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on Game Theory |
| By: | Eric Hoffmann (Department of Economics, The University of Kansas); Tarun Sabarwal (Department of Economics, University of Kansas) |
| Abstract: | In a 2007 paper, “A global game with strategic substitutes and complements”, by Karp, L., I.H. Lee, and R. Mason, Games and Economic Behavior, 60(1), 155-175, an argument is made to show existence of Bayesian-Nash equilibrim in global games that may include both strategic substitutes and complements. This note documents a gap in the proof of that statement and presents an alternative proof for a finite player version of their model. |
| Keywords: | Global games, strategic complements, strategic substitutes, monotone games, equilibrium selection |
| JEL: | C70 C72 |
| Date: | 2015–03 |
| URL: | http://d.repec.org/n?u=RePEc:kan:wpaper:201409&r=gth |
| By: | Sylvain Béal (CRESE, Université de Franche-Comté); Eric Rémila (Université de Saint-Etienne, CNRS UMR 5824 GATE Lyon Saint-Etienne); Philippe Solal (Université de Saint-Etienne, CNRS UMR 5824 GATE Lyon Saint-Etienne) |
| Abstract: | A new class of allocation rules combining marginalistic and egalitarian principles is introduced for cooperative TU-games. It includes some modes of solidarity among the players by taking the collective contribution of some coalitions to the grand coalition into account. Relationships with other class of allocation rules such as the Egalitarian Shapley values and the Procedural values are discussed. Two axiomatic characterizations are provided: one of the whole class of allocation rules, and one of each of its extreme points. |
| Keywords: | TU-games, Solidarity, null player, Egalitarian Shapley value, Procedural values. |
| JEL: | C71 |
| Date: | 2015–03 |
| URL: | http://d.repec.org/n?u=RePEc:crb:wpaper:2015-03&r=gth |
| By: | Olaizola Ortega, María Norma; Valenciano Llovera, Federico |
| Keywords: | network formation, unilateral link-formation, bilateral link-formation, efficiency, stability |
| JEL: | A14 C72 D20 J00 |
| Date: | 2015–02–17 |
| URL: | http://d.repec.org/n?u=RePEc:ehu:ikerla:14746&r=gth |
| By: | Cano Berlanga, Sebastian; Giménez Gómez, José M. (José Manuel); Vilella Bach, Misericòrdia |
| Abstract: | This paper focuses on cooperative games with transferable utility. We propose the computation of two solutions, the Shapley value for n agents and the nucleolus with a maximum of four agents. The current approach is also focused on conflicting claims problems, a particular case of coalitional games. We provide the computation of the most well-known and used claims solutions: the proportional, the constrained equal awards, the constrained equal losses, the Talmud and the random arrival rules. Keywords: Cooperative game, Shapley value, nucleolus, claims problem, claims rule, bankruptcy. |
| Keywords: | Jocs cooperatius, 33 - Economia, |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:urv:wpaper:2072/247653&r=gth |
| By: | Alcalde, José; Romero-Medina, Antonio |
| Abstract: | This paper provides an `escape route' from the efficiency-equity trade-off in the School Choice problem. We achieve our objective by presenting a weak notion of fairness, called τ-fairness, which is always satisfied by some allocation. Then, we propose the adoption of the Student Optimal Compensating Exchange mechanism, a procedure that assigns a τ-fair allocation to each problem. We further identify a condition on students' preferences guaranteeing incentive compatibility of this mechanism. |
| Keywords: | School Choice Problem, Fair Matching, Top Dominance Condition, Strategy-Proofness |
| JEL: | C78 D63 I28 |
| Date: | 2015–03–13 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:62831&r=gth |
| By: | Karsten, Frank; Slikker, M. (Tilburg University, Center For Economic Research); Borm, P.E.M. (Tilburg University, Center For Economic Research) |
| Abstract: | Many cooperative games, especially ones stemming from resource pooling in<br/>queuing or inventory systems, are based on situations in which each player is associated with a single attribute (a real number representing, say, a demand) and in which the cost to optimally serve any sum of attributes is described by an elastic function (which means that the per-demand cost is non-increasing in the total demand served). For this class of situations, we introduce and analyze several cost allocation rules: the proportional rule, the serial cost sharing rule, the benefit-proportional rule, and various Shapley-esque rules. We study their appeal with regard to fairness criteria such as coalitional rationality, benefit ordering, and relaxations thereof. After showing the impossibility of combining coalitional rationality and benefit ordering, we show for each of the cost allocation rules which fairness criteria it satisfies. |
| Keywords: | game/group decisions; cooperative mathematics; convexity, inventory/production; applications, gueues; applications |
