nep-gth New Economics Papers
on Game Theory
Issue of 2011‒02‒12
twenty papers chosen by
Laszlo A. Koczy
Hungarian Academy of Sciences and Obuda University

  1. Extrapolation in Games of Coordination and Dominance Solvable Games By Friederike Mengel; Emanuela Sciubba
  2. Stochastic discounting in repeated games: Awaiting the almost inevitable By Barlo, Mehmet; Urgun, Can
  3. Stability and fairness in models with a multiple membership By LE BRETON, Michel; MORENO-TERNERO, Juan D.; SAVVATEEV, Alexei; WEBER, Shlomo
  4. Binomial menu auctions in government formation By Breitmoser, Yves
  5. Allocation of fixed costs: characterization of the (dual) weighted Shapley value. By Pierre Dehez
  6. Interplay between security providers, consumers, and attackers: a weighted congestion game approach By Patrick Maillé; Peter Reichl; Bruno Tuffin
  7. Data games: Sharing public goods with exclusion. By Pierre Dehez; Daniela Tellone
  8. Repeated Cheap-Talk Games of Common Interest between a Decision-Maker and an Expert of Unknown Statistical Bias By Irene Valsecchi
  9. Fair allocation of indivisible goods among two agents By REMAEKERS, Eve
  10. Minority Language and the Stability of Bilingual Equilibria. By Nagore Iriberri; Jose Ramón Uriarte
  11. An Ascending Multi-Item Auction with Financially Constrained Bidders By Gerard van der Laan; Zaifu Yang
  12. Governing a Common-Pool Resource in a Directed Network By Lionel Richefort; Patrick Point
  13. Generalized Nash Equilibrium and market coupling in the European power system By SMEERS, Yves; OGGIONI, Giorgia; ALLEVI, Elisabetta; SCHAIBLE, Siegfried
  14. Influence networks By LOPEZ-PINTADO, Dunia
  15. Bargaining and delay in patent licensing By MAULEON, Ana; VANNETELBOSCH, Vincent; VERGARI, Cecilia
  16. Strategic manipulations and collusions in Knaster procedure: a comment By Corradi, Corrado; Corradi, Valentina
  17. Where do preferences come from? By Dietrich Franz; List Christian
  18. Rock and roll bands, (in)complete contracts and creativity By CEULEMANS, Cédric; GINSBURGH, Victor; LEGROS, Patrick
  19. Unions' relative concerns and strikes in wage bargaining By MAULEON, Ana; VANNETELBOSCH, Vincent; VERGARI, Cecilia
  20. The benefits of cooperation under uncertainty: the case of climate change By BRECHET, Thierry; THENIE, Julien; ZEIMES, Thibaut; ZUBER, Stéphane

  1. By: Friederike Mengel (Maastricht University); Emanuela Sciubba (Birkbeck College London)
    Abstract: We study extrapolation between games in a laboratory experiment. Participants in our experiment first play either the dominance solvable guessing game or a Coordination version of the guessing game for five rounds. Afterwards they play a 3x3 normal form game for ten rounds with random matching which is either a game solvable through iterated elimination of dominated strategies (IEDS), a pure Coordination game or a Coordination game with pareto ranked equilibria. We find strong evidence that participants do extrapolate between games. Playing a strategically different game hurts compared to the control treatment where no guessing game is played before and in fact impedes convergence to Nash equilibrium in both the 3x3 IEDS and the Coordination games. Playing a strategically similar game before leads to faster convergence to Nash equilibrium in the second game. In the Coordination games some participants try to use the first game as a Coordination device. Our design and results allow us to conclude that participants do not only learn about the population and/or successful actions, but that they are also able to learn structural properties of the games.
