nep-gth New Economics Papers
on Game Theory
Issue of 2010‒10‒16
fourteen papers chosen by
Laszlo A. Koczy
Obuda University

  1. Non-cooperative games with chained confirmed proposals By Attanasi, Giuseppe; Garcia-Gallego, Aurora; Georgantzis, Nikolaos; Montesano, Aldo
  2. Robustness to Strategic Uncertainty (Revision of DP 2010-70) By Andersson, O.; Argenton, C.; Weibull, J.
  3. Stepwise Thinking in Strategic Games with Incomplete Information By Carsten S. Nielsen
  5. Confusion and Learning in the Public Goods Game By Ralph-C Bayer; Elke Renner; Rupert Sausgruber
  6. A Reason for Unreason: Returns-Based Beliefs in Game Theory By Velu, C.; Iyer, S.; Gair, J.R.
  7. Consistency and Population Sensitivity Properties in Marriage and Roommate Markets By Burak Can; Bettina Klaus
  8. The neural basis of bounded rational behavior By Giorgio Coricelli; Rosemarie Nagel
  9. Enjeux stratégiques du concours des Maîtres de Conférences. By Iehlé, Vincent; Haeringer, Guillaume
  10. A New Existence and Uniqueness Theorem for Continuous Games By Seamus Hogan
  11. Strategic Interaction and Conventions By María Paz Espinosa; Jaromír Kovárík; Giovanni Ponti
  12. A Cognitive Hierarchy Model of Behavior in Endogenous Timing Games By Daniel Carvalho; Luis Santos-Pinto
  13. Imitation and the Role of Information in Overcoming Coordination Failures By Carlos Alós-Ferrer; Simon Weidenholzer
  14. Aggregating sets of von Neumann-Morgenstern utilities By Eric Danan; Thibault Gajdos; Jean-Marc Tallon

  1. By: Attanasi, Giuseppe; Garcia-Gallego, Aurora; Georgantzis, Nikolaos; Montesano, Aldo
    Abstract: We propose a bargaining process with alternating proposals as a way of solving non-cooperative games, giving rise to Pareto efficient agreements which will, in general, differ from the Nash equilibrium of the constituent games.
    Keywords: Bargaining; Confirmed proposals; Confirmed agreement
    JEL: C72 C73 C78
    Date: 2010–03
  2. By: Andersson, O.; Argenton, C.; Weibull, J. (Tilburg University, Center for Economic Research)
    Abstract: We model a player’s uncertainty about other players’ strategy choices as smooth probability distributions over their strategy sets. We call a strategy profile (strictly) robust to strategic uncertainty if it is the limit, as uncertainty vanishes, of some sequence (all sequences) of strategy profiles, in each of which every player’s strategy is optimal under under his or her uncertainty about the others. We derive general properties of such robustness, and apply the definition to Bertrand competition games and the Nash demand game, games that admit infinitely many Nash equilibria. We show that our robustness criterion selects a unique Nash equilibrium in the Bertrand games, and that this agrees with recent experimental findings. For the Nash demand game, we show that the less uncertain party obtains the bigger share.
    Keywords: Nash equilibrium;refinement;strategic uncertainty;price competition;Bertrand competition;bargaining;Nash demand game
    JEL: C72 D43 L13
    Date: 2010
  3. By: Carsten S. Nielsen (Department of Economics, University of Copenhagen)
    Abstract: This paper proposes a general incomplete information framework for studying behavior in strategic games with stepwise (viz. `level-k' or `cognitive hierarchy') thinking, which has been found to describe strategic behavior well in experiments involving players' initial responses to games. It is shown that there exist coherent stepwise beliefs, implied by step types, that have the potential to encode all relevant information. In the structure of stepwise beliefs, players are unaware of opponents doing at least as much thinking as themselves. As a result, there exists a Bayesian Nash equilibrium strategy profile in which any player at some step fixes the best responses of opponents at lower steps and then best responds herself.
    Keywords: game theory; interactive epistemology; unawareness; Bayesian Nash equilibrium; bounded rationality; level-k; cognitive hierarchy
    JEL: C70 C72 D80 D82
    Date: 2010–07
    Date: 2010–10–06
  5. By: Ralph-C Bayer (School of Economics, University of Adelaide); Elke Renner (University of Nottingham); Rupert Sausgruber (University of Copenhagen)
    Abstract: We test if confusion and learning could potentially explain all the decay of contributions in the repeated public goods games by implementing a limited information environment to mimic the state of confusion. A comparison shows that the rate of decline is more than twice as high in a standard public goods game. Furthermore, we find that simple learning cannot generate the contribution dynamics, which are commonly attributed to the existence of conditional cooperators. We conclude that cooperative behavior observed in public goods games is not a pure artefact of confusion and learning.
