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on Game Theory |
| By: | Duman, Papatya (Center for Mathematical Economics, Bielefeld University); Trockel, Walter (Center for Mathematical Economics, Bielefeld University) |
| Abstract: | We extend the analysis of van Damme (1987, Section 7.5) of the famous smoothing demand in Nash (1953) as an argument for the singular stability of the symmetric Nash bargaining solution among all Pareto efficient equilibria of the Nash demand game. Van Damme's analysis provides a clean mathematical framework where he substantiates Nash's conjecture by two fundamental theorems in which he proves that the Nash solution is among all Nash equilibria of the Nash demand game the only one that is *H*-essential. We show by generalizing this analysis that for any asymmetric Nash bargaining solution a similar stability property can be established that we call $H_{\alpha}$-essentiality. A special case of our result for α = 1/2 is $H_{1/2}$-essentiality that coincides with van Damme's *H*-essentiality. Our analysis deprives the symmetric Nash solution equilibrium of Nash's demand game of its exposed position and fortifies our conviction that, in contrast to the predominant view in the related literature, the only structural diffeerence between the asymmetric Nash solutions and the symmetric one is that the latter one is symmetric. While our proofs are mathematically straightforward given the analysis of van Damme (1987), our results change drastically the prevalent interpretation of Nash's smoothing of his demand game and dilute its conceptual importance. |
| Keywords: | 2-person bargaining games, α-symmetric Nash solution, Nash demand game, Nash soothing of games, $H_{\alpha}$-essential Nash equilibrium |
| Date: | 2020–02–17 |
| URL: | http://d.repec.org/n?u=RePEc:bie:wpaper:632&r=all |
| By: | Peter Csoka (Department of Finance, Corvinus University of Budapest and Centre for Economic and Regional Studies); Ferenc Illes (Department of Finance, Corvinus University of Budapest); Tamas Solymosi (Department of Operations Research and Actuarial Sciences, Corvinus University of Budapestand Centre for Economic and Regional Studies) |
| Abstract: | In a liability problem, the asset value of aninsolvent firm must be distributed among the creditors and the firm itself, when the firm has some freedom in negotiating with the creditors. We model the negotiations using cooperative game theory and analyze the Shapley value to resolve such liability problems. We establish three main monotonicity properties of the Shapley value. First, creditors can only benefit from the increase in their claims or of the asset value. Second, the firm can only benefit from the increase of a claim but can end up with more or with less if the asset value increases, depending on the configuration of small and large liabilities. Third, creditors with larger claims benefit more from the increase of the asset value.Even though liability games are constant-sum games and we show that the Shapley value can be calculated directly from a liability problem, we prove that calculating the Shapley payoff to the firm is NP-hard. |
| Keywords: | Game theory, Shapley value,constant-sum game,liability game,insolvency |
| JEL: | C71 C78 |
| Date: | 2020–01 |
| URL: | http://d.repec.org/n?u=RePEc:has:discpr:2001&r=all |
| By: | Hitoshi Matsushima (Faculty of Economics, The University of Tokyo) |
| Abstract: | I consider a new model of an infinitely repeated preemption game with random matching, termed the recurrent preemption game, wherein each player's discount factor depends on whether she wins the current game. This model describes sequential strategic technology adoptions in which a company becomes outdated by failing to maintain a position at the forefront of innovation. Assuming incomplete information about the presence of a rival, I clarify how the prominence of the innovator’s dilemma influences the degree of excessive competition in preemption. I also reveal interesting properties demonstrated by the unique symmetric Nash equilibrium of the recurrent preemption game. |
| URL: | http://d.repec.org/n?u=RePEc:tky:fseres:2020cf1143&r=all |
| By: | Zhengxing Zou (Vrije Universiteit Amsterdam); Rene van den Brink (Vrije Universiteit Amsterdam) |
| Abstract: | We introduce a family of proportional surplus division values for TU-games. Each value ï¬ rst assigns to each player a compromise between his stand-alone worth and the average stand-alone worths over all players, and then allocates the remaining worth among the players in proportion to their stand-alone worths. This family contains the proportional division value and the new egalitarian proportional surplus division value as two special cases. We provide characterizations for this family of values, as well as for each single value in this family. |
| Keywords: | Cooperative game, proportional value, surplus sharing, axiomatization, balanced contributions |
| JEL: | C71 |
| Date: | 2020–02–22 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20200014&r=all |
| By: | Enric Boix-Adser\`a; Benjamin L. Edelman; Siddhartha Jayanti |
| Abstract: | We initiate the study of the natural multiplayer generalization of the classic continuous Colonel Blotto game. The two-player Blotto game, introduced by Borel as a model of resource competition across $n$ simultaneous fronts, has been studied extensively for a century and seen numerous applications throughout the social sciences. Our work defines the multiplayer Colonel Blotto game and derives Nash equilibria for various settings of $k$ (number of players) and $n$. We also introduce a "Boolean" version of Blotto that becomes interesting in the multiplayer setting. The main technical difficulty of our work, as in the two-player theoretical literature, is the challenge of coupling various marginal distributions into a joint distribution satisfying a strict sum constraint. In contrast to previous works in the continuous setting, we derive our couplings algorithmically in the form of efficient sampling algorithms. |
