nep-gth New Economics Papers
on Game Theory
Issue of 2005‒04‒16
29 papers chosen by
Gerald Pech
NUI Galway

  1. More strategies, more Nash equilibria By Sophie Bade; Guillaume Haeringer; Ludovic Renou
  2. A Note on the Impossibility of a Satisfactory Concept of Stability for Coalition Formation Games By Salvador Barberà; Anke Gerber
  3. The Harsanyi paradox and the 'right to talk' in bargaining among coalitions By Juan Vidal-Puga
  4. Coordination Failure in Repeated Games with Almost-Public Monitoring By George J. Mailath; Stephen Morris
  5. Gradual Nash Bargaining with Endogenous Agenda: A Path-Dependent Model By Julian J. Arevalo
  6. Duality and optimal strategies in the finitely repeated zero-sum games with incomplete information on both sides By Bernard De Meyer; Alexandre Marino
  7. Trust in surveys and games - a matter of money and location? By Holm, Håkan; Nystedt, Paul
  8. Reinterpreting the meaning of breakdown By Juan Vidal-Puga
  9. On the Existence of Undominated Elements of Acyclic Relations By Hannu Salonen; Hannu Vartiainen
  10. Dynamic Behavior in Minimum Effort Coordination Games - Some Theory of Group Size and Inter-Group Competition as Coordination Devices By Thomas Riechmann
  11. Selfish-biased conditional cooperation: On the decline of contributions in repeated public goods experiments By Tibor Neugebauer; Javier Perote; Ulrich Schmidt; Malte Loos
  12. Coalitional Manipulation on Networks By Biung-Ghi Ju
  13. A game theoretic application of inverse limit By Miklós Pintér
  14. Markov Equilibrium in Models of Dynamic Endogenous Political Institutions By Roger Lagunoff
  15. Comparison of negotiated uniform versus differentiated abatement standards for a transboundary pollution problem. By Basak Bayramoglu; Jean-François Jacques
  16. Majority voting leads to unanimity By Asheim , Geir B.; Claussen , Carl Andreas; Nilssen, Tore
  17. Why Lying Pays: Truth Bias in the Communication with Conflicting Interests By Toshiji Kawagoe; Hirokazu Takizawa
  18. A fair rule in minimum cost spanning tree problems By Gustavo Bergantiños; Juan Vidal-Puga
  19. Fighting against the odds By Mehlum, Halvor; Moene, Karl
  20. On the existence of Nash equilibrium in electoral competition By Alejandro Saporiti
  21. A Game Theoretical Model of Land Contract Choice By Américo Mendes
  22. Social Games: Matching and the Play of Finitely Repeated Games By Matthew O. Jackson; Alison Watts
  23. The Economics of Small Worlds By Matthew O. Jackson; Brian W. Rogers
  24. Search in the Formation of Large Networks: How Random are Socially Generated Networks? By Matthew O. Jackson; Brian W. Rogers
  25. Cooperative investment games or population games By Yaron Azrieli; Ehud Lehrer
  26. Supermodular social games By Ludovic Renou
  27. Exact capacities and star shaped distorted probabilities By Zaier Aouani
  28. Brown's Original Fictitious Play By Ulrich Berger
  29. Trust among Strangers By Teck-Hua Ho; Keith Weigelt

  1. By: Sophie Bade (Department of Economics, Penn State University); Guillaume Haeringer (Department d'Economia i d'Historia Economica, Universitat Autonoma de Barcelona); Ludovic Renou (University of Adelaide, School of Economics)
    Abstract: This short paper isolates a non-trivial class of games for which there exists a monotone relation between the size of pure strategy spaces and the number of pure Nash equilibria (Theorem). This class is that of two- player nice games, i.e., games with compact real intervals as strategy spaces and continuous and strictly quasi-concave payoff functions, assumptions met by many economic models. We then show that the sufficient conditions for Theorem to hold are tight.
    Keywords: Strategic-form games, strategy spaces, Nash equilibrium, two players
    JEL: C7 D8
    Date: 2005–02–03
  2. By: Salvador Barberà; Anke Gerber
    Abstract: In this note we show that no solution to coalition formation games can satisfy a set of axioms that we propose as reasonable. Our result points out that “solutions” to the coalition formation cannot be interpreted as predictions of what would be “resting points” for a game in the way stable coalition structures are usually interpreted.
    Keywords: Hedonic game, coalition formation, stability
    JEL: C71
  3. By: Juan Vidal-Puga (Universidade de Vigo)
    Abstract: We introduce a non-cooperative model of bargaining when players are divided into coalitions. The model is a modification of the mechanism in Vidal-Puga (Economic Theory, 2005) so that all the players have the same chances to make proposals. This means that players maintain their own 'right to talk' when joining a coalition. We apply this model to an intriguing example presented by Krasa, Tamimi and Yannelis (Journal of Mathematical Economics, 2003) and show that the Harsanyi paradox (forming a coalition may be disadvantageous) disappears.
    Keywords: cooperative games bargaining coalition structure Harsanyi paradox
    JEL: C71 C78
    Date: 2005–01–31
  4. By: George J. Mailath (Dept. Economics, University of Pennsylvania); Stephen Morris (Cowles Foundation, Yale University)
    Abstract: Some private-monitoring games, that is, games with no public histories, can have histories that are almost public. These games are the natural result of perturbing public-monitoring games towards private monitoring. We explore the extent to which it is possible to coordinate continuation play in such games. It is always possible to coordinate continuation play by requiring behavior to have bounded recall (i.e., there is a bound L such that in any period, the last L signals are sufficient to determine behavior). We show that, in games with general almost-public private monitoring, this is essentially the only behavior that can coordinate continuation play.
