nep-gth New Economics Papers
on Game Theory
Issue of 2020‒11‒16
eighteen papers chosen by
Sylvain Béal
Université de Franche-Comté

  1. Ising Model for Asymmetric Games on Networks By A. D. Correia; L. L. Leestmaker; H. T. C. Stoof
  2. Open Rule Legislative Bargaining By Volker Britz; Hans Gersbach
  3. Naive analytics equilibrium By Ron Berman; Yuval Heller
  4. A Notion of Prominence for Games with Natural-Language Labels By Alessandro Sontuoso; Sudeep Bhatia
  5. The Evolution of Status Preferences in Anti-Coordination Games By Manuel Staab
  6. Probabilistic Approach to Mean Field Games and Mean Field Type Control Problems with Multiple Populations By Masaaki Fujii
  7. Renewable resource use with imperfect self-control By Strulik, Holger; Werner, Katharina
  8. Per Unit and Ad Valorem Royalties in a Patent Licensing Game By Montinaro, Marta; Pal, Rupayan; Scrimitore, Marcella
  9. Agenda-Setter Power Dynamics: Learning in Multi-Issue Bargaining By Renee Bowen; Ilwoo Hwang; Stefan Krasa
  10. Are women less effective leaders than men? Evidence from experiments using coordination games By Heursen, Lea; Ranehill, Eva; Weber, Roberto A
  11. A new order on embedded coalitions: Properties and applications By José Mª Alonso-Meijide; Mikel Álvarez-Mozos; Mª Gloria Fiestras-Janeiro; Andrés Jiménez-Losada
  12. Pricing, competition and content for internet service providers By Key, Peter; Steinberg, Richard
  13. Managerial Leadership, Truth-Telling and Efficient Coordination By Jordi Brandts; David J. Cooper
  14. Voluntary contributions in cascades: The tragedy of ill-informed leadership By Béatrice Boulu-Reshef; Nina Rapoport
  15. Epistemological Mechanism Design (Revised version of CARF-F-496) By Hitoshi Matsushima; Shunya Noda
  16. Optimal evacuation-decisions facing the trade-off between early-warning precision, evacuation-cost and trust - the Warning Compliance Model (WCM) By Wiens, Marcus; Mahdavian, Farnaz; Platt, Stephen; Schultmann, Frank
  17. Reinterpreting the General Rules of Morality and the Corruption of Moral Sentiments in The Theory of Moral Sentiments with an Evolutionary Game Model By Takahiko Kan
  18. Who’ll stop lying under oath? Empirical evidence from tax evasion games By Nicolas Jacquemet; Stephane Luchini; A. Malézieux; Jason F. Shogren

  1. By: A. D. Correia; L. L. Leestmaker; H. T. C. Stoof
    Abstract: We here study the Battle of the Sexes game on small networks, extending the response strategy analysis to asymmetric games and three players. We model the different steady states, that are obtained in numerical simulations from the various update strategies, as different response strategy equilibria. These are then mapped to a generalized Ising model, describing the correlations between the players' outcomes in a way that is agnostic to the existence of a link, but that coincides with the correlation device if there is one. Going to three players, we look at and compare the equilibrium solutions for three representative types of networks. We find that players that are not directly connected retain a degree of correlation that is proportional to their initial correlation. We also find that the local network structure is the most relevant for small values of the magnetic field and the interaction strength of the Ising model. This research paves the way to a statistical physics description of games on networks that is scale sensitive and has the potential to give an analytical description of both long- and short-range behavior observed in numerical simulations.
    Date: 2020–11
  2. By: Volker Britz (CER–ETH – Center of Economic Research at ETH Zurich, Zurichbergstrasse 18, 8092 Zurich, Switzerland); Hans Gersbach (CER–ETH – Center of Economic Research at ETH Zurich, Zurichbergstrasse 18, 8092 Zurich, Switzerland)
    Abstract: We consider non–cooperative bargaining on the division of a surplus under simple majority rule. We use the “open rule” bargaining protocol as originally suggested by Baron and Ferejohn (1989): Proposals can be amended before they are voted on. It is widely known that there are significant gaps in our understanding of open rule bargaining. In order to address these gaps, we provide a fresh analysis of a particularly simple class of equilibria. Our results shed new light on the efficiency and fairness implications of using an open vs. closed rule in bargaining. In particular, our results on the open rule model suggest that equilibrium delays tend to be longer, and surplus allocations tend to be less egalitarian than originally predicted by Baron and Ferejohn. Understanding the efficiency and fairness properties of different bargaining protocols is crucial for institutional design.