    Keywords: Game Theory, Learning, Extrapolation
    JEL: C72 C91
    Date: 2010–11
  2. By: Barlo, Mehmet; Urgun, Can
    Abstract: This paper studies repeated games with pure strategies and stochastic discounting under perfect information. We consider infinite repetitions of any finite normal form game possessing at least one pure Nash action profile. The period interaction realizes a shock in each period, and the cumulative shocks while not affecting period returns, determine the probability of the continuation of the game. We require cumulative shocks to satisfy the following: (1) Markov property; (2) to have a non-negative (across time) covariance matrix; (3) to have bounded increments (across time) and possess a denumerable state space with a rich ergodic subset; (4) there are states of the stochastic process with the resulting stochastic discount factor arbitrarily close to 0, and such states can be reached with positive (yet possibly arbitrarily small) probability in the long run. In our study, a player’s discount factor is a mapping from the state space to (0,1) satisfying the martingale property. In this setting, we, not only establish the (subgame perfect) folk theorem, but also prove the main result of this study: In any equilibrium path, the occurrence of any finite number of consecutive repetitions of the period Nash action profile, must almost surely happen within a finite time window. That is, any equilibrium strategy almost surely contains arbitrary long realizations of consecutive period Nash action profiles.
    Keywords: Repeated Games; Stochastic Discounting; Stochastic Games; Folk Theorem; Stopping Time
    JEL: C79 C72 C73
    Date: 2011–01
  3. By: LE BRETON, Michel (Université de Toulouse 1, GREMAQ and IDEI, Toulouse, France); MORENO-TERNERO, Juan D. (Universidad de Malaga, Spain; Universidad Pablo de Olavide, Seville, Spain; Université catholique de Louvain, CORE, B-1348 Louvain-la-Neuve, Belgium); SAVVATEEV, Alexei (New Economic School, Moscow, Russia); WEBER, Shlomo (Southern Methodist University, Dallas, USA and New Economic School, Moscow, Russia)
    Abstract: This article studies a model of coalition formation for the joint production (and finance) of public projects, in which agents may belong to multiple coalitions. We show that, if projects are divisible, there always exists a stable (secession-proof) structure, i.e., a structure in which no coalition would reject a proposed arrangement. When projects are in- divisible, stable allocations may fail to exist and, for those cases, we resort to the least core in order to estimate the degree of instability. We also examine the compatibility of stability and fairness on metric environments with indivisible projects. To do so, we explore, among other things, the performance of several well-known solutions (such as the Shapley value, the nucleolus, or the Dutta-Ray value) in these environments.
    Keywords: stability, fairness, membership, coalition formation
    JEL: C71
    Date: 2010–12–01
  4. By: Breitmoser, Yves
    Abstract: In a menu auction, players submit bids for all choices the auctioneer A can make, and A then makes the choice that maximizes the sum of bids. In a binomial menu auction (BMA), players submit acceptance sets (indicating which choices they would support), and A chooses the option that maximizes his utility subject to acceptance of the respective players. Monetary transfers may be implicit, but players may also bid by offering "favors" and the like. BMAs provide a unified representation of both monetary and non-monetary bidding, which I apply to model government formation. First, I analyze general BMAs, characterize the solution under complete information and establish outcome uniqueness (for both, sealed bid and Dutch formats). Second, in case monetary transfers are possible, BMAs are shown to implement VCG mechanisms. Finally, in case transfers are impossible, BMAs extend the model of proto-coalition bargaining and are specifically applied to government formation.
    Keywords: menu auction; demand commitment; proto-coalition bargaining; VCG mechanism
    JEL: C78 D44 C72
    Date: 2011–02–03
  5. By: Pierre Dehez
    Abstract: The weighted value was introduced by Shapley in 1953 as an asymmetric version of his value. Since then several axiomatizations have been proposed including one by Shapley in 1981 specifically addressed to cost allocation, a context in which weights appear naturally. It was at the occasion of a comment in which he only stated the axioms. The present paper offers a proof of Shapley's statement as well as an alternative set of axioms. It is shown that the value is the unique rule that allocates additional fixed costs fairly: only the players who are concerned contribute to the fixed cost and they contribute in proportion to their weights. A particular attention is given to the case where some players are assigned a zero weight.
