certifier would hence make a higher profit if the certifier did not offer inflated certificates and the buyers believed it. The number of inflated certificates, which the certifier offers in equilibrium, depends on the costs of offering inflated certificates. Yet, the certifier may oppose an increase in the costs of offering inflated certificates. We show that whether a certifier welcomes tighter regulation or lobbies against it, may depend on whether the new regulation only imposes higher costs, or also reduces the certifier's commitment problem significantly. |
Keywords: | Certification; commitment problem; credibility |
JEL: | C72 D82 G24 L15 M42 |
Date: | 2011–12 |
URL: | http://d.repec.org/n?u=RePEc:lmu:muenec:12523&r=gth |
By: | Roman Horváth (IES, Charles University Prague); Kateøina Šmídková (IES, Charles University Prague); Jan Zápal (London School of Economics) |
Abstract: | We assess whether the voting records of central bank boards are informative about future monetary policy. First, we specify a theoretical model of central bank board decision-making and simulate the voting outcomes. Three different versions of model are estimated with simulated data: 1) democratic, 2) consensual and 3) opportunistic. These versions differ in the degree of informational influence between the chairman and other board members influence prior to the voting. The model shows that the voting pattern is informative about future monetary policy provided that the signals about the optimal policy rate are noisy and that there is sufficient independence in voting across the board members, which is in line with the democratic version. Next, the model predictions are tested on real data on five inflation targeting countries (the Czech Republic, Hungary, Poland, Sweden and the United Kingdom). Subject to various sensitivity tests, it is found that the democratic version of the model corresponds best to the real data and that in all countries the voting records are informative about future monetary policy, making a case for publishing the records. |
Keywords: | monetary policy, voting record, transparency, collective decision-making. |
JEL: | C78 D78 E52 E58 |
Date: | 2011–12 |
URL: | http://d.repec.org/n?u=RePEc:fau:wpaper:wp2011_37&r=gth |