    Keywords: Bargaining, Legislatures, Open Rules, Baron and Ferejohn, Stationary Equilibrium
    JEL: C72 C78 D72
    Date: 2020–11
  3. By: Ron Berman; Yuval Heller
    Abstract: We study interactions with uncertainty about demand sensitivity. In our solution concept (1) firms choose seemingly-optimal strategies given the level of sophistication of their data analytics, and (2) the levels of sophistication form best responses to one another. Under the ensuing equilibrium firms underestimate price elasticities and overestimate advertising effectiveness, as observed empirically. The misestimates cause firms to set prices too high and to over-advertise. In games with strategic complements (substitutes), profits Pareto dominate (are dominated by) those of the Nash equilibrium. Applying the model to team production games explains the prevalence of overconfidence among entrepreneurs and salespeople.
    Date: 2020–10
  4. By: Alessandro Sontuoso (Smith Institute for Political Economy and Philosophy, Chapman University; Philosophy, Politics and Economics, University of Pennsylvania); Sudeep Bhatia (Department of Psychology, University of Pennsylvania)
    Abstract: We study games with natural-language labels (i.e., strategic problems where options are denoted by words), for which we propose and test a measurable characterization of prominence. We assume that – ceteris paribus – players find particularly prominent those strategies that are denoted by words more frequently used in their everyday language. To operationalize this assumption, we suggest that the prominence of a strategy-label is correlated with its frequency of occurrence in large text corpora, such as the Google Books corpus (“n-gram†frequency). In testing for the strategic use of word frequency, we consider experimental games with different incentive structures (such as incentives to and not to coordinate), as well as subjects from different cultural/linguistic backgrounds. Our data show that frequently-mentioned labels are more (less) likely to be selected when there are incentives to match (mismatch) others. Furthermore, varying one’s knowledge of the others’ country of residence significantly affects one’s reliance on word frequency. Overall, the data show that individuals play strategies that fulfill our characterization of prominence in a (boundedly) rational manner.
    Keywords: focal points; salience; coordination; hide-and-seek; culture; language; level-k
    JEL: C72 C91
    Date: 2020
  5. By: Manuel Staab
    Abstract: This paper analyses how risk-taking behavior and preferences over consumption rank can emerge as an evolutionary stable equilibrium when agents face an anti-coordination task. If in an otherwise homogeneous society information about relative consumption is available, this cannot be ignored. Despite concavity in the objective function, agents are willing to accept risky gambles to differentiate themselves and thus allow for coordination. This suggests status preferences to be salient in settings where miscoordination is particularly costly.
    Date: 2020–11
  6. By: Masaaki Fujii (Quantitative Finance Course, Graduate School of Economics, The University of Tokyo)
    Abstract: In this work, we systematically investigate mean field games and mean field type control problems with multiple populations. We study the mean field limits of the three different situa- tions; (i) every agent is non-cooperative; (ii) the agents within each population are cooperative; and (iii) the agents in some populations are cooperative. We provide several sets of sufficient conditions for the existence of a mean field equilibrium for each case. We also show that, un- der appropriate conditions, each mean field solution actually provides an approximate Nash equilibrium for the corresponding game with a large but finite number of agents.
    Date: 2020–11
  7. By: Strulik, Holger; Werner, Katharina
    Abstract: We investigate renewable resources when the harvesting agents face self-control problems. Individuals are conceptualized as dual selves. The rational long-run self plans for the infinite future while the affective short-run self desires to maximize instantaneous profits. Depending on the degree of self-control, actual behavior is partly driven by short-run desires. This modeling represents impatience and present bias without causing time inconsistent decision making. In a model of a single harvesting agent (e.g. a fishery), we discuss how self-control problems affect harvesting behavior, resource conservation, and sustainability and discuss policies to curb overuse and potential collapse of the resource due to present-biased harvesting behavior. We then extend the model to several harvesting agents and show how limited self-control exacerbates the common pool problem. Finally, we investigate heterogenous agents and show that there are spillover effects of limited self-control in the sense that perfectly rational agents also behave less conservatively when they interact with agents afflicted by imperfect self-control.