    Keywords: cost allocation, Shapley value, fixed cost.
    JEL: C71 D46
    Date: 2011
  6. By: Patrick Maillé (RSM - Département Réseaux, Sécurité et Multimédia - Institut Télécom - Télécom Bretagne - Université européenne de Bretagne); Peter Reichl (FTW - Telecommunications Research Center Vienna [Autriche] - FTW); Bruno Tuffin (INRIA - IRISA - DIONYSOS - INRIA - Université de Rennes I)
    Abstract: Network users can choose among different security solutions to protect their data. Those solutions are offered by competing providers, with possibly different performance and price levels. In this paper, we model the interactions among users as a noncooperative game, with a negative externality coming from the fact that attackers target popular systems to maximize their expected gain. Using a nonatomic weighted congestion game model for user interactions, we prove the existence and uniqueness of a user equilibrium, compute the corresponding Price of Anarchy, that is the loss of efficiency due to user selfishness, and investigate some consequences for the (higher-level) pricing game played by security providers.
    Keywords: Game theory;Weighted games; Security
    Date: 2011–01–30
  7. By: Pierre Dehez; Daniela Tellone
    Abstract: A group of firms decides to cooperate on a project that requires a combination of inputs held by some of them. These inputs are non-rival but excludable goods i.e. public goods with exclusion such as knowledge, data or information, patents or copyrights. We address the question of how firms should be compensated for the inputs they contribute. We show that this problem can be framed within a cost sharing game whose Shapley comes out as a natural solution. The main result concerns the regular structure of the core that enables a simple characterization of the nucleolus. However, compared to the Shapley value, the nucleolus defines compensations that appear to be less appropriate in the context of data sharing. Our analysis is inspired by the problem faced by the European chemical firms within the regulation program REACH that requires submission by 2018 of a detailed analysis of the substances they produce, import or use.
    Keywords: cost sharing, Shapley value, core, nucleolus.
    JEL: C71 H41 M41
    Date: 2011
  8. By: Irene Valsecchi (University of Milano-Bicocca)
    Abstract: Two agents are engaged in a joint activity that yields a common perperiod payoff at two rounds of play. The expert announces the probability that the current state of the world is low, instead of high, at each stage. Having received the report of the expert, the decision-maker takes action at every period according to his posterior beliefs. At the end of each round of play, the true current state is verifiable. The distinctive assumption of the paper is that the decision-maker makes a subjective appraisal of the expert’s reliability: he considers the expert’s true forecasts as the outcomes of an experiment of unknown statistical bias. The paper shows that the expert will have instrumental reputational concerns, related to the future estimate of the systematic error associated to his predictions. In contrast with previous work, reputational concerns are shown to enhance the credibility of the initial messages, and to increase both the agents’ expected payoff at the first round of play in equilibrium. The equilibrium messages will be noisy, but noisiness will be less costly than it would be in single-stage games.
    Keywords: Opinion, Expert, Strategic Communication
    JEL: D81 D84
    Date: 2010–11
  9. By: REMAEKERS, Eve (Chargée de recherches F.R.S.-FNRS, Université catholique de Louvain, CORE, B-1348 Louvain-la-Neuve, Belgium)
    Abstract: One must allocate a finite set of indivisible goods among two agents without monetary compensation. We impose Pareto-efficiency, anonymity, a weak notion of no-envy, a welfare lower bound based on each agent’s ranking of the sets of goods, and a monotonicity property relative to changes in agents’ preferences. We prove that there is a rule satisfying these axioms. If there are three goods, it is the only rule, with one of its subcorrespondences, satisfying each fairness axiom and not discriminating between goods. Further, we confirm the clear gap between these economies and those with more than two agents.
