nep-gth New Economics Papers
on Game Theory
Issue of 2005‒09‒29
twenty-one papers chosen by
László Á. Kóczy
Universiteit Maastricht

  1. The set of undominated imputations and the core: an axiomatic approach By Francesc Llerena and Carles Rafels
  2. Measuring Strategic Uncertainty in Coordination Games By Frank Heinemann; Rosemarie Nagel; Peter Ockenfels
  3. On Noncooperative Games and Minimax Theory By Frenk, J.B.G.; Kassay, G.
  4. Interval values for strategic games in which players cooperate By Luisa Carpente; Balbina Casas-Mendez; Ignacio Garcia-Jurado; Anne van den Nouweland
  5. On the effect of risk aversion in bimatrix games By Berden,Caroline; Peters,Hans
  6. A coordination game to elicit social networks: 3 classroom experiments By Pablo Brañas-Garza; Ramón Cobo-Reyes; Natalia Jiménez; Giovanni Ponti
  7. Dynamic Club Formation with Coordination By Tone Arnold; Myrna Wooders
  8. Monotonicity and Nash Implementation in Matching Markets with Contracts By Haake,Claus-Jochen; Klaus,Bettina
  9. The trust game behind the veil of ignorance : a note on gender differences By Vyrastekova,Jana; Onderstal,Sander
  10. An Axiomatic Model of Non-Bayesian Updating By Larry Epstein
  11. In Search of Stars: Network Formation among Heterogeneous Agents By Goeree,Jacob K.; Riedl,Arno; Ule,Aljaz
  12. The Coordinate-Wise Core for Multiple-Type Housing Markets is Second-Best Incentive Compatible By Klaus,Bettina
  13. Games of School Choice under the Boston Mechanism By Haluk Ergin; Tayfun Sönmez
  14. Informational Smallness and Private Monitoring in Repeated Games By Richard McLean; Ichiro Obara; Andrew Postlewaite
  15. Nash consistent representation of effectivity functions through lottery models By Peleg,Bezalel; Peters,Hans
  16. Uniform-price assignment markets By Marina Núñez and Carles Rafels
  17. Risk-Sharing Networks By Yann Bramoullé; Rachel Kranon
  18. Continuous versus Step-Level Public Good Games By Abele, S.; Stasser, G.
  19. Differentiated Product Markets: An Experimental Test of Two Equilibrium Concepts By Peeters,Ronald; Strobel,Martin
  20. Pairwise Kidney Exchange By Alvin E. Roth; Tayfun Sönmez; M. Utku Ünver
  21. A Modular Agent-Based Environment for Studying Stock Markets By Boer-Sorban, K.; Kaymak, U.; Bruin, A. de

  1. By: Francesc Llerena and Carles Rafels (Universitat de Barcelona)
    Abstract: This paper provides an axiomatic framework to compare the D-core (the set of undominated imputations) and the core of a cooperative game with transferable utility. Theorem 1 states that the D-core is the only solution satisfying projection consistency, reasonableness (from above), -antimonotonicity, and modularity. Theorem 2 characterizes the core replacing -antimonotonicity by antimonotonicity. Moreover, these axioms also characterize the core on the domain of convex games, totally balanced games, balanced games, and superadditive games.
    Keywords: Cooperative TU-game, core, undominated imputations, reasonable outcome.
    JEL: C71
    Date: 2005
  2. By: Frank Heinemann; Rosemarie Nagel; Peter Ockenfels
    Abstract: This paper explores three aspects of strategic uncertainty: its relation to risk, predictability of behavior and subjective beliefs of players. In a laboratory experiment we measure subjects’ certainty equivalents for three coordination games and one lottery. Behavior in coordination games is related to risk aversion, experience seeking, and age. From the distribution of certainty equivalents we estimate probabilities for successful coordination in a wide range of games. For many games, success of coordination is predictable with a reasonable error rate. The best response to observed behavior is close to the global-game solution. Comparing choices in coordination games with revealed risk aversion, we estimate subjective probabilities for successful coordination. In games with a low coordination requirement, most subjects underestimate the probability of success. In games with a high coordination requirement, most subjects overestimate this probability. Estimating probabilistic decision models, we show that the quality of predictions can be improved when individual characteristics are taken into account. Subjects’ behavior is consistent with probabilistic beliefs about the aggregate outcome, but inconsistent with probabilistic beliefs about individual behavior.