| Date: | 2020–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2002.05240&r=all |
| By: | Agnes Cseh (Centre for Economic and Regional Studies, Institute of Economics); Tamas Fleiner (Centre for Economic and Regional Studies, Institute of Economics and Department of Computer Science and Information Theory, Budapest University of Technology and Economics); Petra Harjan (Department of Computer Science and Information Theory, Budapest University of Technology and Economics) |
| Abstract: | We tackle the problem of partitioning players into groups of fixed size, such as allocating eligible students to shared dormitory rooms. Each student submits preferences over the other individual students. We study several settings, which differ in the size of the rooms to be filled, the orderedness or completeness of the preferences, and the way of calculating the value of a coalition---based on the best or worst roommate in the coalition. In all cases, we determine the complexity of deciding the existence, and then finding a Pareto optimal assignment, and the complexity of verifying Pareto optimality for a given assignment. |
| Keywords: | Pareto-optimality, coalition, game theory |
| JEL: | C63 C78 |
| Date: | 2020–01 |
| URL: | http://d.repec.org/n?u=RePEc:has:discpr:2005&r=all |
| By: | Sam Ganzfried |
| Abstract: | We describe a new complete algorithm for computing Nash equilibrium in multiplayer general-sum games, based on a quadratically-constrained feasibility program formulation. We demonstrate that the algorithm runs significantly faster than the prior fastest complete algorithm on several game classes previously studied and that its runtimes even outperform the best incomplete algorithms. |
| Date: | 2020–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2002.04734&r=all |
| By: | Bettina Klaus; Panos Protopapas |
| Abstract: | We consider the problem of choosing a set of locations of a public good on the real line R when agents have single-peaked preferences over points. We ordinally extend preferences over compact subsets of R, and extend the results of Ching and Thomson (1996), Vohra (1999), and Klaus (2001) to choice correspondences. We show that eciency and replacement-dominance characterize the class of target point functions (Corollary 2) while eciency and population-monotonicity characterize the class of target set correspondences (Theorem 1). |
| Keywords: | single-peaked preferences; population-monotonicity; replacement-dominance; target point functions, target set correspondences |
| JEL: | C71 D63 D78 H41 |
| Date: | 2020–02 |
| URL: | http://d.repec.org/n?u=RePEc:lau:crdeep:20.02&r=all |
| By: | Dirk Bergemann (Cowles Foundation, Yale University); Francisco Castro (Anderson School of Management, UCLA); Gabriel Weintraub (Graduate School of Business, Stanford University) |
| Abstract: | We compare the revenue of the optimal third-degree price discrimination policy against a uniform pricing policy. A uniform pricing policy offers the same price to all segments of the market. Our main result establishes that for a broad class of third-degree price discrimination problems with concave revenue functions and common support, a uniform price is guaranteed to achieve one-half of the optimal monopoly proï¬ ts. This revenue bound holds for any arbitrary number of segments and prices that the seller would use in case he would engage in third-degree price discrimination. We further establish that these conditions are tight and that a weakening of common support or concavity leads to arbitrarily poor revenue comparisons. |
| Keywords: | First Degree Price Discrimination, Third Degree Price Discrimination, Uniform Price, Approximation, Concave Demand Function, Market Segmentation |
| JEL: | C72 D82 D83 |
| Date: | 2019–12 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:2213r&r=all |
| By: | Joan Esteban (Institut d'AnaÌ€lisi EconoÌ mica, CSIC and BGSE); Sabine Flamand (Universitat Rovira i Virgili and CREIP); Massimo Morelli (Bocconi University, CEPR, IGIER and Dondena); Dominic Rohner (University of Lausanne and CEPR) |
| Abstract: | This paper builds a dynamic theory of secessions, conflictual or peaceful, analyzing the forward looking interaction between groups in a country. The proposed framework allows us to jointly address several key stylized facts on secession, and generates several novel predictions. We find that if a group out of power is small enough, then the group in power can always maintain peace with an acceptable offer of surplus sharing for every period, while when there is a mismatch between the relative size and the relative surplus contribution of the minority group, conflict followed by secession can occur. Accepted peaceful secession is predicted for large groups of similar prosperity, and higher patience is associated to a higher chance of secession. We formulate as a result a number of policy recommendations on various dimensions of federalism and other institutions. |
| Keywords: | Secessions, Conflict, Surplus Sharing, Mismatch JEL Classification: C7, D74 |
| Date: | 2018–09 |
| URL: | http://d.repec.org/n?u=RePEc:hic:wpaper:276&r=all |
| By: | Marleen Marra (Département d'économie) |