    Keywords: indivisible goods, no monetary compensation, no-envy, lower bound, preference-monotonicity
    JEL: D61 D63
    Date: 2010–12–01
  10. By: Nagore Iriberri (Universitat Pompeu Fabra); Jose Ramón Uriarte (Universidad del País Vasco)
    Abstract: We investigate a society with two official languages: A, shared by all individuals and B, spoken by a bilingual mirority. Thus, it is only B that needs t increase its population share, and therefore, only the language dynamics that derive from the intearctions that occur inside the bilingual population are both empirically and theoretically relevant. To this end, a model is developed in which the bilingual agents must make strategic decisions about the language to be used in a conversation. Decisions are taken under imperfect information about the linguistic type of the participants in the interaction. We first study all the posiblle equilibria the model might produce and the language used in each of them. Then, in a dynamic setting, we study the building of a language convention by the bilingual speakers. The main result is that there is a mixed strategy Nash equilibrium in which bilingual agents use both the A and B languages. This equilibrium is evolutionary stable, and dynamically, it is asymptotically stable for the one-population replicator dynamics. In this equilibrium, the use of B between bilingual individuals could be very low.
    Keywords: Imperfect Information, Majority/Minority Language, Language Competition
    JEL: C72 D81
    Date: 2011–01–31
  11. By: Gerard van der Laan; Zaifu Yang
    Abstract: A number of heterogeneous items are to be sold to a group of potential bidders. Every bidder knows his own values over the items and his own budget privately. Due to budget constraint, bidders may not be able to pay up to their values. In such a market, a Walrasian equilibrium typically fails to exist and furthermore no existing allocation mechanism can tackle this case. We propose the notion of an `equilibrium under allotment' to such markets and develop an ascending auction mechanism that always finds such an equilibrium assignment and corresponding price system in finitely many rounds. The auction can be viewed as an appropriate and proper generalization of the ascending auction of Demange, Gale and Sotomayor from settings without financial constraints to settings with financial constraints. We examine various properties of the auction and its outcome.
    Keywords: Ascending auction, Financial constraint, Equilibrium under allotment.
    JEL: D44
    Date: 2011–02
  12. By: Lionel Richefort (Nantes-Atlantic Economics and Management Laboratory (LEMNA), University of Nantes – IEMN); Patrick Point (Research Group on Theoretical and Applied Economics (GREThA),University of Bordeaux 4 – CNRS)
    Abstract: A local public-good game played on directed networks is analyzed. The model is motivated by one-way flows of hydrological influence between cities of a river basin that may shape the level of their contribution to the conservation of wetlands. It is shown that in many (but not all) directed networks, there exists an equilibrium, sometimes socially desirable, in which some stakeholders exert maximal effort and the others free ride. It is also shown that more directed links are not always better. Finally, the model is applied to the conservation of wetlands in the Gironde estuary (France).
    Keywords: Common-pool Resource, Digraph, Cycle, Independent Set, Empirical Example
    JEL: C72 D85 H41
    Date: 2010–11
  13. By: SMEERS, Yves (CORE and School of Engineering (INMA), Université catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium); OGGIONI, Giorgia (University of Brescia, Department of Quantitative Methods, I-25122 Brescia, Italy); ALLEVI, Elisabetta (University of Brescia, Department of Quantitative Methods, I-25122 Brescia, Italy); SCHAIBLE, Siegfried (Chung Yuan Christian University, Department of Applied Mathematics, 32023 Chung-Li, Taiwan)
    Abstract: “Market Coupling” is currently seen as the most advanced market design in the restructuring of the European electricity market. Market coupling, by construction, introduces what is generally referred to as an incomplete market: it leaves several constraints out of the market and hence avoids pricing them. This may or may not have important consequences in practice depending on the case on hand. Quasi-Variational Inequality problems and the associated Generalized Nash Equilibrium can be used for representing incomplete markets. Recent papers propose methods for finding a set of solutions of Quasi-Variational Inequality problems. We apply one of these methods to a subproblem of market coupling namely the coordination of counter-trading. This problem is an illustration of a more general question encountered for instance in hierarchical planning in production management. We first discuss the economic interpretation of the Quasi-Variational Inequality problem. We then apply the algorithmic approach to a set of stylized case studies in order to illustrate the impact of different organizations of counter-trading. The paper emphazises the structuring of the problem. A companion paper considers the full problem of market coupling and counter-trading and presents a more extensive numerical analysis.