    Keywords: Belief Formation, Coordination Games, Global Game, Lotteries, Risk Aversion, Strategic Uncertainty
    JEL: C72 C91 D81 D84
    Date: 2004–12
  3. By: Frenk, J.B.G.; Kassay, G. (Erasmus Research Institute of Management (ERIM), RSM Erasmus University)
    Abstract: In this note we review some known minimax theorems with applications in game theory and show that these results form an equivalent chain which includes the strong separation result in finite dimensional spaces between two disjoint closed convex sets of which one is compact. By simplifying the proofs we intend to make the results more accessible to researchers not familiar with minimax or noncooperative game theory.
    Keywords: Noncooperative Game Theory;Minimax Results;
    Date: 2005–06–01
  4. By: Luisa Carpente (Universidade da Coruna); Balbina Casas-Mendez (Universidade de Santiago de Compostela); Ignacio Garcia-Jurado (Universidade de Santiago de Compostela); Anne van den Nouweland (University of Oregon)
    Abstract: In this paper we propose a method to associate a coalitional interval game with each strategic game. The method is based on the lower and upper values of finite two-person zero-sum games. We axiomatically characterize this new method. As an intermediate step, we provide some axiomatic characterizations of the upper value of finite two-person zero-sum games.
    Keywords: Strategic Games, Coalitional Interval Games, Superadditive Games, Axiomatic Characterization
    JEL: C71 C72
    Date: 2005–09–22
  5. By: Berden,Caroline; Peters,Hans (METEOR)
    Abstract: Nash equilibria with identical supports are compared for bimatrix games that are different with respect to the risk aversion of player 2. For equilibria in 2 by 2-bimatrix games and for equilibria with efficient supports in coordination games it is established for which cases increased risk aversion of player 2 benefits or hurts player 2.
    Keywords: microeconomics ;
    Date: 2005
  6. By: Pablo Brañas-Garza (Department of Economic Theory and Economic History, University of Granada); Ramón Cobo-Reyes (Department of Economic Theory and Economic History, University of Granada); Natalia Jiménez (Universidad de Alicante); Giovanni Ponti (Universidad de Alicante)
    Abstract: Experiments of social networks basically focus on coordination and cooperation games. Surprisingly, the economic literature does not provide a useful procedure to obtain existent networks. This paper proposes an innovative mechanism to elicit latent social networks. Subjects belonging to three different groups are invited to reveal their friends’ name and surname. In addition, they also have to define a score for each relationship. The latter, is one of the main innovations of our device. We obtained that a very large percentage of links sent are corresponded. According to our original purpose, this mechanism largely captures friendship relations and practically ignores weak relations. In order to further analyze individuals behavior, a model of friend—regarding preferences is developed.
    Keywords: friendship, networks, experiments, other—regarding preferences.
    JEL: C93 D85 Z13
    Date: 2005–09–12
  7. By: Tone Arnold (Department of Economics, University of Hohenheim); Myrna Wooders (Department of Economics, Vanderbilt University)
    Abstract: We present a dynamic model of club formation in a society of identical people. Coalitions consisting of members of the same club can form for one period and coalition members can jointly deviate. The dynamic process is described by a Markov chain defined by myopic optimization on the part of coalitions. We define a Nash club equilibrium (NCE) as a strategy profile that is immune to such coalitional deviations. For single--peaked preferences, we show that, if one exists, the process will converge to a NCE profile with probability one. NCE is unique up to a renaming of players and locations. Further, NCE corresponds to strong Nash equilibrium in the club formation game. Finally, we deal with the case where NCE fails to exist due to a nonbalancedness problem. When the population size is not an integer multiple of an optimal club size, there may be 'left over' players who prevent the process from `settling down'. To treat this case, we define the concept of k-remainder NCE, which requires that all but k players are playing a Nash club equilibrium, where k is defined by the minimal number of left over players. We show that the process converges to an ergodic NCE, that is, a set of states consisting only of k-remainder NCE.
