nep-gth New Economics Papers
on Game Theory
Issue of 2012‒05‒15
25 papers chosen by
Laszlo A. Koczy
Hungarian Academy of Sciences and Obuda University

  1. A Strategic Implementation of the Average Tree Solution for Cycle-Free Graph Games By Rene van den Brink; Gerard van der Laan; Nigel Moes
  2. Following Recommendations to Avoid Coordination-Failure in 2 x 2 Games By John Bone; Michalis Drouvelis; Indrajit Ray
  3. Sharing the surplus in games with externalities within and across issues By Effrosyni Diamantoudi; Inés Macho-Stadler; David Pérez-Castrillo; Licun Xue
  4. A Detail-Free Mediator By Vida, Péter; Azacis, Helmuts
  5. Solving payoff sets of perfect public equilibria: an example By Du, Chuang
  6. Coordination structures By Alfonso Rosa García; Hubert Janos Kiss
  7. Asymmetrically Fair Rules for an Indivisible Good Problem with a Budget Constraint By Paula Jaramillo; Çagatay Kayi; Flip Klijn
  8. Static Multi-Criteria Model of Investing in Innovative Projects on a Set of Coalitional Partitions By X. V. Grigorieva; Oleg A. Malafeyev
  9. A Cantor Set of Games with No Shift-Homogeneous Equilibrium Selection By Yehuda (John) Levy
  10. Everyone Wants a Chance : Initial Positions and Fairness in Ultimatum Games By Grimalda, Gianluca; Kar, Anirban; Proto, Eugenio
  11. Carbon capture and storage and transboundary pollution: a differential game approach By Luisito Bertinelli; Carmen Camacho; Benteng Zou
  12. Simple Mediation in a Cheap-Talk Game By Chirantan Ganguly; Indrajit Ray
  13. A proportional approach to bankruptcy. Problems with a guaranteed minimum By José M. Jiménez Gómez; Josep Enric Peris Ferrando
  14. Sand in the Wheels: A Dynamic Global-Game Approach By Laurent Mathevet; Jakub Steiner
  15. A Web Gaming Facility for Research and Teaching By Martin Shubik
  16. Are Self-regarding Subjects More Rational? By Benito Arruñada; Marco Casari; Francesca Pancotto
  17. Welfare of Naive and Sophisticated Players in School Choice By Jose Apesteguia; Miguel A. Ballester
  18. Strategic interactions, incomplete information and learning By Berardi, Michele
  19. Bayesian Estimation of a Dynamic Game with Endogenous, Partially Observed, Serially Correlated State By A. Ronald Gallant; Han Hong; Ahmed Khwaja
  20. Strategically Stable Technological Alliance By Nikolai V. Kolabutin; Nikolay A. Zenkevich
  21. Quotient Spaces of Boundedly Rational Types By Davide Cianciaruso; Fabrizio Germano
  22. Competing for Customers in a Social Network (R) By Pradeep Dubey; Rahul Garg; Bernard De Meyer
  23. The value of lies in an ultimatum game with imperfect information By Damien Besancenot; Delphine Dubart; Radu Vranceanu
  24. Ingratiation and Favoritism : Experimental Evidence By Stéphane Robin; Agnieszka Rusinowska; Marie-Claire Villeval
  25. Let's (Not) Talk about Sex: The Effect of Information Provision on Gender Differences in Performance under Competition By Nagore Iriberri; Pedro Rey-Biel

  1. By: Rene van den Brink (VU University Amsterdam); Gerard van der Laan (VU University Amsterdam); Nigel Moes (VU University Amsterdam)
    Abstract: In this note we provide a strategic implementation of the average tree solution for zero-monotonic cycle-free graph games. That is, we propose a non-cooperative mechanism of which the unique subgame perfect equilibrium payoffs correspond to the average hierarchical outcome of the game. This mechanism takes into account that a player is only able to communicate with other players (i.e., to make proposals about a division of the surplus of cooperation) when they are connected in the graph.
