nep-gth New Economics Papers
on Game Theory
Issue of 2006‒03‒25
nine papers chosen by
Laszlo A. Koczy
Universiteit Maastricht

  1. A General Structure Theorem for the Nash Equilibrium Correspondence By Predtetchinski Arkadi
  2. Monotonicity and Nash Implementation in Matching Markets with Contracts By Haake Claus-Jochen; Klaus Bettina
  3. Nested identification of subjective probabilities By Jacques H. , DREZE
  4. On the effect of risk aversion in two-person, two-state finance economies By Berden Caroline; Peters Hans
  5. Methods of Social Comparison in Games of Status By Ed Hopkins; Tatiana Kornienko
  6. Does Contributing Sequentially Increase the Level of Cooperation in Public Goods Games ? An Experimental Investigation By David Masclet; Marc Willinger
  7. Voting Power Derives from the Poll Distribution. Shedding Light on Contentious Issues of Weighted Votes and the Constitutional Treaty By Paterson, Iain
  8. Endogenous Herding and The Gold Rush: Timing Models with Both Explosive and Timed Entry By Lones Smith; Andreas Park
  9. A Note on Expanding Networks and Monopoly Pricing By Jean J., GABSZEWICZ; Filomena, GARCIA

  1. By: Predtetchinski Arkadi (METEOR)
    Abstract: We consider n--person normal form games where the strategy set of each player is a non--empty compact convex subset of a Euclidean space, and the payoff function of player i is continuous in joint strategies and continuously differentiable and concave in player i''s strategy. No further restrictions (such as multilinearity of the payoff functions or the requirement that the strategy sets be polyhedral) are imposed. We demonstrate that the graph of the Nash equilibrium correspondence on this domain is homeomorphic to the space of games. This result generalizes a well--known structure theorem in Kohlberg and Mertens (On the Strategic Stability of Equilibria, Econometrica, 54, 1003--1037, 1986). It is supplemented by an extension analogous to the unknottedness theorems in Demichelis and Germano (On (Un)knots and Dynamics in Games, Games and Economic Behavior, 41, 46--60, 2002): the graph of the Nash equilibrium correspondence is ambient isotopic to a trivial copy of the space of games.
    Keywords: mathematical economics;
    Date: 2006
  2. By: Haake Claus-Jochen; Klaus Bettina (METEOR)
    Abstract: We consider general two-sided matching markets, so-called matching with contracts markets as introduced by Hatfield and Milgrom (2005), and analyze (Maskin) monotonic and Nash implementable solutions. We show that for matching with contracts markets the stable correspondence is monotonic and implementable (Theorems 1 and 3). Furthermore, any solution that is Pareto efficient, individually rational, and monotonic is a supersolution of the stable correspondence (Theore m 2). In other words, the stable correspondence is the minimal solution that is Pareto efficient, individually rational, and implementable.
    Keywords: microeconomics ;
    Date: 2006
  3. By: Jacques H. , DREZE
    Abstract: The theory of games against nature relies on complete preferences among all conceivable acts, i.e. among all potential assignments of consequeces to states of nature (case 1). Yet most decision problems call for choosing an element from a limited set of acts. And in games of strategy, the set of strategies available to a player is givent and not amenable to artificial extensions. In “Assessing Strategic Risk”,(ECON DP 2005-20) R.J. Aumann and J.H. Drèze extend the basic result of decision theory (maximisation of subjectvely expected utility) to situations where preferences are defined only for a given set of acts, and for lotteries among these and sure consequences (case 2). In this paper, we provide a similar extension for two other situations : those where only the set of optimal elements from a given set of acts is known (case 3); and those where only a single optimal act is known (case 4). To these four cases correspond four nested sets of admissible subjective probabilities over the states or the opponent’s strategies, namely a singleton in case 1 and increasing sets in cases 2-4. The results for case 3 and 4 also define the extent to which subjective probabilities must be specified in order to solve a given decision problem or play a given name.
    Date: 2005–11–19
  4. By: Berden Caroline; Peters Hans (METEOR)