    Keywords: Club formation, cooperation, best-reply dynamics, Nash club equilibrium, ergodic Nash club equilibrium
    JEL: C72 C73 D62 D71
    Date: 2005–09
  8. 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: 2005
  9. By: Vyrastekova,Jana; Onderstal,Sander (Tilburg University, Center for Economic Research)
    Abstract: We analyse gender differences in the trust game in a "behind the veil of ignorance" design. This method yields strategies that are consistent with actions observed in the classical trust game experiments. We observe that, on averge, men and women do not differ in "trust", and that women are slightly more "trustworthy". However, men's strategies are bimodal, peaking at the subgame perfect Nash equilibrium and the Pareto efficient frontier, while women's strategies are single peaked at moderate tranfers. Moreover, if a man [woman] exhibits low trust, he [she] is likely to be a money-maximizer [a risk or betrayal averse reciprocator].
    Keywords: trust game;experiment;strategy method behind the veil of ignorance; gender differences
    JEL: C72 C91
    Date: 2005
  10. By: Larry Epstein (University of Rochester)
    Abstract: This paper models an agent in a three-period setting who does not update according to Bayes'Rule, and who is self-aware and anticipates her updating behavior when formulating plans. The agent is rational in the sense that her dynamic behavior is derived from a single stable preference order on a domain of state-contingent menus of acts. A representation theorem generalizes the (dynamic version of) Anscombe-Aumann's theorem so that both the prior and the way in which it is updated are subjective.
    Keywords: Bayes' Rule, non-Bayesian updating, asset price volatility, no-trade theorems, agreeing to bet, common knowledge, temptation, self-control, conservatism, representativeness, overconfidence
    JEL: D81 D83 D9
    Date: 2005–09
  11. By: Goeree,Jacob K.; Riedl,Arno; Ule,Aljaz (METEOR)
    Abstract: This paper reports the results of a laboratory experiments on network formation among heterogeneous agents. The experimental design extends the basic Bala-Goyal (2000) model of network formation with decay and two-way flow of benefits by allowing for agents with lower linking costs or higher benefits to others. We consider treatments where agents’ types are common knowledge and treatments where agents’ types are private information. In all treatments, the (efficient) equilibrium network has a “star” structure. We find that with homogeneous agents, equilibrium predictions fail completely. In Contrast, with heterogeneous agents stars frequently occur, often with the high-value or low- cost agent in the center. Stars are not borne but rather develop: in treatments with a high-value agents, the network’s centrality, stability, and efficiency all increase over time. Our results suggest that agents’ heterogeneity is a major determinant for the predominance of star-like structures in real-life social networks.
    Keywords: microeconomics ;
    Date: 2005
  12. By: Klaus,Bettina (METEOR)
    Abstract: We consider the generalization of Shapley and Scarf''s (1974) model of trading indivisible objects (houses) to so-called multiple-type housing markets. We show (Theorem 1) that the prominent solution for these markets, the coordinate-wise core rule, is second-best incentive compatible. In other words, there exists no other strategy-proof trading rule that Pareto dominates the coordinate-wise core rule. Given that for multiple-type housing markets Pareto efficiency, strategy-proofness, and individual rationality are not compatible, by Theorem 1 we show that applying the coordinate-wise core rule is a minimal concession with respect to Pareto efficiency while preserving strategy-proofness and individual rationality.
    Keywords: microeconomics ;
    Date: 2005
  13. By: Haluk Ergin (MIT); Tayfun Sönmez (Boston College)
    Abstract: Many school districts in the U.S. use a student assignment mechanism that we refer to as the Boston mechanism. Under this mechanism a student loses his priority at a school unless his parents rank it as their first choice. Therefore parents are given incentives to rank high on their list the schools where the student has a good chance of getting in. We characterize the Nash equilibria of the induced preference revelation game. An important policy implication of our result is that a transition from the Boston mechanism to the student-optimal stable mechanism would lead to unambiguous efficiency gains.