    Keywords: implementation; cycle-free graph game; tree game; hierarchical outcome; average tree solution; weighted hierarchical outcome
    JEL: C71 C72
    Date: 2012–05–07
  2. By: John Bone; Michalis Drouvelis; Indrajit Ray
    Abstract: We consider 2 x 2 games like Battle of the Sexes and Chicken, to test whether or not players are able to coordinate on pure Nash equilibria following recommendations from correlation devices. We use two different correlation devices, public and private, for these games, with the same expected payoffs, in equilibrium. We find that the players overall do achieve coordination by playing the recommended strategies. However, coordination and following recommendations vary significantly among these games.
    Keywords: Coordination, Public message, Recommendation, Correlated Equilibrium
    JEL: C72 C92 D83
    Date: 2012–05
  3. By: Effrosyni Diamantoudi; Inés Macho-Stadler; David Pérez-Castrillo; Licun Xue
    Abstract: We consider environments in which agents can cooperate on multiple issues and externalities are present both within and across issues. We propose a way to extend (Shapley) values that have been put forward to deal with externalities within issues to games where there are externalities within and across issues. We characterize our proposal through axioms that extend the Shapley axioms to our more general environment.
    Keywords: externalities, cooperative game theory, Shapley value, linked issues
    JEL: C71 D62
    Date: 2011–08
  4. By: Vida, Péter; Azacis, Helmuts (Cardiff Business School)
    Abstract: We present an extension to any finite complete information game with two players. In the extension, players are allowed to communicate directly and, additionally, send private messages to a simple, detail-free mediator, which, in turn, makes public announcements as a deterministic function of the private messages. The extension captures situations in which people engage in face-to-face communication and can observe the opponent's face during the conversation before choosing actions in some underlying game. We prove that the set of Nash equilibrium payoffs of the extended game approximately coincides with the set of correlated equilibrium payoffs of any underlying game.
    Keywords: Correlated equilibrium; detail-free mechanism; mediated pre-play communication
    JEL: C72
    Date: 2012–05
  5. By: Du, Chuang
    Abstract: We study an example of infinitely repeated games in which symmetric duopolistic firms produce experience goods. After consuming the products, short-run consumers only observe imperfect public information about product quality. We characterize perfect public equilibrium payoff set E(δ) of firms for each fixed discount factor δ∈[0,1) when each firm has two action choices, signals follow binomial distributions and the game has a product structure. The set E(δ) turns out a single point or symmetric pentagon for fixed δ. And δ∈[0, 1) can be divided into countable infinite subintervals in which E(δ) remains constant. The strategies to implement payoffs in boundaries of E(δ) are constructed in a recursive way, in which infinite repetition of Nash Equilibrium of stage game could be viewed as an absorbing state in a Markov Process where state transitions are controlled through public signals and optimal punishments in each period.
    Keywords: repeated games; imperfect public monitoring; equilibrium payoff sets; duopoly
    JEL: D21 L13 D82 L15 C73 C72
    Date: 2012–05–07
  6. By: Alfonso Rosa García (Universidad de Murcia); Hubert Janos Kiss (Universidad Autónoma de Madrid)
    Abstract: We study a coordination problem where agents act sequentially. Agents are embedded in anobservation network that allows them to observe the actions of their neighbors. We find thatcoordination failures do not occur if there exists a sufficiently large clique. Its existence isnecessary and sufficient when agents are homogenous and sufficient when agents differ and theirtypes are private. Other structures guarantee coordination when agents decide in some particularsequences or for particular payoffs. The coordination problem embodied in our game is appliedto the problems of revolts and bank runs.
    Keywords: Social networks, coordination failures, multiple equilibria, revolts, bank runs.