    Keywords: public goods experiments, learning, limited information, confusion, conditional cooperation
    JEL: C90 D83 H41
    Date: 2010–10
  6. By: Velu, C.; Iyer, S.; Gair, J.R.
    Abstract: Players cooperate in experiments more than game theory would predict. We introduce the ‘returns-based beliefs’ approach: the expected returns of a particular strategy in proportion to total expected returns of all strategies. Using a decision analytic solution concept, Luce’s (1959) probabilistic choice model, and ‘hyperpriors’ for ambiguity in players’ cooperability, our approach explains empirical observations in various classes of games including the Prisoner’s and Traveler’s Dilemmas. Testing the closeness of fit of our model on Selten and Chmura (2008) data for completely mixed 2 × 2 games shows that with loss aversion, returns-based beliefs explain the data better than other equilibrium concepts.
    Keywords: Rationality, Subjective Probabilities, Returns-Based Beliefs
    Date: 2010–10–01
  7. By: Burak Can; Bettina Klaus
    Abstract: We consider one-to-one matching markets in which agents can either be matched as pairs or remain single. In these so-called roommate markets agents are consumers and resources at the same time. Klaus (2010) introduced two new "population sensitivity" properties that capture the effect newcomers have on incumbent agents: competition sensitivity and resource sensitivity. On various roommate market domains (marriage markets, no odd rings roommate markets, solvable roommate markets), we characterize the core using either of the population sensitivity properties in addition to weak unanimity and consistency. On the domain of all roommate markets, we obtain two associated impossibility results.
    Keywords: consistency; competition and resource sensitivity; core; marriage and roommate markets
    JEL: C78 D63
    Date: 2010–01
  8. By: Giorgio Coricelli (University of Southern California and Centre of Cognitive Neuroscience, Bron (Lyon), France.); Rosemarie Nagel (Universitat Pomepu Fabra)
    Abstract: Bounded rational behaviour is commonly observed in experimental games and in real life situations. Neuroeconomics can help to understand the mental processing underlying bounded rationality and out-of-equilibrium behaviour. Here we report results from recent studies on the neural basis of limited steps of reasoning in a competitive setting – the beauty contest game. We use functional magnetic resonance imaging (fMRI) to study the neural correlates of human mental processes in strategic games. We apply a cognitive hierarchy model to classify subject’s choices in the experimental game according to the degree of strategic reasoning so that we can identify the neural substrates of different levels of strategizing. We found a correlation between levels of strategic reasoning and activity in a neural network related to mentalizing, i.e. the ability to think about other’s thoughts and mental states. Moreover, brain data showed how complex cognitive processes subserve the higher level of reasoning about others. We describe how a cognitive hierarchy model fits both behavioural and brain data.
    Keywords: Game theory, Bounded rationality, Neuroeconomics
    Date: 2010–10–01
  9. By: Iehlé, Vincent; Haeringer, Guillaume
    Abstract: Le recrutement des jeunes enseignants chercheurs en France se fait de manière centralisée Le ministère calcule les affectations en fonction des listes de classements soumis par les comités de sélection et des listes de vœux soumis par les candidats. Les enjeux stratégiques du recrutement en France sont souvent mal compris, ou du moins peu connus. Nous montrons que la procédure d’affectation, tout en restant opaque pour les candidats, satisfait des propriétés souhaitables de stabilité et d’optimalité qui favorisent les candidats. Pour ce faire, nous identifions la règle d’affectation utilisée par le ministère à partir des informations mises à disposition des candidats. La structure de l’algorithme qui permet de produire ces affectations est également analysée. Enfin, nous discutons de l’existence des quotas sur le nombre des candidats classés et des ultimes changements apportés au concours de Maîtres de Conférences ainsi que de leurs relations avec des comportements localistes.
    Abstract: Contrary to most countries, the recruitment of assistant professors in France is centralized: recruitment committees submit a ranking of candidates to the Ministry of Education, the candidates submit their own ranking over the faculties that rank them and the Ministry compute the final match accordingly to these lists. The strategic stakes of this procedure are not well known in France. We show that the procedure satisfies desirable properties of stability and optimality. In order to do so, we identify the matching rule used by the Ministry using the information available to the candidates. The structure of the algorithm that produce the final matching is also analyzed. Finally, we discuss the existence of quotas on Departments rankings, the new features of the next campaign of recruitment and their relationships with job mobility.