    Keywords: self-control,temptation,renewable resource use,sustainability,common pool resource management
    JEL: D60 D90 Q20 Q50 Q58 O40
    Date: 2020
  8. By: Montinaro, Marta; Pal, Rupayan; Scrimitore, Marcella
    Abstract: In a context of product innovation, we study two-part tariff licensing between a patentee and a potential rival which compete in a differentiated product market characterized by network externalities. The latter are shown to crucially affect the relative profitability of Cournot vs. Bertrand when a per unit royalty is applied. By contrast, we find that Cournot yields higher profits than Bertrand under ad valorem royalties, regardless of the strength of network effects.
    Keywords: Production Economics
    Date: 2020–11–05
  9. By: Renee Bowen; Ilwoo Hwang; Stefan Krasa
    Abstract: We study a dynamic bargaining model between a fixed agenda-setter and responder over successive issues. If the responder rejects the setter’s proposal, the setter can attempt to assert her will to implement her ideal and will succeed with a probability that depends on her “personal power”. The players learn about the setter’s power as gridlock persists. Gridlock occurs when the setter’s perceived power is either too high or too low, and the players reach compromise in an intermediate interval of beliefs. The presence of “difficult” issues can induce more compromise as the players have incentives to avoid learning.
    JEL: C78 D72 D74 D83
    Date: 2020–10
  10. By: Heursen, Lea (Department of Economics, Humboldt University Berlin); Ranehill, Eva (Department of Economics, School of Business, Economics and Law, Göteborg University); Weber, Roberto A (Department of Economics, University of Zurich)
    Abstract: We study whether one reason behind female underrepresentation in leadership is that female leaders are less effective at coordinating action by followers. Two experiments using coordination games investigate whether female leaders are less successful than males in persuading followers to coordinate on efficient equilibria. Group performance hinges on higher-order beliefs about the leader’s capacity to convince followers to pursue desired actions, making beliefs that women are less effective leaders potentially self-confirming. We find no evidence that such bias impacts actual leadership performance, identifying a precisely-estimated null effect. We show that this absence of an effect is surprising given experts’ priors.
    Keywords: gender; coordination games; leadership; experiment
    JEL: C72 C92 D23 J10
    Date: 2020–11
  11. By: José Mª Alonso-Meijide (Universidade de Santiago de Compostela); Mikel Álvarez-Mozos (Universitat de Barcelona); Mª Gloria Fiestras-Janeiro (Universidade de Vigo); Andrés Jiménez-Losada (Universidad de Sevilla)
    Abstract: Given a finite set of agents, an embedded coalition consists of a coalition and a partition of the rest of agents. We study a partial order on the set of embedded coalitions of a finite set of agents. An embedded coalition precedes another one if the first coalition is contained in the second and the second partition equals the first one after removing the agents in the second coalition. This poset is not a lattice. We describe the maximal lower bounds and minimal upper bounds of a finite subset, whenever they exist. It is a graded poset and we are able to count the number of elements at a given level as well as the total number of chains. The study of this structure allows us to derive results for games with externalities. In particular, we introduce a new concept of convexity and show that it is equivalent to having non-decreasing contributions to embedded coalitions of increasing size.
    Keywords: Partial order, Embedded coalition, Partition function, Convexity.
    JEL: C71
    Date: 2019
  12. By: Key, Peter; Steinberg, Richard
    Abstract: We examine competition between two Internet Service Providers (ISPs), where the first ISP provides basic Internet service, while the second ISP provides Internet service plus content, i.e., enhanced service , where the first ISP can partner with a Content Provider to provide the same content as the second ISP. When such a partnering arrangement occurs, the Content Provider pays the first ISP a transfer price for delivering the content. Users have heterogeneous preferences, and each in general faces three options: (1) buy basic Internet service from the first ISP; (2) buy enhanced service from the second ISP; or (3) buy enhanced service jointly from the first ISP and the Content Provider. We derive results on the existence and uniqueness of a Nash equilibrium, and provide closed-form expressions for the prices, user masses, and profits of the two ISPs and the Content Provider. When the first ISP has the ability to choose the transfer price, then when congestion is linear in the load, it is never optimal for the first ISP to set a negative transfer price in the hope of attracting more revenue from additional customers desiring enhanced service. Conversely, when congestion is sufficiently super-linear, the optimal strategy for the first ISP is either to set a negative transfer price (subsidizing the Content Provider) or to set a high transfer price that shuts the Content Provider out of the market.