    JEL: C72 D82 D85 G21 Z13
    Date: 2012–04
  7. By: Paula Jaramillo; Çagatay Kayi; Flip Klijn
    Abstract: We study a particular restitution problem where there is an indivisible good (land or property) over which two agents have rights: the dispossessed agent and the owner. A third party, possibly the government, seeks to resolve the situation by assigning rights to one and compensate the other. There is also a maximum amount of money available for the compensation. We characterize a family of asymmetrically fair rules that are immune to strategic behavior, guarantee minimal welfare levels for the agents, and satisfy the budget constraint.
    Keywords: fairness, strategy-proofness, indivisible good, land restitution
    JEL: D61 D63
    Date: 2012–02
  8. By: X. V. Grigorieva; Oleg A. Malafeyev
    Abstract: Static multi-criteria problem of investing in innovative projects on a set of coalitional partitions finding means compromise vector (one or more) of investment programs, where each component is an investment program of the corresponding innovative project. The search of compromise vector is made under coalitional interaction of all participants in innovative projects. In the process of solving this problem several game problems with different coalitional partitions are considered. As the principles of optimality, Pareto optimum, Nash arbitration scheme, Shapley value, compromise solution are used.
    Keywords: coalitional games, Pareto optimality, a compromise solution.
    Date: 2011–09
  9. By: Yehuda (John) Levy
    Abstract: We construct a continuum of games on a countable set of players that does not possess a measurable equilibrium selection that satisfies a natural homogeneity property. The explicit nature of the construction yields counterexamples to the existence of equilibria in models with overlapping generations and in games with a continuum of players.
    Date: 2012–04
  10. By: Grimalda, Gianluca (Universitat Jaume I, Castelló, Spain.); Kar, Anirban (Delhi School of Economics, University of Delhi); Proto, Eugenio (University of Warwick)
    Abstract: Fairness emerges as a relevant factor in redistributive preferences in surveys and experiments. We study experimentally the impact of varying the probability with which players are assigned to initial positions in Ultimatum Games (UGs). In the baseline case players have equal opportunities of being assigned the proposer position –arguably the more advantaged one in UGs. Chances become increasingly unequal across three treatments. We also manipulate the inter-temporal allocation of opportunities over rounds. We find that : (1) The more initial chances are distributed unequally, the lower the acceptance rates of a given offer ; consequently, offers increase ; (2) Being assigned a mere 1% chance of occupying the proposer role compared to none, significantly increases acceptance rates and decreases offers ; (3) Players accept even extreme amounts of unequal chances within each round in exchange for overall equality of opportunities across rounds. Procedural fairness – both static and dynamic - has clear relevance for individuals.
    Date: 2012
  11. By: Luisito Bertinelli (CREA, University of Luxembourg); Carmen Camacho (CNRS, Centre d’Economie de la Sorbonne, Paris 1); Benteng Zou (CREA, University of Luxembourg)
    Abstract: We study the strategic behavior of two countries facing transboundary pollution under a differential game setting. In our model, the reduction of both pollution and CO2 concentration occur through the creation of pollution sinks, rather than through the adoption of cleaner technologies. To our knowledge, this is the first formal attempt to model carbon capture and storage. Furthermore, we provide the explicit short-run dynamics for this game with symmetric open-loop and a special Markovian Nash strategies. Furthermore, we analyze and compare these strategies and the games’ steady states along some balanced growth paths. Our results show that if the initial level of pollution is relatively high, state dependent emissions reductions can lead to higher overall environmental quality, hence, feedback strategy leads to less social waste.
    Keywords: Transboundary pollution, carbon capture and storage, differential game
    JEL: Q58 Q55 Q52 C73
    Date: 2011
  12. By: Chirantan Ganguly; Indrajit Ray
    Abstract: In the Crawford-Sobel (uniform, quadratic utility) cheap-talk model, we consider a simple mediation scheme (a communication device) in which the informed agent reports one of the N possible elements of a partition to the mediator and then the mediator suggests one of the N actions to the uninformed decision-maker according to the probability distribution of the device. We show that no such simple mediated equilibrium can improve unpon the unmediated N-partition Crawford-Sobel equilibrium when the preference divergence parameter (bias is small).