| JEL: | D74 D71 |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:tiu:tiucen:e6c6ce3e-6168-40b2-bf64-04ed197e7871&r=gth |
| By: | Olga Gorelkina (Max Planck Institute for Research on Collective Goods, Bonn) |
| Abstract: | Mechanism design theory strongly relies on the concept of Nash equilibrium. However, studies of experimental games show that Nash equilibria are rarely played and that subjects may be thinking only a finite number of iterations. We study one of the most influential benchmarks of mechanism design theory, the expected externality mechanism (D’Aspremont, Gerard-Varet, 1979) in a finite-depth environment described by the Lk model. While efficient implementation fails under certain conditions, our results provide a vindication of the mechanism in the convex quasi-linear environment with finitely-rational agents. |
| Keywords: | Bounded Rationality, Expected externality, externality mechanisms, Level-K |
| JEL: | D71 D82 C72 |
| Date: | 2015–01 |
| URL: | http://d.repec.org/n?u=RePEc:mpg:wpaper:2015_03&r=gth |
| By: | Kai A. Konrad; Florian Morath |
| Abstract: | This paper considers evolutionarily stable strategies (ESS) in a take-it-or-leave-it offer bargaining game with incomplete information. We find responders reject offers which yield a higher positive material payoff than their outside option. Proposers, in turn, make more attractive offers than in the perfect Bayesian equilibrium. Efficiency-enhancing trade may break down even when the responder has no private information. Overall, the probability of trade and ex post efficiency is lower in the ESS equilibrium than in the corresponding perfect Bayesian equilibrium. The results are observationally equivalent to behavioral explanations such as in-group favoritism and a preference for punishing selfish proposers but are driven by concerns about relative material payoff infinite populations. |
| Keywords: | Evolutionary stability, Finite population, Take-it-or-leave-it offer bargaining, Asymmetric information |
| JEL: | C73 C78 D82 |
| Date: | 2014–09 |
| URL: | http://d.repec.org/n?u=RePEc:mpi:wpaper:tax-mpg-rps-2014-16&r=gth |
| By: | Gómez-Rúa, María; Vidal-Puga, Juan |
| Abstract: | We present a new model for cost sharing in minimum cost spanning tree problems, so that the planner can identify the agents that merge. Under this new framework, and as opposed to the traditional model, there exist rules that satisfy merge-proofness. Besides, by strengthening this property and adding some other properties, such as population-monotonicity and solidarity, we characterize a unique rule that coincides with the weighted Shapley value of an associated cost game. |
| Keywords: | Minimum cost spanning tree problems, cost sharing, core selection, cost-monotonicity, merge-proofness, weighted Shapley value. |
| JEL: | C71 D61 D63 D7 |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:62923&r=gth |
| By: | Fabrizio Germano; Peio Zuazo-Garin |
| Abstract: | Economic predictions are highly sensitive to model and informational specifications. Weinstein and Yildiz (2007) show that, in static games with incomplete information, only very weak predictions, namely, the interim correlated rationalizable (ICR) actions, are robust to higher-order belief misspecifications. This paper extends their robustness analysis to allow for higher-order uncertainty about rationality. We introduce interim correlated p-rationalizability (ICRp) as a solution concept for games with incomplete information. We first confirm the robustness of the ICR predictions to small departures from common belief in rationality by showing the continuity of ICRp actions at p = 1, where they coincide with ICR. At the same time, we show that Weinstein and Yildiz's (2007) deeper results on the structure of rationalizability, most notably, their discontinuity and generic local uniqueness properties, fail as soon as any arbitrarily small amount of higher-order uncertainty about rationality is introduced. Thus, we find that common belief in rationality is a necessary condition for Weinstein and Yildiz's (2007) discontinuity property to hold. Among other things, this reveals the diminishing strategic impact of higher-order belief constraints. |
| Keywords: | robustness, rationalizability, uncertain rationality, incomplete information, belief hierarchies |
| JEL: | C72 D82 D83 |
| Date: | 2015–02 |
| URL: | http://d.repec.org/n?u=RePEc:bge:wpaper:814&r=gth |
| By: | Takafumi Yamakawa (Osaka University); Yoshitaka Okano (School of Economics and Management, Kochi University of Technology); Tatsuyoshi Saijo (School of Economics and Management, Kochi University of Technology) |