    Keywords: communication networks; competition; content provider; optimal pricing; Nash equilibrium; profit
    JEL: R14 J01
    Date: 2020–10–01
  13. By: Jordi Brandts; David J. Cooper
    Abstract: We study the tradeoffs between managerial control and delegation using a new experimental game, the manager-subordinate game. Actions for two subordinates are either chosen independently by the subordinates (delegation) or imposed by a manager (managerial control). The manager-subordinate game combines four properties: (1) All parties benefit if the subordinates coordinate their actions. (2) The state of the world varies, changing which outcome is efficient. (3) Subordinates have differing preferences over which common course of action should be chosen. (4) Subordinates know the state of the world, but the manager does not. Efficient coordination requires coordinating subordinates’ action and utilizing their private information. We find that total efficiency is highest with a combination of managerial control and free-form chat between the three players. This combination works because subordinates rarely lie about their private information, making efficient coordination possible. The frequency of truth-telling contrasts with findings from the experimental literature on lying.
    Keywords: Coordination, experiments, Organizations, communication, truth-telling
    JEL: C92 D23 L20
    Date: 2020–10
  14. By: Béatrice Boulu-Reshef (LEO - Laboratoire d'Économie d'Orleans - UO - Université d'Orléans - Université de Tours - CNRS - Centre National de la Recherche Scientifique); Nina Rapoport (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, UP1 - Université Panthéon-Sorbonne, PSE - Paris School of Economics)
    Abstract: Voluntary contributions are often solicited in sequential and public settings where information on the quality of the fundraising project unfolds with the sequence of decisions. This paper examines how the different sources of information available to potential donors in such settings influence their decision-making. Contrary to most of the leadership literature, neither leaders nor followers in these settings have certainty about the quality of the fundraising project. We explore whether leaders remain influential, the extent to which they use their influence strategically, and the consequences on followers when leaders are misinformed. We combine an information cascade method with a modified public goods game to create a "Voluntary Contributions in Cascades" paradigm. Participants sequentially receive private signals about the state of the world, which determines the potential returns from the public good, and take two public actions: an incentivized prediction about the state of the world and a contribution to the public good. We find that participants' predictions mostly align with Bayesian predictions, and find no evidence for strategic or misleading predictions. Leaders' contributions are positively correlated with followers', suggesting they remain influential despite their limited informational advantage. This influence takes a tragic turn when leaders happen to be misinformed, as most misinformed leaders end up unintentionally misleading followers. We find that having a misleading leader is associated with a reduction in gains from contributions roughly twice as large as the reduction that stems from dividing the marginal-per-capita-return by two. Our results stress the significance of having well-informed leaders.
    Keywords: voluntary contribution,information cascade,fundraising,sequential public good game,leadership
    Date: 2020–10
  15. By: Hitoshi Matsushima (University of Tokyo); Shunya Noda (University of British Columbia)
    Abstract: This study demonstrates a new approach to mechanism design from an epistemological perspective. We introduce an epistemological type space in which agents are either selfish or honest, and show that a slight possibility of honesty in higher-order beliefs motivates all selfish agents to behave sincerely. Specifically, we consider a situation in which a central planner attempts to elicit correct information from informed agents through mutual monitoring. We assume severe restrictions on incentive device availability: neither public monitoring nor allocation rules are available. Thus, the central planner uses only monetary payment rules. If “all agents are selfish†is common knowledge, eliciting correct information as unique equilibrium behavior is generally impossible. However, we show a very permissive result in our epistemological model by designing a quadratic scoring rule as the monetary payment rule: the central planner can elicit correct information from all agents as unique Bayes Nash equilibrium behavior if “all agents are selfish†is never common knowledge. This result holds even if honest agents are mostly motivated by monetary interest.