    Keywords: Cheap Talk, Mediated Equilibrium
    JEL: C72
    Date: 2012–04
  13. By: José M. Jiménez Gómez (Universidad Politécnica de Cartagena); Josep Enric Peris Ferrando (Universidad de Alicante)
    Abstract: In a distribution problem, and specifically in bankruptcy issues, the Proportional (P) and theEgalitarian (EA) divisions are two of the most popular ways to resolve the conflict. TheConstrained Equal Awards rule (CEA) is introduced in bankruptcy literature to ensure that noagent receives more than her claim, a problem that can arise when using the egalitarian division.We propose an alternative modification, by using a convex combination of P and EA. Therecursive application of this new rule finishes at the CEA rule. Our proposal ensures a minimumamount to each agent, and distributes the remaining estate in a proportional way.
    Keywords: Bankruptcy problems, Proportional rule, Equal Awards, Convex combination of rules, Lorenz dominance.
    JEL: C71 D63 D71
    Date: 2012–04
  14. By: Laurent Mathevet; Jakub Steiner
    Abstract: We study the impact of frictions on the prevalence of systemic crises. Agents privately learn about a fixed payoff parameter, and repeatedly adjust their investments while facing transaction costs in a dynamic global game. The model has a rich structure of externalities: payoffs may depend on the volume of aggregate investment, on the concentration of investment, or on its volatility. We examine how small frictions, including those similar to the Tobin tax, affect the equilibrium. We identify conditions under which frictions discourage harmful behavior without compromising investment volume. The analysis is driven by a robust invariance result: the volume of aggregate investment (measured in a pivotal contingency) is invariant to a large family of frictions.
    Keywords: coordination; dynamic global game; frictions; Tobin tax;
    JEL: C72 D82 H23
    Date: 2012–04
  15. By: Martin Shubik (Cowles Foundation, Yale University)
    Abstract: This essay considers the potential for utilizing web games for research and teaching. It discusses a specific gaming facility that has been constructed and utilized. The gaming facility can be made available for use for those interested in utilizing it for teaching and/or research purposes. The goal is to have this facility be of use for both single play and repeated matrix games. Much of the discussion here is aimed at single play games as a desirable benchmark preliminary to the study of repeated games. Properties of the one stage games are discussed and instructions for the use of the system are supplied. Extensions to multistage games and incomplete information are noted.
    Keywords: Matrix games, Experimental, Teaching and computerized games
    JEL: C7 C9 D03
    Date: 2012–05
  16. By: Benito Arruñada; Marco Casari; Francesca Pancotto
    Abstract: Through an experiment, we investigate how the level of rationality relates to concerns for equality and efficiency. Subjects perform dictator games and a guessing game. More rational subjects are not more frequently of the self-regarding type. When performing a comparison within the same degree of rationality, self-regarding subjects show more strategic sophistication than other subjects.
    Keywords: steps of reasoning, other-regarding preferences
    JEL: C91 C92 D63
    Date: 2012–01
  17. By: Jose Apesteguia; Miguel A. Ballester
    Abstract: Two main school choice mechanisms have attracted the attention in the literature: Boston and deferred acceptance (DA). The question arises on the ex-ante welfare implications when the game is played by participants that vary in terms of their strategic sophistication. Abdulkadiroglu, Che and Yasuda (2011) have shown that the chances of naive participants getting into a good school are higher under the Boston mechanism than under DA, and some naive participants are actually better off. In this note we show that these results can be extended to show that, under the veil of ignorance, i.e. students not yet knowing their utility values, all naive students may prefer to adopt the Boston mechanism.