| Abstract: | This paper presents, solves, and estimates the first structural auction model with seller selection. This allows me to quantify network effects arising from endogenous bidder and seller entry into auction platforms, facilitating the estimation of theoretically ambiguous fee impacts by tracing them through the game. Relevant model primitives are identified from variation in second-highest bids and reserve prices. My estimator builds off the discrete choice literature to address the double nested fixed point characterization of the entry equilibrium. Using new wine auction data, I estimate that this platform’s revenues increase up to 60% when introducing a bidder discount and simultaneously increasing seller fees. More bidders enter when the platform is populated with lower-reserve setting sellers, driving up prices. Moreover, I show that meaningful antitrust damages can be estimated in a platform setting despite this two-sidedness. |
| Keywords: | Auctions with entry; Two-sided markets; Nonparametric identification; Estimation; Nested fixed point |
| JEL: | D44 C52 C57 L81 |
| Date: | 2019–12 |
| URL: | http://d.repec.org/n?u=RePEc:spo:wpmain:info:hdl:2441/5kht5rc22p99sq5tol4efe4ssb&r=all |
| By: | Zachary Schaller; Stergios Skaperdas |
| Abstract: | We examine settings - such as litigation, labor relations, or arming and war - in which players first make non-contractible up-front investments to improve their bargaining position and gain advantage for possible future conflict. Bargaining is efficient ex post, but we show that a player may prefer Conflict ex ante if there are sufficient asymmetries in strength. There are two sources of this finding. First, up-front investments are more dissimilar between players under Conflict, and they are lower than under Bargaining when one player is much stronger than the other. Second, the probability of the stronger player winning in Conflict is higher than the share received under Nash bargaining. We thus provide a rationale for conflict to occur under complete information that does not depend on long-term commitment problems. Greater balance in institutional support for different sides is more likely to maintain peace and settlements. |
| Keywords: | power asymmetries, war, litigation, contests |
| JEL: | C70 D74 J53 K41 |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_8030&r=all |
| By: | Francisco Cabo (Universitad de Valladolid); Mabel Tidball (CEE-M - Centre d'Economie de l'Environnement - Montpellier - FRE2010 - INRA - Institut National de la Recherche Agronomique - UM - Université de Montpellier - CNRS - Centre National de la Recherche Scientifique - Montpellier SupAgro - Institut national d’études supérieures agronomiques de Montpellier) |
| Abstract: | We analyze a dynamic environmental agreement between two regions. We assume that the agreement is jointly protable, because the eort associated with emission reductions is overcompensated by a cleaner environment in the future The two regions are asymmetric in two respects: their value of a cleaner environment is dierent, and they are responsible for the initial environmental problem in dierent ways. Because the benets of a cleaner environment cannot be transferred, we propose a mechanism on how to share the eorts of lowering current emissions, satisfying two main properties. The rst property is a benets pay principle: the greater one region's relative benet from cooperation, the greater must be its relative contribution. The second property is, a polluter pay principle: a region's relative contribution increases with its responsibility. Moreover, the sharing scheme must be time consistent. At any intermediate time, no country can do better by deviating from cooperation. * |
| Keywords: | Cooperative dierential game,Distribution procedure,Time consistency,Polluter pay principle,Benets pay principle |
| Date: | 2020 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-02462071&r=all |
| By: | Bahel, Eric; Gómez-Rúa, María; Vidal-Puga, Juan |
| Abstract: | We study three remarkable cost sharing rules in the context of shortest path problems, where agents have demands that can only be supplied by a source in a network. The demander rule requires each demander to pay the cost of their cheapest connection to the source. The supplier rule charges to each demander the cost of the second-cheapest connection and splits the excess payment equally between her access suppliers. The alexia rule averages out the lexicographic allocations, each of which allows suppliers to extract rent in some pre-specified order. We show that all three rules are anonymous and demand-additive core selections. Moreover, with three or more agents, the demander rule is characterized by core selection and a specific version of cost additivity. Finally, convex combinations of the demander rule and the supplier rule are axiomatized using core selection, a second version of cost additivity and two additional axioms that ensure the fair compensation of intermediaries. |
| Keywords: | Shortest path, cost sharing, core selection, additivity. |
| JEL: | C71 D85 |
| Date: | 2020–01 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:98504&r=all |
| By: | Fabio Galeotti (GATE Lyon Saint-Étienne - Groupe d'analyse et de théorie économique - ENS Lyon - École normale supérieure - Lyon - UL2 - Université Lumière - Lyon 2 - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - UJM - Université Jean Monnet [Saint-Étienne] - Université de Lyon - CNRS - Centre National de la Recherche Scientifique); Maria Montero (UON - University of Nottingham, UK); Anders Poulsen (UEA - University of East Anglia [Norwich]) |
| Abstract: | The Attraction Effect and Compromise Effect (AE and CE) were introduced for individual choice situations. We define and experimentally investigate the AE and CE for bargaining situations. Our data suggest that the AE and CE are significant in bargaining, when certain conditions, related to focal equilibrium selection criteria based on payoff equality, efficiency, and symmetry, are met. |
| Keywords: | Bargaining,attraction effect,compromise effect,focality,equality,efficiency,symmetry |
| Date: | 2020–02–04 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:halshs-02466032&r=all |