    Keywords: Generalized Nas Equilibrium, Quasi-Variational Inequalities, market coupling, counter-trading, European electricity market
    JEL: D52 D58 Q40
    Date: 2010–09–01
  14. By: LOPEZ-PINTADO, Dunia (Universidad Pablo de Olavide, Department of Economics, Sevilla, Spain; Université catholique de Louvain, CORE, B-1348 Louvain-la-Neuve, Belgium)
    Abstract: Some behaviors, ideas or technologies spread and become persistent in society, whereas others vanish. This paper analyzes the role of social influence in determining such distinct collective outcomes. Agents are assumed to acquire information from others through a certain sampling process that generates an influence network, and they use simple rules to decide whether to adopt or not depending on the observed sample. We characterize, as a function of the primitives of the model, the diffusion threshold (i.e., the spreading rate above which the adoption of the new behavior becomes persistent in the population) and the endemic state (i.e., the fraction of adopters in the stationary state of the dynamics). We find that the new behavior will easily spread in the population if there is a high correlation between how influential (visible) and how easily influenced an agent is, which is determined by the sampling process and the adoption rule. We also analyze how the density and variance of the out-degree distribution affect the diffusion threshold and the endemic state.
    Keywords: social influence, networks, diffusion threshold, endemic state
    JEL: C73 L14
    Date: 2010–12–01
  15. By: MAULEON, Ana (Facultés universitaires Saint-Louis, CEREC, B-1000 Brussels, Belgium and Université catholique de Louvain, CORE, B-1348 Louvain-la-Neuve, Belgium); VANNETELBOSCH, Vincent (Université catholique de Louvain, CORE, B-1348 Louvain-la-Neuve, Belgium); VERGARI, Cecilia (Department of Economic Sciences, University of Bologna, I-40125 Bologna, Italy)
    Abstract: We consider a model of licensing of a non-drastic innovation in which the patent holder (an outside innovator) negotiates either up-front fixed fees or per-unit royal- ties with two firms producing horizontally differentiated brands and competing à la Cournot. We investigate how licensing schemes (fixed fee or per-unit royalty) and the number of licenses sold (exclusive licensing or complete technology diffusion) affect price agreements and delays in reaching an agreement. We show that the patent holder prefers to license by means of up-front fixed fees except if market competition is mild and the innovation size is small. Once there is private information about the relative bargaining power of the parties, the patent holder may prefer licensing by means of per-unit royalties even if market competition is strong. Moreover, the delay in reaching an agreement is greater whenever the patent holder chooses to negotiate up-front fixed fees instead of per-unit royalties.
    Keywords: patent licensing, fixed fee, royalty, bargaining, private information
    JEL: C78 D43 D45 L13
    Date: 2010–12–01
  16. By: Corradi, Corrado; Corradi, Valentina
    Abstract: The note examines the susceptibility of envy-free variants of Knaster procedure to manipulations and collusions .
    Keywords: Steinhaus-Knaster procedure; auction; insincere bidding.
    JEL: C70
    Date: 2010–10
  17. By: Dietrich Franz; List Christian (METEOR)
    Abstract: Rational choice theory analyzes how an agent can rationally act, given his or her preferences, but says little about where those preferences come from. Instead, preferences are usually assumed to be .xed and exogenously given. We introduce a framework for conceptualizing preference formation and preference change. In our model, an agent.s preferences are based on certain .motivationally of the alternatives over which the preferences are held. Preferences may change as new properties of the alternatives become salient or previously salient ones cease to be so. We suggest that our approach captures endogenous preferences in various contexts, and helps to illuminate the distinction between formal and substantive concepts of rationality, as well as the role of perception in rational choice.