    Keywords: School Choice; Naive Players; Welfare; Veil of Ignorance
    JEL: C7 D0 D6
    Date: 2011–09
  18. By: Berardi, Michele
    Abstract: In a model of incomplete, heterogeneous information, with externalities and strategic interactions, we analyze the possibility for learning to act as coordination device. We build on the framework proposed by Angeletos and Pavan (2007) and extend it to a dynamic multiperiod setting where agents need to learn to coordinate. We analyze conditions under which adaptive and eductive learning obtain, and show that adaptive learning conditions are less demanding than the eductive ones: in particular, when actions are strategic substitutes, the equilibrium is always adaptively learnable, while it might not be eductively so. In case of heterogeneous preferences, moreover, convergence only depends on the average characteristic of agents in the economy. We also show that adaptive learning dynamics converge to the game theoretical strategic equilibrium, which means that agents can learn to act strategically in a simple and straightforward way.
    Keywords: Learning; heterogeneity; interaction; coordination
    JEL: D83 C73 C62
    Date: 2012–05–06
  19. By: A. Ronald Gallant; Han Hong; Ahmed Khwaja
    Abstract: We consider dynamic games that can have state variables that are partially observed, serially correlated, endogenous, and heterogeneous. We propose a Bayesian method that uses a particle filter to compute an unbiased estimate of the likelihood within a Metropolis chain. Unbiasedness guarantees that the stationary density of the chain is the exact posterior, not an approximation. The number of particles required is easily determined. The regularity conditions are weak. Results are verified by simulation from two dynamic oligopolistic games with endogenous state. One is an entry game with feedback to costs based on past entry and the other a model of an industry with a large number of heterogeneous firms that compete on product quality.
    Keywords: Dynamic Games, Partially Observed State, Endogenous State, Serially Correlated State, Particle Filter
    JEL: E00 G12 C51 C52
    Date: 2012
  20. By: Nikolai V. Kolabutin; Nikolay A. Zenkevich
    Abstract: There are two conditions that are important to investigate the stability problem when considering the long-term cooperative agreements: the dynamic stability (time consistency), and strategic stability. This paper presents the results based on the profit distribution procedure (PRP), which implement a model of stable cooperation. The paper also shows the relationship between the dynamic and strategic stability of cooperative agreement and the numerical results showing the influence of parameters on the character of participants’ development.
    Keywords: Differential Game, Coalition, Shapley Value, Dynamic Stability, Strategic Stabilty
    Date: 2011–09
  21. By: Davide Cianciaruso; Fabrizio Germano
    Abstract: By identifying types whose low-order beliefs up to level ℓ<sub>i</sub> about the state of nature coincide, we obtain quotient type spaces that are typically smaller than the original ones, preserve basic topological properties, and allow standard equilibrium analysis even under bounded reasoning. Our Bayesian Nash (ℓ<sub>i</sub>; ℓ<sub>ii</sub>)-equilibria capture players inability to distinguish types belonging to the same equivalence class. The case with uncertainty about the vector of levels (ℓ<sub>i</sub>; ℓ<sub>ii</sub>) is also analyzed. Two examples illustrate the constructions.
    Keywords: Incomplete-information games, high-order reasoning, type space, quotient space, hierarchies of beliefs, bounded rationality
    JEL: C72 D03 D83
    Date: 2011–09
  22. By: Pradeep Dubey (Center for Game Theory, Stony Brook University); Rahul Garg (Opera Solutions, India); Bernard De Meyer (CERMSEM, Universite Paris 1)
    Abstract: There are many situations in which a customer’s proclivity to buy the product of any firm depends not only on the classical attributes of the product such as its price and quality, but also on who else is buying the same product. Under quite general circumstances, it turns out that customers’ influence on each other dynamically converges to a steady state. Thus we can model these situations as games in which firms compete for customers located in a "social network." A canonical example is provided by competition for advertisement on the web. Nash Equilibrium (NE) in pure strategies exist in general. In the quasi-linear version of the model, NE turn out to be unique and can be precisely characterized. If there are no a priori biases between customers and firms, then there is a cut-off level above which high cost firms are blockaded at an NE, while the rest compete uniformly throughout the network. Otherwise there is a tendency towards regionalization, with firms dominating disjoint territories. We also explore the relation between the connectivity of a customer and the money firms spend on him. This relation becomes particularly transparent when externalities are dominant: NE can be characterized in terms of the invariant measures on the recurrent classes of the Markov chain underlying the social network. Finally we consider convex (instead of linear) cost functions for the firms. Here NE need not be unique as we show via an example. But uniqueness is restored if there is enough competition between firms or if their valations of clients are anonymous.