| Abstract: | This study clarifies the types of motives that are important as a source of cooperation in a linear public goods experiment. Our experimental design separates the contributions due to confusion, one-shot motives (which includes altruism, warm-glow, inequality aversion, and conditional cooperation), and multi-round motives (which includes a strategic motive under incomplete information, a failure of backward induction, and reciprocity). The experiment reveals that multi-round motives plays an important role in driving cooperative behavior. Confusion and one-shot motives play a minor role. |
| Keywords: | Cooperation, Motives, Public goods |
| JEL: | C72 C92 H41 |
| Date: | 2015–03 |
| URL: | http://d.repec.org/n?u=RePEc:kch:wpaper:sdes-2015-15&r=gth |
| By: | Dridi, Dhouha; Ben Youssef, Slim |
| Abstract: | Game theory is a relevant and powerful tool for analyzing strategic interactions in a supply chain in which the decision of each player affect the payoff of other players. In order to relax the classical two supply chain members’ situation to a three supply chain members’ situation and to integrate the problem of competition at retail level, we consider a supply chain consisting of a monopolistic manufacturer and two duopolistic retailers. The latter two are geographically related. Our paper examines the optimal decisions on advertising (local, national and cooperative advertising) in a centralized and a decentralized supply chain using Stackelberg – Cournot game, Stackelberg - Collusion game and Cooperative games, and we investigate the impact of the existing of competition at retail level, the retailer coalition and the cooperation between all supply chain members’ on the channel members’ optimal decisions, on the sales volume and on the profits. Applying the equilibrium analysis and using numerical example, comparing results indicates that all advertising, the sales volume of each member and the total profit in the centralized decision-making are larger than those in the decentralized decision-making. Retailer coalition harms themselves (in terms of profit) despite the increasing of sales, but is beneficial to the manufacturer. We identify also the feasible solutions of the best cooperative advertising scheme that members are interesting in cooperation. |
| Keywords: | Game theory; Cooperative advertising; Supply chain coordination; Retail competition, retail coalition |
| JEL: | C7 M3 |
| Date: | 2015–03–08 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:62697&r=gth |
| By: | Luisa Herbst; Kai A. Konrad; Florian Morath |
| Abstract: | We study the role of an imbalance in fighting strengths when players bargain in the shadow of conflict. Our experimental results suggest: In a simple bargaining game with an exogenous mediation proposal, the likelihood of conflict is independent of the balance of power. If bargaining involves endogenous demand choices, however, the likelihood of conflict is higher if power is more imbalanced. Even though endogenous bargaining outcomes reflect the players unequal fighting strengths, strategic uncertainty causes outcomes to be most efficient when power is balanced. In turn, the importance of exogenous mediation proposals depends on the balance of power. |
| Keywords: | Conflict, balance of power, contest, bargaining, Nash demand game, conflict resolution, asymmetries, experiment |
| JEL: | C78 C91 D72 D74 |
| Date: | 2014–07 |
| URL: | http://d.repec.org/n?u=RePEc:mpi:wpaper:tax-mpg-rps-2014-13_2&r=gth |
| By: | Tatsuyoshi Saijo (School of Management, Kochi University of Technology) |
| Abstract: | This paper proposes an alternative explanation for the sandwich property in voluntary contribution mechanism experiments. This property refers to the phenomenon of experimental data being ``sandwiched'' between a Nash equilibrium above the midpoint of the endowment and a Nash equilibrium below this midpoint. The explanation is in terms of the instability of the system with best response dynamics, i.e., ``pulsing'' behaviors, in nonlinear environments rather than the quantal response equilibrium analysis. Since most experimental models are unstable in quasilinear environments (where the utility function is linear in a private good and nonlinear in a public good), and Cobb–Douglas environments, using equilibrium analysis is problematic. |
| JEL: | C62 C72 C92 H41 |
| Date: | 2015–03 |
| URL: | http://d.repec.org/n?u=RePEc:kch:wpaper:sdes-2015-13&r=gth |
| By: | Sylvain Béal (CRESE, Université de Franche-Comté); André Casajus (Economics and Information Systems, HHL Leipzig Graduate School of Management and LSI Leipziger Spieltheoretisches Institut, Leipzig, Germany); Frank Huettner (Economics and Information Systems, HHL Leipzig Graduate School of Management and LSI Leipziger Spieltheoretisches Institut, Leipzig, Germany) |