    Keywords: Concours "Maître de Conférences"; Modèle d'appariement; Stabilité; Comportement stratégique; French Academic Job Market; Matching Model; Stability; Strategic Behavior;
    JEL: J41 C62 C78
    Date: 2010
  10. By: Seamus Hogan (University of Canterbury)
    Abstract: This paper derives a general sufficient condition for existence and uniqueness in continuous games using a variant of the contraction mapping theorem applied to mapping from a subset of the real line on to itself. We first prove this contraction mapping variant, and then show how the existence of a unique equilibrium in the general game can be shown by proving the existence of a unique equilibrium in an iterative sequence of games involving such R-to-R mappings. Finally, we show how a general condition for this to occur is that a matrix derived from the Jacobean matrix of best-response functions be have positive leading principal minors, and how this condition generalises some existing uniqueness theorems for particular games.
    Keywords: Existence; Uniqueness; Continuous Games; Contraction Mapping Theorem
    JEL: C62 C72 D43
    Date: 2010–10–01
  11. By: María Paz Espinosa (Universidad del País Vasco); Jaromír Kovárík (Universidad del País Vasco); Giovanni Ponti (Universidad de Alicante and Università di Ferrara)
    Abstract: The scope of the paper is to review the literature that employs coordination games to study social norms and conventions from the viewpoint of game theory and cognitive psychology. We claim that those two alternative approaches are complementary, as they provide different insights to explain how people converge to a unique system of self-fulfilling expectations in presence of multiple, equally viable, conventions. While game theory explains the emergence of conventions relying on efficiency and risk considerations, the psychological view is more concerned with frame and labeling effects. The interaction between these alternative (and, sometimes, competing) effects leads to the result that coordination failures may well occur and, even when coordination takes place, there is no guarantee that the convention eventually established will be the most efficient.
    Keywords: Behavioral Game Theory, conventions, social norms
    Date: 2010–10–01
  12. By: Daniel Carvalho; Luis Santos-Pinto
    Abstract: This paper applies the cognitive hierarchy model of Camerer, Ho and Chong (2004) to the action commitment game of Hamilton and Slutsky (1990). The model generates the heterogeneity of behavior reported in Huck, Müeller and Normann (2002). The model predicts the spike in the leadership quantity in the first period as well as the spike in the Cournot quantity in the second period. The model predicts delay, a feature that cannot be explained by social preferences. The also model predicts very well the percentage of Stackelberg outcomes, double leadership outcomes, and Stackelberg leaders punished by followers. Notwithstanding, the model produces low first period movement and is unable to generate sufficient percentages of sequential play of Cournot quantities and collusive market outcomes.
    Keywords: endogenous timing games; thinking steps; cognitive hierarchy
    JEL: C72 D43 L13
    Date: 2010–01
  13. By: Carlos Alós-Ferrer; Simon Weidenholzer
    Abstract: We model the structure of a firm or an organization as a network and consider minimum-effort games played on this network as a metaphor for cooperations failing due to coordination failures. For a family of behavioral rules, including Imitate the Best and the Proportional Imitation Rule, we show that inefficient conventions arise independently of the interaction structure, if information is limited to the interaction neighborhoods. However, in the presence of informational spillovers, a minimal condition on the network guarantees that efficient conventions will eventually dominate. An analogous result is established for average opinion games.
    JEL: C72 D83
    Date: 2010–09
  14. By: Eric Danan (THEMA - THéorie Economique, Modélisation et Applications - université de Cergy-Pontoise); Thibault Gajdos (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I); Jean-Marc Tallon (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I, EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics - Ecole d'Économie de Paris)
    Abstract: We analyze the aggregation problem without the assumption that individuals and society have fully determined and observable preferences. More precisely, we endow individuals ans society with sets of possible von Neumann-Morgenstern utility functions over lotteries. We generalize the classical neutrality assumption to this setting and characterize the class of neutral social welfare function. This class turns out to be considerably broader for indeterminate than for determinate utilities, where it basically reduces to utilitarianism. In particular, aggregation rules may differ by the relationship between individual and social indeterminacy. We characterize several subclasses of neutral aggregation rules and show that utilitarian rules are those that yield the least indeterminate social utilities, although they still fail to systematically yield a determinate social utility.
    Keywords: Aggregation, vNM utility, indeterminacy, neutrality, utilitarianism.
    Date: 2010–07

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