    Keywords: student assignment, Boston mechanism, induced preference revelation, mechanism design
    JEL: C78 D61 D78 I20
    Date: 2005–09–12
  14. By: Richard McLean (Department of Economics, Rutgers University); Ichiro Obara (Department of Economics, UCLA); Andrew Postlewaite (Department of Economics, University of Pennsylvania)
    Abstract: For repeated games with noisy private monitoring and communication, we examine robustness of perfect public equilibrium/subgame perfect equilibrium when private monitoring is "close" to some public monitoring. Private monitoring is "close" to public monitoring if the private signals can generate approxi-mately the same public signal once they are aggregated. Two key notions on private monitoring are introduced: Informational Smallness and Distributional Variability. A player is informationally small if she believes that her signal is likely to have a small impact when private signals are aggregated to generate a public signal. Distributional variability measures the variation in a player’s conditional beliefs over the generated public signal as her private signal varies. When informational size is small relative to distributional variability (and private signals are sufficiently close to public monitoring), a uniformly strict equilibrium with public monitoring remains an equilibrium with private monitoring and communication. To demonstrate that uniform strictness is not overly restrictive, we prove a uniform folk theorem with public monitoring which, combined with our robustness result, yields a new folk theorem for repeated games with private monitoring and communication.
    Keywords: Communication, Informational size, Perfect Public Equilibrium, Private monitoring, Public monitoring, Repeated games, Robustness
    JEL: C72 C73 D82
    Date: 2001–05–01
  15. By: Peleg,Bezalel; Peters,Hans (METEOR)
    Abstract: Effectivity functions for finitely many players and alternatives are considered. It is shown that every monotonic and superadditive effectivity function can be augmented with equalchance lotteries to a finite lottery model---i.e., an effectivity function that preserves the original effectivity in terms of supports of lotteries---which has a Nash consistentrepresentation. In other words, there exists a finite game form which represents the lottery model and which has a Nash equilibrium for any profile of utility functions, where lotteriesare evaluated by their expected utility. No additional condition on the original effectivity function is needed.
    Keywords: microeconomics ;
    Date: 2005
  16. By: Marina Núñez and Carles Rafels (Universitat de Barcelona)
    Abstract: Uniform-price assignment games are introduced as those assignment markets with the core reduced to a segment. In these games, for all active agents, competitive prices are uniform although products may be non-homogeneous. A characterization in terms of the assignment matrix is given. The only assignment markets where all submarkets are uniform are the Bohm-Bawerk horse markets. We prove that for uniform-price assignment games the kernel, or set of symmetrically-pairwise bargained allocations, either coincides with the core or reduces to the nucleolus
    JEL: C71 C78
    Date: 2005
  17. By: Yann Bramoullé; Rachel Kranon
    Abstract: This paper considers the formation of risk-sharing networks. Following empirical findings, we build a model where risk-sharing takes place between pairs of individuals. We ask what structures emerge when pairs can agree to form links, but people cannot coordinate links across a population. We consider a benchmark model where identical individuals commit to share their monetary holdings equally with linked partners. We compare efficient networks to equilibrium networks. Efficient networks can (indirectly) connect all individuals and involve full insurance. However, equilibrium networks connect fewer individuals. There is an externality: when breaking a link individuals do not take into account the negative effect on others distant in the network. The network formation process can lead identical individuals to be in different positions and thus have different risk-sharing outcomes. These results may help explain empirical findings that risk-sharing is often not symmetric or complete.