| Abstract: | We study values for transferable utility games enriched by a communication graph. The most well-known such values are component-efficient and characterized by some link-deletion property. We study efficient extensions of such values: for a given component-efficient value, we look for a value that (i) satisfies efficiency, (ii) satisfies the link-deletion property underlying the original component-efficient value, and (iii) coincides with the original component-efficient value whenever the underlying graph is connected. Béal, Casajus and Huettner (forthcoming, Scoail Choice and Welfare) prove that the Myerson value (Myerson, 1977) admits a unique efficient extension, which has been introduced by van den Brink, van der Laan and Khmelnitskaya (2012). We pursue this line of research by showing that the average tree solution (Herings, van der Laan and Talman, 2008) and the compensation solution (Béal, Rémila and Solal, 2012) admit similar unique efficient extensions, and that there exists no efficient extension of the position Value (Meessen, 1988, Borm, Owen and Tijs, 1992). As byproducts, we obtain new characterizations of the average tree solution and the compensation solution, and of their efficient extensions. |
| Keywords: | Efficient extension, average tree solution, compensation solution, position value, component fairness, relative fairness, balanced total threats, Myerson value, component-wise egalitarian solution |
| JEL: | C71 |
| Date: | 2015–03 |
| URL: | http://d.repec.org/n?u=RePEc:crb:wpaper:2015-04&r=gth |
| By: | Noldeke, Georg (University of Basel); Larry Samuelson (Cowles Foundation, Yale University) |
| Abstract: | We use the theory of abstract convexity to study adverse-selection principal-agent problems and two-sided matching problems, departing from much of the literature by not requiring quasilinear utility. We formulate and characterize a basic underlying implementation duality. We show how this duality can be used to obtain a sharpening of the taxation principle, to obtain a general existence result for solutions to the principal-agent problem, to show that (just as in the quasilinear case) all increasing decision functions are implementable under a single crossing condition, and to obtain an existence result for stable outcomes featuring positive assortative matching in a matching model. |
| Keywords: | Implementation, Duality, Galois connection, Imperfectly transferable utility, Principal-agent model, Two-sided matching |
| JEL: | C62 C78 D82 D86 |
| Date: | 2015–03 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:1993&r=gth |
| By: | Luisito Bertinelli (CREA, Université de Luxembourg); Amer Tabakovic (CREA, Université de Luxembourg); Luca Marchiori (Central Bank of Luxembourg); Benteng Zou (CREA, Université de Luxembourg) |
| Abstract: | The present study explores the strategic interactions of countries setting pollution abatement policies in a dynamic two-player game. To reach a common target of environmental quality, countries can choose to commit to a stream of pollution abate- ment right from the beginning of the game or decide upon abatement at each moment in time. Most of the literature studies homogenous strategies, where no country or all countries commit to a (same) predefined policy. The main novelty of this paper resides in the introduction of heterogeneous strategies, where only one country commits to a specific abatement policy and which is actually the kind of strategic behavior currently observed among large pollution nations. We find that the pollution level can be lower under heterogeneous than under homogenous strategies. A stringent environmental quality target will induce the committed player to produce an abatement effort that more than compensates the free-riding attitude of the non-committed player. |
| Keywords: | Heterogeneous strategies, differential games, transboundary pollution, abatement. |
| JEL: | Q55 C61 Q59 |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:luc:wpaper:15-02&r=gth |
| By: | Daniel Kaimann (University of Paderborn) |
| Abstract: | Depending on which combination of factors is used in empirical analyses, regression results lead to varying levels of significance or even insignificance and, consequently, to inconsistent results. Linear algebra and linear regression models are apparently not able to analyze complex causal structures in dynamic markets. Boolean algebra, qualitative comparative analysis (QCA) and the game theoretical-based model of the Shapley value could be more suitable for covering dynamic market structures and, consequently, for helping us to understand what significantly affects complex cause-effect relationships. Using proprietary data from the volatile motion-picture industry, we show that a segmentation and brand extension strategy are sufficient for achieving high market performance and that certain conditions (e.g., production budget, critic reviews and brand extension products) appear particularly appropriate for gaining a competitive advantage. |
| Keywords: | Dynamic markets, Qualitative comparative analysis, Shapley value, Motion-Picture economics |
| JEL: | C18 C71 L10 L82 |
| Date: | 2014–08 |
| URL: | http://d.repec.org/n?u=RePEc:pdn:dispap:12&r=gth |