    Keywords: microeconomics ;
    Date: 2011
  18. By: CEULEMANS, Cédric (Université Libre de Bruxelles, ECARES, B-1050 Brussels, Belgium); GINSBURGH, Victor (Université Libre de Bruxelles, ECARES, B-1050 Brussels, Belgium and Université catholique de Louvain, CORE, B-1348 Louvain-la-Neuve, Belgium); LEGROS, Patrick (Université Libre de Bruxelles, ECARES, B-1050 Brussels, Belgium)
    Abstract: Members of a rock and roll band are endowed with different creativity. They match and eventually obtain credit for song writing as well as a share of the returns from sales. More creative members increase the probability of success but may also claim a larger share of the pie. In our theoretical model, the nature of matching (postive or negative assortative) as well as the covariation between the probability of having a “hit” and the dispersion of credits given to individual members are a function of the completeness of contracting. When members adopt a “gentleman’s agreement” to share credits equally, the covariation between the probability of a hit and the dispersion of credits is negative, which is the consequence of positive assortative matching in creativity. The data show that the relation between dispersion and success is significantly negative, and that rock bands are thus likely to sign incomplete contracts.
    Keywords: overlapping generations, resource management, common pool resource, spatial interdependence, strategic behaviour, cooperative behaviour
    JEL: H21 K11 Q20
    Date: 2010–11–01
  19. By: MAULEON, Ana (Facultés universitaires Saint-Louis, CEREC, B-1000 Brussels, Belgium and Université catholique de Louvain, CORE, B-1348 Louvain-la-Neuve, Belgium); VANNETELBOSCH, Vincent (Université catholique de Louvain, CORE, B-1348 Louvain-la-Neuve, Belgium); VERGARI, Cecilia (Department of Economic Sciences, University of Bologna, I-40125 Bologna, Italy)
    Abstract: We consider a model of wage determination with private information in a duopoly. We investigate the effects of unions having relative concerns on the negotiated wage and the strike activity. We show that an increase of unions' relative concerns has an ambiguous effect on the strike activity.
    Keywords: relative position, wage bargaining, private information, strike activity
    JEL: C70 J50 D60
    Date: 2010–12–01
  20. By: BRECHET, Thierry (Université catholique de Louvain, CORE and Chair Lhoist Berghmans in Environmental Eonomics and Management, B- 1348 Louvain-la-Neuve, Belgium); THENIE, Julien (Université catholique de Louvain, CORE and Chair Lhoist Berghmans in Environmental Eonomics and Management, B- 1348 Louvain-la-Neuve, Belgium; ORDECSYS Company, Chêne-Bougeries, Switzerland.); ZEIMES, Thibaut (Université catholique de Louvain, CORE and Chair Lhoist Berghmans in Environmental Eonomics and Management, B- 1348 Louvain-la-Neuve, Belgium); ZUBER, Stéphane (Université catholique de Louvain, CORE and Chair Lhoist Berghmans in Environmental Eonomics and Management, B- 1348 Louvain-la-Neuve, Belgium)
    Abstract: This article presents an analysis of the behavior of countries defining their climate policies in an uncertain context. The analysis is made using the S-CWS model, a stochastic version of an integrated assessment growth model. The model includes a stochastic definition of the climate sensitivity parameter. We show that the impact of uncertainty on policy design critically depends on the shape of the damage function. We also examine the benefits of cooperation in the context of uncertainty: we highlight the existence of an additional benefit of cooperation, namely risk reduction.
    Keywords: cooperation, uncertainty, climate change, integrated assessment model
    JEL: C71 C73 D9 D62 F42 Q2
    Date: 2010–10–01

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