    Date: 2020–11
  16. By: Wiens, Marcus; Mahdavian, Farnaz; Platt, Stephen; Schultmann, Frank
    Abstract: In this article, we analyze the phenomenon of flood evacuation compliance from a both decision-theoretic and game-theoretic perspective presenting the Warning Compliance Model (WCM). This discrete decision model incorporates a Bayesian information system, which formalizes the statistical effects of a warning forecast based on the harmonious structure of a Hidden Markov Model (HMM). The game-theoretical part of the model incorporates the evacuation order decision of a local government and people's compliance regarding their evacuation-decisions. The strengths of this novel approach lie in the joint consideration of probabilistic and communicative risk aspects of a dynamic setting, in the simultaneous consideration of escalation and de-escalation phases and of two differently exposed risk groups, which requires differential risk communication. For each scenario, we derive the explicit and generic solution of the model, which makes it possible to identify the scope for warning compliance and its effects independent from the parameter constellation. Applying empirical data from flood and risk studies yields plausible results for the escalation-scenario of the model and reveal the limits of compliance if people face a Black Swan flood event.
    Date: 2020
  17. By: Takahiko Kan
    Abstract: Adam Smith is the author of An Inquiry into the Nature and Causes of the Wealth of Nations. He is known mainly as a pioneer of political economy. However, he was not only an economist but also a moral philosopher. He published The Theory of Moral Sentiments (TMS) in 1759. In TMS, he explained an establishment of a social order based on sympathy between people in a society. Sympathy is sharing of sentiments with others by imaginarily swapping situations with others. People in TMS form the impartial spectator and regulate their conduct to be sympathized by the impartial spectator. The impartial spectator is often considered as an important concept in TMS. However, even if people formed the impartial spectator, this does not mean that they can always regulate their conduct. To regulate their conduct absolutely, people need general rules of morality (GRM). People can establish a social order thanks to GRM. Some preceding studies have reinterpreted TMS with various research results in contemporary economics. For example, Meardon & Ortmann (1996) reinterprets self-command by using a repeated game theory model. Ashraf et al. (2005) indicates that Smith foresaw some research findings of behavioral economics. Tajima (2007) reinterprets TMS from a perspective of institutional economics. Breban (2012) formularizes a behavior of people in TMS with a utility function, and compares this function with utility functions in behavioral economics. Khalil (2017) reinterprets TMS from a perspective of rational choice theory. These reinterpretations have shed light on modern significance of TMS. However, there is room for reinterpreting important concepts in TMS with research results in contemporary economics. Following the preceding studies, this paper reinterprets the GRM formation process and the corruption of moral sentiments (CMS) by using a replicator dynamics model, which is a basic model of evolutionary game theory. GRM are the social norms in TMS that concern what is fit and proper either to be done or to be avoided. In TMS, people form GRM through interactions with others. They continually observe conduct of others, and this can lead them to form certain GRM. This paper interprets this observation process as a trial-and-error learning process. To formularize this process, this paper uses a replicator dynamics model. The results of the model clarify the character of sympathy in the CRM. The more sympathetic players exist in a player set, the more corrupted situation is likely to be realized. This result mathematically supports an interpretation in preceding studies (Brown 1994, Griswold 1999) that sympathy involves risk that CMS is progressing. The paper is organized as follows. In the section 2, we briefly describe GRM and the CMS. In the section 3, we construct a model of replicator dynamics. In the section 4, we discuss the results of the model. In the last section, we conclude this paper.
    Date: 2020–09–11
  18. By: Nicolas Jacquemet (PSE - Paris School of Economics, CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique); Stephane Luchini (AMSE - Aix-Marseille Sciences Economiques - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique); A. Malézieux (CEREN - Centre de Recherche sur l'ENtreprise [Dijon] - BSB - Burgundy School of Business (BSB) - Ecole Supérieure de Commerce de Dijon Bourgogne (ESC)); Jason F. Shogren (UW - University of Wyoming)
    Abstract: Using two earned income/tax declaration experimental designs we show that only partial liars are affected by a truth-telling oath, a non-price commitment device. Under oath, we see no change in the number of chronic liars and fewer partial liars. Rather than smoothly increasing their compliance, we also observe that partial liars who respond to the oath, respond by becoming fully honest under oath. Based on both response times data and the consistency of subjects when several compliance decisions are made in a row, we show that partial lying arises as the result of weak preferences towards profitable honesty. The oath only transforms people with weak preferences for lying into being committed to the truth.
    Keywords: part-time Lying,honesty,oath,commitment,Tax evasion
    Date: 2020–05

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