nep-gth New Economics Papers
on Game Theory
Issue of 2010‒06‒11
twenty papers chosen by
Laszlo A. Koczy
Obuda University

  1. Cores of games with positive externalities By CHANDER, Parkash
  2. Multi-Level Trust Game with “Insider” Communication By Roman M. Sheremeta; Jingjing Zhang
  3. Cooperation Spillovers in Coordination Games By Timothy N. Cason; Anya Savikhin; Roman M. Sheremeta
  4. Pre-Electoral Coalitions and Post-Election Bargaining By Siddhartha Bandyopadhyay; Kalyan Chatterjee; Tomas Sjostrom
  5. Nested potentials and robust equilibria By UNO, Hiroshi
  6. Long-run equilibria, dominated strategies, and local interactions By Simon Weidenholzer
  7. Regret matching with finite memory By Rene Saran; Roberto Serrano
  8. Network formation with heterogeneous agents and absolute friction By J. VANDENBOSSCHE; T. DEMUYNCK;
  9. A Noncooperative Approach to Bankruptcy Problems with an Endogenous Estate By Karagözoğlu Emin
  10. The stability of the roommate problem revisited By INARRA, Elena; LARREA, Conchi; MOLIS, Elena
  11. The 11-20 Money Request Game: Evaluating the Upper Bound of k-Level Reasoning By Ayala Arad; Ariel Rubinstein
  12. Tacit Collusion in an Infinitely Repeated Prisoners’ Dilemma By Joseph E. Harrington, Jr. and Wei Zhao
  13. Can Groups Solve the Problem of Over-Bidding in Contests By Roman M. Sheremeta; Jingjing Zhang
  14. Optimal Search, Learning and Implementation By Alex Gershkov; Benny Moldovanu
  15. Signaling and indirect taxation By TRUYTS, Tom
  16. Simultaneous Decision-Making in Competitive and Cooperative Environments By Anya Savikhin; Roman M. Sheremeta
  17. The Equivalence of Contests By Subhasish M. Chowdhury; Roman M. Sheremeta
  18. A generalized Tullock contest By Subhasish M. Chowdhury; Roman M. Sheremeta
  19. An experimental study on learning about voting powers By Gabriele Esposito; Eric Guerci; Nobuyuki Hanaki; Xiaoyan Lu; Naoki Watanabe
  20. Experimental Comparison of Multi-Stage and One-Stage Contests By Roman M. Sheremeta

  1. By: CHANDER, Parkash (National University of Singapore and UniversitŽ catholique de Louvain, CORE, B-1348 Louvain-la-Neuve, Belgium)
    Abstract: This paper introduces a core concept, called the -core, in the primitive framework of a strategic game. For a certain class of strategic games, it is a weaker concept than the strong Nash equilibrium, but in general stronger than the conventional - and - cores. We argue that the coalition formation process is an infinitely repeated game and show that the grand coalition forms if the -core is nonempty. This is a weaker sufficient condition than the previous such condition (Maskin (2003, Theorem 4)). As an application of this result, it is shown that the - core of an oligopolistic market is nonempty and thus the grand coalition forms.
    Keywords: positive externalities, strategic game, core, repeated game, coalition formation
    JEL: C7 D62
    Date: 2010–01–01
  2. By: Roman M. Sheremeta (Argyros School of Business and Economics, Chapman University); Jingjing Zhang (Department of Economics, McMaster University)
    Abstract: This experiment studies the internal and external effects of communication in a multilevel trust game. In this trust game, the first player can send any part of his endowment to the second player. The amount sent gets tripled. The second player decides how much to send to the third player. The amount is again tripled, and the third player then decides the allocation among the three players. The baseline treatment with no communication shows that the first and second players send significant amounts and the third player reciprocates. When we allow communication only between the second and third players, the amounts sent and returned between these two increase. The new interesting finding is that there are external effects of communication: the first player who is outside communication sends 60% more and receives 140% more than in the no communication treatment. As a result, social welfare and efficiency increase from 48% to 73%.
    Keywords: multi-level trust games, experiments, reciprocity, communication
    JEL: C72 C91 D72
    Date: 2009–09
  3. By: Timothy N. Cason (Department of Economics, Krannert School of Management, Purdue University); Anya Savikhin (The University of Chicago); Roman M. Sheremeta (Argyros School of Business and Economics, Chapman University)
    Abstract: Motivated by problems of coordination failure observed in weak-link games, we experimentally investigate behavioral spillovers for order-statistic coordination games. Subjects play the minimum- and median-effort coordination games simultaneously and sequentially. The results show the precedent for cooperative behavior spills over from the median game to the minimum game when the games are played sequentially. Moreover, spillover occurs even when group composition changes, although the effect is not as strong. We also find that the precedent for uncooperative behavior does not spill over from the minimum game to the median game. These findings suggest guidelines for increasing cooperative behavior within organizations.
