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on Game Theory |
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Issue of 2011‒08‒02
fourteen papers chosen by Laszlo A. Koczy Hungarian Academy of Sciences and Obuda University |
| By: | Dinko Dimitrov (Chair of Economic Theory, Saarland University); Shao Chin Sung (Department of Industrial and Systems Engineering, Aoyama Gakuin University) |
| Abstract: | We show that the core of each strongly size monotonic hedonic game is not empty and is externally stable. This is in sharp contrast to other sufficient conditions for core non-emptiness which do not even guarantee the existence of a stable set in such games. |
| Keywords: | Core, Hedonic Games, Monotonicity, Stable Sets |
| JEL: | C71 |
| Date: | 2011–07 |
| URL: | http://d.repec.org/n?u=RePEc:fem:femwpa:2011.52&r=gth |
| By: | Dongshuang Hou (Department of Applied Mathematics [Twente] - University of Twente); Theo Driessen (Department of Applied Mathematics [Twente] - University of Twente); Aymeric Lardon (GATE Lyon Saint-Etienne - Groupe d'analyse et de théorie économique - CNRS : UMR5824 - Université Lumière - Lyon II - École Normale Supérieure de Lyon) |
| Abstract: | The Bertrand Oligopoly situation with Shubik's demand functions is modelled as a cooperative TU game. For that purpose two optimization problems are solved to arrive at the description of the worth of any coalition in the so-called Bertrand Oligopoly Game. Under certain circumstances, this Bertrand oligopoly game has clear affinities with the well-known notion in statistics called variance with respect to the distinct marginal costs. This Bertrand Oligopoly Game is shown to be totally balanced, but fails to be convex unless all the firms have the same marginal costs. Under the complementary circumstances, the Bertrand Oligopoly Game is shown to be convex and in addition, its Shapley value is fully determined on the basis of linearity applied to an appealing decomposition of the Bertrand Oligopoly Game into the difference between two convex games, besides two nonessential games. One of these two essential games concerns the square of one non- essential game. |
| Keywords: | Bertrand Oligopoly situation, Bertrand Oligopoly Game, Convexity, Shapley Value, Total Balancedness. |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:halshs-00610838&r=gth |
| By: | Theo Driessen (Department of Applied Mathematics [Twente] - University of Twente); Dongshuang Hou (Department of Applied Mathematics [Twente] - University of Twente); Aymeric Lardon (GATE Lyon Saint-Etienne - Groupe d'analyse et de théorie économique - CNRS : UMR5824 - Université Lumière - Lyon II - École Normale Supérieure de Lyon) |
| Abstract: | In this article we consider Stackelberg oligopoly TU-games in gamma-characteristic function form (Chander and Tulkens 1997) in which any deviating coalition produces an output at a first period as a leader and outsiders simultaneously and independently play a quantity at a second period as followers. We assume that the inverse demand function is linear and that firms operate at constant but possibly distinct marginal costs. Generally speaking, for any TU-game we show that the 1-concavity property of its dual game is a necessary and sufficient condition under which the core of the initial game is non-empty and coincides with the set of imputations. The dual game of a Stackelberg oligopoly TU-game is of great interest since it describes the marginal contribution of followers to join the grand coalition by turning leaders. The aim is to provide a necessary and sufficient condition which ensures that the dual game of a Stackelberg oligopoly TU-game satisfies the 1-concavity property. Moreover, we prove that this condition depends on the heterogeneity of firms' marginal costs, i.e., the dual game is 1-concave if and only if firms' marginal costs are not too heterogeneous. This last result extends Marini and Currarini's core non-emptiness result (2003) for oligopoly situations. |
| Keywords: | Stackelberg oligopoly TU-game; Dual game; 1-concavity |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:halshs-00610840&r=gth |
| By: | Lombardi, Michele; Yoshihara, Naoki |
| Abstract: | This paper studies implementation problems in the wake of a recent trend of implementation of non-consequentialist nature, which draws on the evidence taken from experimental and behavioral economics. Specifically, following the seminal works by Matsushima (2008) and Dutta and Sen (2009), the paper considers implementation problems with partially-honest agents, which presume that there is at least one individual in society who concerns herself with not only outcomes but also honest behavior at least in a limited manner. Given this setting, the paper provides a general characterization of Nash implementation with partially-honest individuals. It also provides the necessary and sufficient condition for Nash implementation with partially-honest individuals by mechanisms with some types of strategy-space reductions. As a consequence, it shows that in contrast to the case of the standard framework, the equivalence between Nash implementation and Nash implementation with strategy space reduction no longer holds. |
| Keywords: | Nash implementation, canonical-mechanisms, s-mechanisms, self-relevant mechanisms, partial-honesty, permissive results |