    Keywords: Nash equilibrium, Social network, Advertisement on the web
    JEL: C7 D2 D4 L1
    Date: 2012–05
  23. By: Damien Besancenot (CEPN - Centre d'Economie de l'Université Paris Nord - Université Paris XIII - Paris Nord - CNRS : UMR7234); Delphine Dubart (ESSEC Business School - ESSEC Business School); Radu Vranceanu (Economics Department - ESSEC Business School)
    Abstract: Humans often lie strategically. We study this problem in an ultimatum game involving informed proposers and uninformed responders, where the former can send an unverifiable statement about their endowment. If there are some intrinsically honest proposers, a simple message game shows that the rest of them are likely to declare a lower-than-actual endowment to the responders. In the second part of the paper, we report on an experiment testing this game. On average, 88.5% of the proposers understate the actual endowment by 20.5%. Regression analysis shows that a one-dollar gap between the actual and declared amounts prompts proposers to reduce their offer by 19 cents. However, responders appear not to take such claims seriously, and thus the frequency of rejections should increase. The consequence is a net welfare loss, that is specific to such a "free-to-lie" environment.
    Keywords: Ultimatum game; Asymmetric information; Lying costs; Strategic lies; Deception; Welfare loss
    Date: 2012–04–16
  24. By: Stéphane Robin (Université de Lyon, Lyon, F-69007, France ; CNRS, GATE Lyon St Etienne,F-69130 Ecully, France); Agnieszka Rusinowska (CES (Centre d'Economie de la Sorbonne), Paris School of Economics – CNRS, 106-112 Bd de l'Hôpital, 75647 Paris, France); Marie-Claire Villeval (Université de Lyon, Lyon, F-69007, France ; CNRS, GATE Lyon St Etienne,F-69130 Ecully, France)
    Abstract: We provide experimental evidence of workers’ ingratiation by opinion conformity and of managers’ discrimination in favor of workers with whom they share similar opinions. In our Baseline, managers can observe both workers’ performance at a task and opinions before assigning unequal payoffs. In the Ingratiation treatment, workers can change their opinion after learning that held by the manager. In the Random treatment, workers can also change opinion but payoffs are assigned randomly, which gives a measure of non-strategic opinion conformism. We find evidence of high ingratiation indices, as overall, ingratiation is effective. Indeed, managers reward opinion conformity, and even more so when opinions cannot be manipulated. Additional treatments reveal that ingratiation is cost sensitive and that the introduction of performance pay for managers as well as a less noisy measure of performance increase the role of relative performance in the assignment of payoffs, without eliminating the reward of opinion conformity.
    Keywords: Ingratiation, opinion conformity, favoritism, discrimination, social distance,experiment
    JEL: C7 C92 D03 D86 M51
    Date: 2012
  25. By: Nagore Iriberri; Pedro Rey-Biel
    Abstract: We study how gender differences in performance under competition are affected by the provision of information regarding rivals gender and/or differences in relative ability. In a laboratory experiment, we use two tasks that differ regarding perceptions about which gender outperforms the other. We observe womens underperformance only under two conditions: 1) tasks are perceived as favoring men and 2) rivals gender is explicitly mentioned. This result can be explained by stereotype-threat being reinforced when explicitly mentioning gender in tasks in which women already consider they are inferior. Omitting information about gender is a safe alternative to avoid womens underperformance in competition.
    Keywords: gender differences, competition, feedback information, gender perception, stereotype-threat
    JEL: C72 C91 D81
    Date: 2011–09

This nep-gth issue is ©2012 by Laszlo A. Koczy. It is provided as is without any express or implied warranty. It may be freely redistributed in whole or in part for any purpose. If distributed in part, please include this notice.
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