    Keywords: coordination, order-statistic games, experiments, cooperation, minimum game, behavioral spillover
    JEL: C72 C91
    Date: 2009–11
  4. By: Siddhartha Bandyopadhyay; Kalyan Chatterjee; Tomas Sjostrom
    Abstract: We study a game-theoretic model where political parties can form coalitions both before and after the elections. Before election, coalitions can commit to a seat-sharing arrangement, but not to a policy or to a division of rents from office; coalition members are free to break up and join other coalitions after the election. Equilibrium pre-electoral coalitions are not necessarily made up of the most ideologically similar parties, and they form under proportional representation as well as plurality rule. They do so to avoid "splitting the vote", but also because seat-sharing arrangements will influence the ex post bargaining and coalition formation.
    Keywords: Ex ante coalition, ex post bargaining
    JEL: C72 D72 H19
    Date: 2010–05
  5. By: UNO, Hiroshi (UniversitŽ catholique de Louvain, CORE, B-1348 Louvain-la-Neuve, Belgium)
    Abstract: This paper introduces the notion of nested best response potentials for complete information games. It is shown that a unique maximizer of such a potential is a Nash equilibrium that is robust to incomplete information in the sense of Kajii and Morris (1997, mimeo).
    Keywords: incomplete information, potential games, robustness, refinements
    JEL: C72 C73
    Date: 2010–03–01
  6. By: Simon Weidenholzer
    Abstract: The present note revisits a result by Kim and Wong (2010) showing that any strict Nash equilibrium of a coordination game can be supported as a long run equilibrium by properly adding dominated strategies. We show that in the circular city model of local interactions the selection of 1/2 -dominant strategies remains when adding strictly dominated strategies if interaction is decentral". Conversely, if the local interaction structure is central" by adding properly suited dominated strategies any equilibrium strategy of the original game can be supported as long run equilibrium. Classification- JEL: C72, D83
    Date: 2010–05
  7. By: Rene Saran (Maastricht University); Roberto Serrano (Brown University)
    Abstract: We consider the regret matching process with finite memory. For general games in normal form, it is shown that any recurrent class of the dynamics must be such that the action profiles that appear in it constitute a closed set under the “same or better reply” correspondence (CUSOBR set) that does not contain a smaller product set that is closed under “same or better replies,” i.e., a smaller PCUSOBR set. Two characterizations of the recurrent classes are offered. First, for the class of weakly acyclic games under better replies, each recurrent class is monomorphic and corresponds to each pure Nash equilibrium. Second, for a modified process with random sampling, if the sample size is sufficiently small with respect to the memory bound, the recurrent classes consist of action profiles that are minimal PCUSOBR sets. Our results are used in a robust example that shows that the limiting empirical distribution of play can be arbitrarily far from correlated equilibria for any large but finite choice of the memory bound.
    Keywords: regret matching; nash equilibria; closed sets under same or better replies; correlated equilibria
    JEL: C72 C73 D83
    Date: 2010–06–04
    Abstract: We present a model of endogenous network formation with absolute friction and heterogeneous agents. The individual payoffs from a given network are determined by the difference of an agent specific utility function that depends on the number of his/her direct links and the sum of his/her link-costs. These link-costs decompose in a symmetric function that represents the social and geographical distance between the two agents and an agent specific function representing the partner’s wealth and status. From a theoretical point of view, we define a new stability concept that is situated between the notions of pairwise stability (see Jackson and Wolinsky (1996)) and strong stability (see Dutta and Mutuswami (1997)). We show that our model has a unique stable network and we demonstrate that it is also strongly stable. As such, we provide uniqueness and existence for a whole range of stability concepts situated between our new stability concept and strong stability. From a practical point of view, we provide an algorithm that reproduces this stable network from information on the individual payoff structure. We illustrate the use of this algorithm by applying it to an informal insurance data set from the village of Nyakatoke in rural Tanzania.
    Keywords: network formation, heterogeneity, absolute friction
    JEL: C62 C78 C79
    Date: 2010–02
  9. By: Karagözoğlu Emin (METEOR)
    Abstract: We introduce a new class of bankruptcy problems in which the value of the estate is endogenous and depends on agents'' investment decisions. There are two investment alternatives: investing in a company and becoming a shareholder (risky asset) and depositing money into a savings account (risk-free asset). Bankruptcy is a possible event only for the risky asset. We define a game between agents each of which aims to maximize his expected payoff by choosing an investment alternative and a company management which aims to maximize profits by choosing a bankruptcy rule. There are two types of agents in our basic model, who are differentiated by their incomes. We, first, consider three well-known bankruptcy rules: the proportional rule, the constrained equal awards rule and the constrained equal losses rule. We show that there always exists a pure strategy subgame perfect Nash equilibrium, which involves the proportional rule. This result is independent of the income distribution in the economy and holds even under one-sided uncertainty on the income distribution. Moreover, if the company optimally chooses the return rate to be paid to investors, the unique subgame perfect Nash equilibrium involves the proportional rule. We also extend our model in two dimensions: (i) to a larger set of rules containing the Talmud rule and (ii) to two companies competing over potential investors.