| JEL: | C72 D71 |
| Date: | 2011–07 |
| URL: | http://d.repec.org/n?u=RePEc:hit:ccesdp:43&r=gth |
| By: | Rothe, Jorn |
| Abstract: | This paper formulates a rationality concept for extensive games in which deviations from rational play are interpreted as evidence of irrationality. Instead of confirming some prior belief about the nature of nonrational play, we assume that such a deviation leads to genuine uncertainty. Assuming complete ignorance about the nature of non-rational play and extreme uncertainty aversion of the rational players, we formulate an equilibrium concept on the basis of Choquet expected utility theory. Equilibrium reasoning is thus only applied on the equilibrium path, maximin reasoning applies off the equilibrium path. The equilibrium path itself is endogenously determined. In general this leads to strategy profiles differ qualitatively from sequential equilibria, but still satisfy equilibrium and perfection requirements. In the centipede game and the finitely repeated prisoners’ dilemma this approach can also resolve the backward induction paradox. |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:ner:lselon:http://eprints.lse.ac.uk/37541/&r=gth |
| By: | Martins-da-Rocha, Victor Filipe; Yannelis, Nicholas C. |
| Abstract: | We prove non-emptiness of the alpha-core for balanced games with non-ordered preferences, extending and generalizing in several aspects the results of Scarf (1971), Border (1984), Florenzano (1989), Yannelis (1991) and Kajii (1992). In particular we answer an open question in Kajii (1992) regarding the applicability of the non-emptiness results to models with infinite dimensional strategy spaces. We provide two models with Knightian and voting preferences for which the results of Scarf (1971) and Kajii (1992) cannot be applied while our non-emptiness result applies. |
| Date: | 2011–05–06 |
| URL: | http://d.repec.org/n?u=RePEc:fgv:epgewp:716&r=gth |
| By: | Ahmad Naimzada (University of Milano-Bicocca); Fabio Tramontana (Department of Economics and Quantitative Methods, University of Pavia) |
| Abstract: | We move from a triopoly game with heterogeneous players (E.M.Elabassy et al., 2009. Analysis of nonlinear triopoly game with heterogeneous players. Computers and Mathematics with Applications 57, 488-499). We remove the nonlinearity from the cost function and introduce it in the demand function. We also introduce a different decisional mechanism for one of the three competitors. A double route to complex dynamics is shown to exist, together with the possibility of multistability of different attractors, requiring a global analysis of the dynamical system. |
| Keywords: | Triopoly game; Heterogeneous players; Global analysis |
| Date: | 2011–06 |
| URL: | http://d.repec.org/n?u=RePEc:pav:wpaper:272&r=gth |
| By: | Lars Peter Metzger |
| Abstract: | Second price allpay auctions (wars of attritions) have an evolutionarily stable equilibrium in pure strategies if valuations are private information. I show that for any level of uncertainty there exists a pure deviation strategy close to the equilibrium strategy such that for some valuations the equilibrium strategy has a selective disadvantage against the deviation if the population mainly plays the deviation strategy. There is no deviation strategy with this destabilizing property for all valuations if the distribution of valuations has a monotonic hazard rate. I argue that in the Bayesian game studied here, a mass deviation can be caused by the entry of a small group of agents. Numeric calculations indicate that the closer the deviation strategy to the equilibrium strategy, the less valuations are destabilizing. I show that the equilibrium strategy does not satisfy continuous stability. |
| Keywords: | Continuous Strategies, Evolutionary Stability, War of Attrition, Strict Equilibrium, Neighborhood Invader Strategy, Continuous Stability, Evolutionary Robustness |
| JEL: | C72 C73 D44 |
| Date: | 2011–07 |
| URL: | http://d.repec.org/n?u=RePEc:bon:bonedp:bgse09_2011&r=gth |
| By: | Gerdes, Christer (SOFI, Stockholm University); Gränsmark, Patrik (SOFI, Stockholm University); Rosholm, Michael (Aarhus School of Business) |
| Abstract: | We examine rational learning among expert chess players and how they update their beliefs in repeated games with the same opponent. We present a model that explains how equilibrium play is affected when players change their choice of strategy when receiving additional information from each encounter. We employ a large international panel dataset with controls for risk preferences and playing skills whereby the latter accounts for ability. Although expert chess players are intelligent, productive and equipped with adequate data and specialized computer programs, we find large learning effects. Moreover, as predicted by the model, risk-averse players learn substantially faster. |
| Keywords: | rational learning, risk aversion, beliefs |
| JEL: | C73 D83 |
| Date: | 2011–07 |
| URL: | http://d.repec.org/n?u=RePEc:iza:izadps:dp5862&r=gth |
| By: | George J. Mailath (Dept. of Economics, University of Pennsylvania); Andrew Postlewaite (Dept. of Economics, University of Pennsylvania); Larry Samuelson (Cowles Foundation, Yale University) |