    Abstract: The effect of replacing an agent in a two-person two-state finance economy by a more risk averse agent is studied. It is established under which conditions the other agent benefitsor looses in equilibrium from dealing with a more risk averse agent. If one agent becomes more risk averse, then the equilibrium allocation moves towards that agent''s certainty line. Whether or not that is beneficial for the other agent, depends on the location of the endowment point.
    Keywords: microeconomics ;
    Date: 2006
  5. By: Ed Hopkins; Tatiana Kornienko
    Date: 2006–03–03
  6. By: David Masclet (CREM - Centre de Recherche en Economie et Management - - [CNRS : UMR6211] - [Université Rennes I][Université de Caen] - []); Marc Willinger (LAMETA - Laboratoire Montpellierain d'économie théorique et appliquée - - [CNRS : UMR5474][INRA] - [Université Montpellier I] - [Ecole Nationale Supérieure Agronomique de Montpellier])
    Abstract: We run a series of experiments in which subjects have to choose their level of contribution to a pure public good. Our design differs from the standard public good game with respect to the decision procedure. Instead of deciding simultaneously in each round, subjects are randomly ordered in a sequence which differs from round to round. We compare sessions in which subjects can observe the exact contributions from earlier decisions ("Sequential treatment with Information") to sessions in which subjects decide sequentially but cannot observe earlier contributions ("Sequential treatment without information"). Furthermore, we investigate the effect of group size on aggregate contributions. Our result indicate that contributing sequentially increases the level of contribution to the public good when subjects are informed about the contribution levels of lower ranked subjects. Moreover, we observe that earlier players in the sequence try to influence positively the contributions of subsequent decision makers in the sequence, by making a large contribution. Such behaviour is motivated by the belief that subsequent players will reciprocate by also making a large contribution.
    Keywords: Public good; sequential Game; contribution
    Date: 2006–03–17
  7. By: Paterson, Iain (Department of Economics and Finance, Institute for Advanced Studies, Vienna, Austria)
    Abstract: Analysis of the Constitutional Treaty of the European Union shows that there is a serious discrepancy between the voting power gradient of Member States computed by the Shapley-Shubik and Banzhaf indices. Given the lack of compelling arguments to choose between these indices on purely axiomatic grounds, we turn to a probabilistic approach as pioneered by Straffin (1977) focusing on the probability distribution of voting poll outcomes. We present a unifying model of power indices as expected decisiveness, which shows that the defining feature of each approach is a particular distribution of the voting poll. Empirical evidence drawn from voting situations, in addition to a consideration of first principles, leads us to reject one of these approaches. The unified formulation allows us to develop useful related concepts of efficiency and blocking leverage, previously used solely by a 'Banzhaf' approach, for the case of Shapley-Shubik, and a comparison of results is shown.
    Keywords: Voting power indices, Power gradient, Coefficient of representation, Expected decisiveness, Efficiency, Blocking leverage, Constitution of the European Union
    JEL: C43 C71 D71 D81
    Date: 2006–03
  8. By: Lones Smith; Andreas Park (Economics University of Toronto)
    Keywords: Games of Timing, War of Attrition, Preemption Game
    JEL: C73 D81
    Date: 2005
  9. By: Jean J., GABSZEWICZ (UNIVERSITE CATHOLIQUE DE LOUVAIN, Center for Operations Research and Econometrics (CORE)); Filomena, GARCIA
    Abstract: We obtain explicitly the optimal path of prices for a monopolist operating in a network industry during a finite number of periods. We describe this optimal path as a function of network intensity and horizon length and show that the prices are increasing in time and that, for very low network intensity, or very high horizon length, the monopolist will offer the good at zero price in the initial period.
    Date: 2005–12–15

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