    Keywords: Economics (Jel: A)
    Date: 2010
  10. By: INARRA, Elena (University of the Basque Country, Dep. Ftos. A. Econ—mico I, E-48007 Bilbao, Spain); LARREA, Conchi (University of the Basque Country, Dpto Econom’a Aplicada IV (Mathematics), E-48007 Bilbao, Spain); MOLIS, Elena (FacultŽs Universitaires Saint-Louis, CEREC, B-1000 Bruxelles, Belgium and UniversitŽ catholique de Louvain, CORE, B-1348 Louvain-la-Neuve, Belgium)
    Abstract: The lack of stability in some matching problems suggests that alternative solution concepts to the core might be a step towards furthering our understanding of matching market performance. We propose absorbing sets as a solution for the class of roommate problems with strict preferences. This solution, which always exists, either gives the matchings in the core or predicts other matchings when the core is empty. Furthermore, it satisfies the interesting property of outer stability. We also determine the matchings in absorbing sets and find that in the case of multiple absorbing sets a similar structure is shared by all.
    Keywords: roommate problem, core, absorbing sets
    JEL: C78
    Date: 2010–02–01
  11. By: Ayala Arad; Ariel Rubinstein
    Date: 2010–05–30
  12. By: Joseph E. Harrington, Jr. and Wei Zhao
    Abstract: In the context of an infinitely repeated Prisoners’ Dilemma, we explore how cooperation is initiated when players communicate and coordinate through their actions. There are two types of players - patient and impatient - which are private information. An impatient type is incapable of cooperative play, while if both players are patient types - and this is common knowledge - then they can cooperate with a grim trigger strategy. We find that the longer that players have gone without cooperating, the lower is the probability that they’ll cooperate in the next period. While the probability of cooperation emerging is always positive, there is a positive probability that cooperation never occurs.
    Date: 2010–06
  13. By: Roman M. Sheremeta (Argyros School of Business and Economics, Chapman University); Jingjing Zhang (Department of Economics, McMaster University)
    Abstract: This study reports an experiment that examines whether groups can better comply with theoretical predictions than individuals in contests. Our experiment replicates previous findings that individual players significantly overbid relative to theoretical predictions, incurring substantial losses. There is high variance in individual bids and strong heterogeneity across individual players. The new findings of our experiment are that groups make 25% lower bids, their bids have lower variance, and group bids are less heterogeneous than individual bids. Therefore, groups receive significantly higher and more homogeneous payoffs than individuals. We elicit individual and group preferences towards risk using simple lotteries. The results indicate that groups make less risky decisions, which is a possible explanation for lower bids in contests. Most importantly, we find that groups learn to make lower bids from communication and negotiation between group members.
    Keywords: rent-seeking, contest, experiments, risk, over-dissipation, group decision-making
    JEL: C72 C91 C92 D72
    Date: 2009–09
  14. By: Alex Gershkov; Benny Moldovanu
    Abstract: We characterize the incentive compatible, constrained efficient policy ("second-best") in a dynamic matching environment, where impatient, privately informed agents arrive over time, and where the designer gradually learns about the distribution of agents' values. We also derive conditions on the learning process ensuring that the complete-information, dynamically efficient allocation of resources ("first-best") is incentive compatible. Our analysis reveals and exploits close, formal relations between the problem of ensuring implementable allocation rules in our dynamic allocation problems with incomplete information and learning, and between the classical problem, posed by Rothschild [19], of finding optimal stopping policies for search that are characterized by a reservation price property .
    Date: 2010–04
  15. By: TRUYTS, Tom (Katholieke Universiteit Leuven, CES, B-3000 Leuven, Belgium; UniversitŽ catholique de Louvain, CORE, B-1348 Louvain-la-Neuve, Belgium)
    Abstract: Commodities communicate. Consumers choose a consumption bundle both for its intrinsic characteristics and for what this bundle communicates about their qualities (or 'identity') to spectators. We investigate optimal indirect taxation when consumption choices are motivated by two sorts of concerns: intrinsic consumption and costly signaling. Optimal indirect taxes are introduced into a monotonic signaling game with a finite typespace of consumers. We provide sufficient conditions for the uniqueness of the D1 sequential equilibrium in terms of strategies. In the case of pure costly signaling, signaling goods can in equilibrium be taxed without burden and the optimal quantity taxes on these goods are infinite. When commodities serve both intrinsic consumption and signaling, optimal taxes can be characterized by a generalization of the Ramsey rule, which also deals with the distortions resulting from signaling.
