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on Game Theory |
| By: | Tobias Guse (Department of Economics and Social Sciences, University of Dortmund); Burkhard Hehenkamp (Department of Economics and Social Sciences, University of Dortmund); Alex Possajennikov (School of Economics, University of Nottingham) |
| Abstract: | This paper provides sufficient and partially necessary conditions for the equivalence of Nash and evolutionary equilibrium in symmetric games played by finite populations. The focus is on symmetric equilibria in pure strategies. The conditions are based on properties of the payoff function that generalize the constant-sum property and the ”smallness” property, the latter of which is known from models of perfect competition and non-atomic, anonymous, or large games. The conditions are illustrated on examples of Bertrand and Cournot oligopoly games. |
| Keywords: | Nash equilibrium, Evolutionary stability, Finite populations |
| JEL: | C72 C73 |
| Date: | 2008–04 |
| URL: | http://d.repec.org/n?u=RePEc:cdx:dpaper:2008-06&r=gth |
| By: | Izquierdo, Luis R. |
| Abstract: | This thesis advances game theory by formally analysing the implications of replacing some of its most stringent assumptions with alternatives that –at least in certain contexts– have received greater empirical support. Specifically, this thesis makes two distinct contributions in the field of learning game theory and one in the field of evolutionary game theory. The method employed has been a symbiotic combination of computer simulation and mathematical analysis. Computer simulation has been used extensively to enhance our understanding of various formal systems beyond the current limits of mathematical tractability, and also to illustrate, complement and extend various analytical derivations. The two extensions to learning game theory presented here abandon the orthodox assumption that players are fully rational, and assume instead that players follow one of two alternative decision-making processes –case-based reasoning or reinforcement learning– that have received strong support from cognitive science research. The formal results derived in this part of the thesis add to the growing body of work in learning game theory that supports the general principle that the stability of outcomes in games depends not only on how unilateral deviations affect the deviator but also, and crucially, on how they affect the non-deviators. Outcomes where unilateral deviations hurt the deviator (strict Nash) but not the non-deviators (protected) tend to be the most stable. The contribution of this thesis to evolutionary game theory is a systematic study of the extent to which the assumptions made in mainstream evolutionary game theory for the sake of tractability are affecting its conclusions. Our results show that the type of strategies that are likely to emerge and be sustained in evolutionary contexts is strongly dependent on assumptions that traditionally have been thought to be unimportant or secondary (e.g. number of players, continuity of the strategy space, mutation rate, population structure…). This latter contribution is focused on the evolutionary emergence of cooperation. Following the presentation of the main results and the discussion of their implications, this thesis provides some guidance on how the models analysed here could be parameterised and validated. |
| Keywords: | Game Theory; Learning Game Theory; Evolutionary Game Theory; Computer modelling; Stochastic Approximation; Slow Learning; Reinforcement Learning; Case-based Reasoning; Markov Chains; Stochastic Process; |
| JEL: | C63 D83 C72 C73 |
| Date: | 2008–04–24 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:8664&r=gth |
| By: | De Francesco, Massimo A.; Salvadori, Neri |
| Abstract: | The paper extends the analysis of price competition among capacity-constrained sellers beyond the cases of duopoly and symmetric oligopoly. We first provide some general results for the oligopoly and then focus on the triopoly, providing a complete characterization of the mixed strategy equilibrium of the price game. The region of the capacity space where the equilibrium is mixed is partitioned according to the features of the mixed strategy equilibrium arising in each subregion. Then computing the mixed strategy equilibrium becomes a quite simple task. The analysis reveals features of the mixed strategy equilibrium which do not arise in the duopoly (some of them have also been discovered by Hirata (2008)). |
| Keywords: | Bertrand-Edgeworth; Price game; Oligopoly; Triopoly; Mixed strategy equilibrium |
| JEL: | L13 D43 C72 |
| Date: | 2008–05–07 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:8634&r=gth |
| By: | László Á. Kóczy (Budapest Tech) |
| Abstract: | While they use the language of game theory known measures of a priory voting power are hardly more than statistical expectations assuming voters behave randomly. Focusing on normalised indices we show that rational players would behave differently from the indices predictions and propose a model that captures such strategic behaviour. |
| Keywords: | Banzhaf index, Shapley-Shubik index, a priori voting power, rational players |
| JEL: | C72 C71 D72 |
| Date: | 2006–05 |
| URL: | http://d.repec.org/n?u=RePEc:pkk:wpaper:0803&r=gth |
| By: | Alexander Elbittar (Centro de Investigacion y Docencia Economica (CIDE)); Andrei Gomberg (Centro de Investigacion Economica (CIE), Instituto Tecnologico Autonomo de Mexico (ITAM)) |