| Abstract: | Different markets are cleared by different types of prices -- seller-specific prices that are uniform across buyers in some markets, and personalized prices tailored to the buyer in others. We examine a setting in which buyers and sellers make investments before matching in a competitive market. We introduce the notion of premuneration values -- the values to the transacting agents prior to any transfers -- created by a buyer-seller match. Personalized price equilibrium outcomes are independent of premuneration values and exhibit inefficiencies only in the event of "coordination failures," while uniform-price equilibria depend on premuneration values and in general feature inefficient investments even without coordination failures. There is thus a trade-off between the costs of personalizing prices and the inefficient investments under uniform prices. We characterize the premuneration values under which uniform-price equilibria similarly exhibit inefficiencies only in the event of coordination failures. |
| Keywords: | Directed search, Matching, Premuneration value, Prematch investments, Search |
| JEL: | C78 D40 D41 D50 D83 |
| Date: | 2011–07 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:1810&r=gth |
| By: | Omar J. Casas; Rosario Romera |
| Abstract: | This paper provides a formulation of a stochastic dynamic game that arise in the real scenario of international environmental agreements on the transnational pollution control. More specifically, this agreements try to reduce the environmental damage caused by the stock pollutant that accumulates in the atmosphere, such as CO2. To improve the non-cooperative equilibrium among countries, we propose the criteria of the minimization of the expected discounted total cost with monetary transfers between the countries involved as an incentive to cooperation. Moreover, it considers the formulation of Stochastic Dynamic Games as Markov Decision Processes, using tools of Stochastic Optimal Control and Stochastic Dynamic Programming. The performance of the proposed schemes is illustrated by its application to such environmental problem. |
| Keywords: | Environmental pollutant control, Markov decision processes, Stochastic dynamic programming, Stochastic dynamic games, Optimal abatement policies |
| Date: | 2011–07 |
| URL: | http://d.repec.org/n?u=RePEc:cte:wsrepe:ws112217&r=gth |
| By: | Torero, Maximo; Viceisza, Angelino |
| Abstract: | We conduct framed trust games using contract dairy farmers in Vietnam as first movers to assess the impact of potential collusion on trust. Disaggregated analysis suggests that female farmers are more likely to trust overall, but are also more responsive to the addition of a third party and potential collusion. A third party induces them to trust at higher levels, but potential collusion between the trustee and the third party also induces them to trust at lower levels. Our findings corroborate well with existing studies on gender differences in decision making, which suggest that women's social preferences are more context-specific than men's. |
| Keywords: | collusion, field experiment, Gender, trust game, |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:fpr:ifprid:1100&r=gth |
| By: | Heinz, Matthias; Juranek, Steffen; Rau, Holger A. |
| Abstract: | We analyze dictator allocation decisions in an experiment where the recipients have to earn the pot to be divided with a real-effort task. As the recipients move before the dictators, their effort decisions resemble the first move in a trust game. Depending on the recipients' performance, the size of the pot is either high or low. We compare this real-effort treatment to a baseline treatment where the pot is a windfall gain and where a lottery determines the pot size. In the baseline treatment, reciprocity cannot play a role. We find that female dictators show reciprocity and decrease their taking-rates significantly in the real-effort treatment. This treatment effect is larger when female dictators make a decision on recipients who successfully generated a large pot compared to the case where the recipients performed poorly. By contrast, there is no treatment effect with male dictators, who generally exhibit more sefish behavior. -- |
| Keywords: | Gender,Reciprocity,Dictator Game,Real Effort |
| JEL: | C72 C91 |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:dicedp:24&r=gth |
| By: | E. Farvaque; A. Mihailov; A. Naghavi |
| Abstract: | This paper aims to explain the rise and fall of communism by exploring the interplay between economic incentives and social preferences in different economic systems. We introduce inequality-averse and inefficiency-averse agents responding to economic incentives and transmitting their ideology as they are affected by evolving outcomes. We analyze their con.ict through the interaction between leaders with economic power and followers with ideological determination. The socioeconomic dynamics of our model generate a pendulum-like switch from markets to a centrally-planned economy abolishing private ownership, and back to restoring market incentives. The grand experiment of communism is thus characterized to have led to the discovery of a trade-off between equality and efficiency at the scale of alternative economic systems. |
| JEL: | C72 D31 D63 D74 D83 P51 |
| Date: | 2011–07 |
| URL: | http://d.repec.org/n?u=RePEc:bol:bodewp:wp776&r=gth |