    Keywords: optimal taxation, indirect taxation, costly signaling, identity
    JEL: C72 H21
    Date: 2010–04–01
  16. By: Anya Savikhin (The University of Chicago); Roman M. Sheremeta (Argyros School of Business and Economics, Chapman University)
    Abstract: MWe experimentally investigate simultaneous decision-making in two contrasting environments: a competitive environment (a contest) and a cooperative environment (a voluntary contribution mechanism). We find that the cooperative nature of the voluntary contribution mechanism spills over to the contest, decreasing sub-optimal overbidding in the contest. However, contributions to the public good are not affected by simultaneous participation in the contest. There is a significant negative correlation between decisions made in competitive and cooperative environments, i.e. more cooperative subjects tend to be less competitive and vice versa. This correlation can be rationalized by heterogeneous social preferences towards inequality but not by bounded rationality theory.
    Keywords: cooperation, competition, public goods, contests, experiments, behavioral spillover
    JEL: C72 C91
    Date: 2010–04
  17. By: Subhasish M. Chowdhury (School of Economics, University of East Anglia); Roman M. Sheremeta (Argyros School of Business and Economics, Chapman University)
    Abstract: We use a Tullock-type contest model to show that intuitively and structurally different contests can be strategically and revenue equivalent to each other. We consider a two-player contest, where outcome-contingent payoffs are linear functions of prizes, own effort, and the effort of the rival. We identify strategically equivalent contests that generate the same family of best response functions and, as a result, the same revenue. However, two strategically equivalent contests may yield different equilibrium payoffs. Finally, we discuss possible contest design applications and avenues for future theoretical and empirical research.
    Keywords: rent-seeking, contest, spillover, equivalence, revenue equivalence, contest design
    JEL: C72 D72 D74
    Date: 2010–02
  18. By: Subhasish M. Chowdhury (School of Economics, University of East Anglia); Roman M. Sheremeta (Argyros School of Business and Economics, Chapman University)
    Abstract: We construct a generalized Tullock contest under complete information where contingent upon winning or losing, the payoff of a player is a linear function of prizes, own effort, and the effort of the rival. This structure nests a number of existing contests in the literature and can be used to analyze new types of contests. We characterize the unique symmetric equilibrium and show that small parameter modifications may lead to substantially different types of contests and hence different equilibrium effort levels.
    Keywords: rent-seeking, contest, spillover
    JEL: C72 D72 D74
    Date: 2010–03
  19. By: Gabriele Esposito; Eric Guerci; Nobuyuki Hanaki; Xiaoyan Lu; Naoki Watanabe
    Abstract: We investigate experimentally whether subjects can learn, from their limited experiences, about relationships between the distribution of votes in a group and associated voting powers in weighted majority voting systems (WMV). Subjects are asked to play two-stage games repeatedly. In the second stage of the game, a group of four subjects bargains over how to divide fixed amount of resources among themselves through the WMV determined in the first stage. In the first stage, two out of four subjects in the group, independently and simultaneously, choose from two options that jointly determine the distribution of a given number of votes among four members. These two subjects face a 2 × 2 matrix that shows the distribution of votes, but not associated voting powers, among four members for each outcome. Therefore, to obtain higher rewards, subjects need to learn about the latter by actually playing the second stage. The matrix subjects face in the first stage changes during the experiment to test subjects' understanding of relationships between distribution of votes and voting power. The results of our experiments suggest that although (a) many subjects learn to choose, in the votes apportionment stage, the option associated with a higher voting power, (b) it is not easy for them to learn the underlying relationships between the two and correctly anticipate their voting powers when they face a new distribution of votes.
    Date: 2010–06
  20. By: Roman M. Sheremeta (Argyros School of Business and Economics, Chapman University)
    Abstract: This article experimentally studies a two-stage elimination contest and compares its performance with a one-stage contest. Contrary to the theory, the two-stage contest generates higher revenue than the equivalent one-stage contest. There is significant over-dissipation in both stages of the two-stage contest and experience diminishes over-dissipation in the first stage but not in the second stage. Our experiment provides evidence that winning is a component in a subject’s utility. A simple behavioral model that accounts for a non-monetary utility of winning can explain significant over-dissipation in both contests. It can also explain why the two-stage contest generates higher revenue than the equivalent one-stage contest.
    Keywords: rent-seeking, contest, contest design, experiments, risk aversion, over-dissipation
    JEL: C72 C91 D72
    Date: 2009–07

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