| Abstract: | We report results of an experimental study of multi-object uniform and discriminatory-price auctions in an environment of publicly known common values, concentrating on an environment where theory predicts sharply different results of the two auction formats. We find that the bidding behavior in the uniform case exhibits two clear regularities: agents consistently play weakly dominated strategies by overbidding on the first unit and have moderate difficulty coordinating on the high payoff (low auction revenue) equilibrium predicted by theory. However, subjects with experience in the same environment are better at reducing demand to achieve higher payoff. Bidders in discriminatory auctions, as predicted, tend to submit bids close to value for all units and are not generally successful in attempts at collusion. |
| Keywords: | Experimental economics, Second price auctions |
| Date: | 2008–02 |
| URL: | http://d.repec.org/n?u=RePEc:cie:wpaper:0801&r=gth |
| By: | Nicolas Jacquemet (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I, Ecole d'économie de Paris - Paris School of Economics - Université Panthéon-Sorbonne - Paris I); Stephane Luchini (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - Université de la Méditerranée - Aix-Marseille II - Université Paul Cézanne - Aix-Marseille III - Ecole des Hautes Etudes en Sciences Sociales - CNRS : UMR6579); Robert-Vincent Joule (LPS - Laboratoire de Psychologie Sociale - Ecole des Hautes Etudes en Sciences Sociales); Jason Shogren (Departement Economy and Finance, University of Wyoming - University of Wyoming) |
| Abstract: | Recent work in experimental economics has explored whether observed behavior depends on whether wealth was windfall or earned. This paper extends this work by considering whether earned wealth ffects bidding behavior in an induced-value second-price auction. We find people bid more sincerely in the auction with earned wealth given monetary incentives; earned wealth did not induce sincere bidding in hypothetical auctions. |
| Keywords: | Auctions; Demand revelation; Experimental valuation; Hypothetical bias; Earned Money |
| Date: | 2008–05–06 |
| URL: | http://d.repec.org/n?u=RePEc:hal:papers:halshs-00277283_v1&r=gth |
| By: | Ping Zhang (School of Economics, University of Nottingham) |
| Abstract: | We compare uniform price auctions with fixed price offerings in Initial Public Offerings (IPO) using laboratory experiments. The experimental environment is based on the Biais and Faugeron-Grouzet (2002) model. Standard predictions based on tacit collusion equilibria (TCE) suggest lower revenues in uniform price auctions, although alternative equilibria allow for higher revenues. In our experiment, there is no evidence that TCE are played. The experiment suggests that the uniform price auctions are superior to fixed price offerings in terms of raising revenues. |
| Keywords: | Experiment, IPO, Uniform price auction, Fixed price offering, Share auction |
| JEL: | D44 G12 C91 |
| Date: | 2008–04 |
| URL: | http://d.repec.org/n?u=RePEc:cdx:dpaper:2008-05&r=gth |
| By: | Salvador Barberà (Departament d'Economia i d'Historia Economica and CODE, Universitat Autonoma de Barcelona); Bernardo Moreno (Department of Economic Theory, Universidad de Málaga) |
| Abstract: | When the members of a voting body exhibit single peaked preferences, majority winners exist. Moreover, the median(s) of the preferred alternatives of voters is (are) indeed the majority (Condorcet) winner(s). This important result of Duncan Black (1958) has been crucial in the development of public economics and political economy, even if it only provides a sufficient condition. Yet, there are many examples in the literature of environments where voting equilibria exist and alternative versions of the median voter results are satisfied while single peakedness does not hold. Some of them correspond to instances where other relevant conditions, apparently not connected with single eakedness, are satisfied. For example preferences may satisfy the single-crossing property (Mirrlees, 1971, Gans and Smart, 1996, and Milgrom and Shannon, 1994), intermediateness (Grandmont, 1978) or order restriction (Rothstein, 1990). Still other interesting cases of existence of voting equilibria do not fall in any of these categories. We present a new and weak domain restriction which encompasses all the above mentioned ones, llows for new cases, still guarantees the existence of Condorcet winners and preserves a version of the median voter result. We illustrate how this new condition, that we call top monotonicity, arises naturally in different economic contexts. |
| Keywords: | Single peaked, single crossing and intermediate preferences, majority (Condorcet) winners |
| JEL: | D72 D71 |
| Date: | 2008–05 |
| URL: | http://d.repec.org/n?u=RePEc:mal:wpaper:2008-9&r=gth |
| By: | Aadland, David; Kolpin, Van |
| Abstract: | The successful formation and long-term stability of a cooperative venture is often linked to the perceived fairness of the associated cost or resource allocation. In particular, the effectiveness of such collaborations can be hampered by the lack of a consensus view on what basis should be used for gauging an allocation’s “fairness.” Standards of equity in traditional cost-sharing applications could be assessed on many dimensions: per capita, per unit of demand, or per unit of revenue, to mention a few. This multiplicity of logically compelling “equity bases” is a feature common to many practical cost-sharing applications. Our analysis shows that features of the allocation environment are capable of explaining a substantial amount of the variation in the equity bases employed in practice and are consistent with the axiomatic principles of collective behavior. |
| Keywords: | cooperative games; cost allocation; equity; probit model |
| JEL: | D63 C71 C25 |
| Date: | 2008–03–01 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:8725&r=gth |
| By: | Tanya Araújo; Francisco Louçã |
| Date: | 2008–04 |
| URL: | http://d.repec.org/n?u=RePEc:ise:isegwp:wp272008&r=gth |