    Keywords: Informal insurance, social networks
    JEL: O17 D85 Z13
    Date: 2005
  18. By: Abele, S.; Stasser, G. (Erasmus Research Institute of Management (ERIM), RSM Erasmus University)
    Abstract: We will firstly outline the rationale of a public good game and explain the distinction between a continuous public good game and a threshold public good game. As a vast majority of experimental research in social psychology on public good games has used threshold public good games, we will then outline the structure of a dilemma game with a provision point. Our point is that dilemma games with a provision point violate two important assumptions commonly held for public good games: a) there is always a conflict between the group’s interest and the individual’s interest; and b) an individual is always better off defecting. A threshold dilemma game is a dilemma with a coordination game embedded in it. Hence it provides focal point solutions and may as a consequence leave less room for other factors to affect behavior. Moreover, games with a provision point might yield different results than games without a provision point. We will argue that above that threshold dilemma games do not provide good models of many the public goods problems that are encountered in real life. We will propose that a public good game with a tilted S function provides a more appropriate model of real life dilemmas while fulfilling the defining properties of public good games.
    Keywords: Step-level Public Good Game;Continuous Public Good Game;
    Date: 2005–04–03
  19. By: Peeters,Ronald; Strobel,Martin (METEOR)
    Abstract: In markets with differentiated products Bertrand-Nash equilibria in pure strategies may not exist. Mixed strategies are difficult to calculate. For these cases Morgan and Shy (2000) suggest an alternative solution concept, the undercut-proof equilibrium (UPE). While the Nash-equilibrium is motivated by the question of how ones own behavior influences one''s payoff, the UPE is motivated by the question of how others'' behavior influence one''s payoff. We report on an experiment where we test these two concepts with respect to their comparative statics. Moreover we investigate the nature of subjects'' underlying thinking process. Our results provide strong evidence against the UPE and in favor of Bertrand-Nash.
    Keywords: microeconomics ;
    Date: 2005
  20. By: Alvin E. Roth (Harvard University); Tayfun Sönmez (Boston College); M. Utku Ünver (Koç University)
    Abstract: In connection with an earlier paper on the exchange of live donor kidneys (Roth, Sönmez, and Ünver 2004) the authors entered into discussions with New England transplant surgeons and their colleagues in the transplant community, aimed at implementing a Kidney Exchange program. In the course of those discussions it became clear that a likely first step will be to implement pairwise exchanges, between just two patient-donor pairs, as these are logistically simpler than exchanges involving more than two pairs. Furthermore, the experience of these surgeons suggests to them that patient and surgeon preferences over kidneys should be 0-1, i.e. that patients and surgeons should be indifferent among kidneys from healthy donors whose kidneys are compatible with the patient. This is because, in the United States, transplants of compatible live kidneys have about equal graft survival probabilities, regardless of the closeness of tissue types between patient and donor (unless there is a rare perfect match). In the present paper we show that, although the pairwise constraint eliminates some potential exchanges, there is a wide class of constrained-efficient mechanisms that are strategy-proof when patient- donor pairs and surgeons have 0-1 preferences. This class of mechanisms includes deterministic mechanisms that would accomodate the kinds of priority setting that organ banks currently use for the allocation of cadaver organs, as well as stochastic mechanisms that allow considerations of distributive justice to be addressed.
    Keywords: pairwise exchanges, transplants
    JEL: C78 D63 I10
    Date: 2004–08–04
  21. By: Boer-Sorban, K.; Kaymak, U.; Bruin, A. de (Erasmus Research Institute of Management (ERIM), RSM Erasmus University)
    Abstract: Artificial stock markets are built with diffuse priors in mind regarding trading strategies and price formation mechanisms. Diffuse priors are a natural consequence of the unknown relation between the various elements that drive market dynamics and the large variety of market organizations, findings, however, might hold only within the specific market settings. In this paper we propose a framework for building agent-based artificial stock markets. We present the mechanism of the framework based on a previously identified list of organizational and behavioural aspects. Within the framework experiments with arbitrary many trading strategies, acting in various market organizations can be conducted in a flexible way, without changing its architecture. In this way experiments of other artificial stock markets, as well as theoretical models can be replicated and their findings compared. Comparisons of the different experimental results might indicate whether findings are due to traders’ behaviour or to the chosen market structure and could suggest how to improve market quality.
    Keywords: Computational economics;agent-based modelling;artificial stock markets;behavioural finance;
    Date: 2005–04–03

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