    Keywords: Repeated games, Private monitoring, Almost-public monitoring, Coordination, Bounded recall
    JEL: C72 C73 D82
    Date: 2004–09
  5. By: Julian J. Arevalo (Universidad Externado de Colombia)
    Abstract: This article proposes a method for considering the bargaining agenda as an endogenous phenomenon in gradual bargaining games, understood as being path-dependent processes. Some short, medium and long-term results for bargaining are presented, as well as a possible application for the model.
    Keywords: Game theory, Bargaining, Path-Dependent Processes
    JEL: C7 D8
    Date: 2005–02–07
  6. By: Bernard De Meyer (CERMSEM); Alexandre Marino (CERMSEM)
    Abstract: The recursive formula for the value of the zero-sum repeated games with incomplete information on both sides is known for a long time. As it is explained in the paper, the usual proof of this formula is in a sense non constructive : it just claims that the players are unable to guarantee a better payoff than the one prescribed by formula, but it does not indicates how the players can guarantee this amount. In this paper we aim to give a constructive approach to this formula using duality techniques. This will allow us to recursively describe the optimal strategies in those games and to apply these results to games with infinite action spaces.
    Keywords: Repeated games, dual games, incomplete information, recurrence formula
    Date: 2005–03
  7. By: Holm, Håkan (Department of Economics, Lund University); Nystedt, Paul (Department of Economics, Lund University)
    Abstract: This paper explores methods to study trust. Answers to survey questions and choices in a trust game are obtained from subjects approached by mail executing their tasks at home as well as from classroom subjects. No discernable differences between the results obtained by these methods were observed. Furthermore, one group of subjects played the trust game with hypothetical payments. This changed trust behavior dramatically, whereas trustworthiness was unaffected. Subjects without financial incentives exhibited less trust. Trust choices with hypothetical payments were significantly correlated with survey trust answers whereas there was no such correlation for the corresponding choices with real payments.
    Keywords: Trust; Financial incentives; Location; Survey answers
    JEL: C72 C81 C90 C93
    Date: 2005–04–07
  8. By: Juan Vidal-Puga (Universidade de Vigo)
    Abstract: A typical assumption of the standard alternating-offers model under risk is that the breakdown event means a complete and irrevocable halt in negotiations. We reinterpret the meaning of breakdown as the imposition to finish negotiations immediately. Specifically, after breakdown the last offer becomes definitive. A full characterization of the set of subgame perfect equilibrium payoffs is provided. We show that Rubinstein's allocation (1/(1+?),?/(1+?)) is obtained under non- stationary strategies. Moreover, the payoffs in delayed equilibria are potentially better for the proposer than those in which agreement is immediately reached.
    Keywords: breakdown bargaining
    JEL: C72 C78
    Date: 2005–01–31
  9. By: Hannu Salonen (Department of Economics, University of Turku); Hannu Vartiainen (The Yrjo Jahnsson Foundation)
    Abstract: We study the existence of undominated elements of acyclic and irreflexive relations. A sufficient condition for the existence is given in the general case without any topological assumptions. Sufficient conditions are also given when the relation in question is defined on a compact Hausdorff space. We study the existence of fixed points of acyclic correspondences, the existence of stable sets, and the possibility of representing the relation by a real valued function.
    Keywords: acyclic relations, undominated elements
    JEL: C7 D8
    Date: 2005–03–23
  10. By: Thomas Riechmann (University of Magdeburg)
    Abstract: This paper presents a model of individual behavior in minimum effort coordination games, focusing primarily on the effects of the number of players and the introduction of inter-group competition. It is shown that independent of the number of players and the number of competing groups, the most inefficient equilibrium is always the stochastically stable one. Yet, it turns out that the `security' of more efficient equilibria increases with a decrease of the number of players and with an increase of the number of competing groups.
    Keywords: Minimum Effort Coordination, Group Competition, Stochastic Stability, Dynamic Games
    JEL: C72 C92
    Date: 2005–03–30
  11. By: Tibor Neugebauer (University Hannover); Javier Perote (Juan Carlos University Madrid); Ulrich Schmidt (University Hannover); Malte Loos (University Kiel)
    Abstract: The recent literature suggests that people have social preferences with a self-serving bias. Our data analysis reveals that the stylized fact of declining cooperation in repeated public goods experiments results from this bias and adaptation.
    Keywords: experimental economics, information feedback, public goods, voluntary contributions, conditional cooperation
    JEL: C72 C92 H41
    Date: 2005–03–25
  12. By: Biung-Ghi Ju (Department of Economics, The University of Kansas)
    Abstract: We consider an abstract model of division problems where each agent is identi- fied by a characteristic vector. Agents are situated on a network (a non-directed graph) and any connected coalition can reallocate members¡¯ characteristics (e.g. reallocation of claims in bankruptcy problems). A reallocation-proof rule prevents any coalition from benefiting, in terms of its total award, through a reallocation. We offer a full characterization of reallocation-proof rules without any assumption on the network structure. This result yields a variety of useful corollaries for specific networks such as the complete network, trees, networks without a ¡°bridge¡± etc. Our model has various special examples such as bankruptcy, surplus sharing, cost sharing, income redistribution, social choice with transferable utility, etc.
    Keywords: Division problem; Coalitional manipulation; Network; Graph; Reallocationproofness
    JEL: C71 D30 D63 D71
    Date: 2004–08
  13. By: Miklós Pintér (Corvinus University of Budapest)
    Keywords: Incomplete information, type space, hierarchies of beliefs
    JEL: C7 D8
    Date: 2005–03–14
  14. By: Roger Lagunoff (Georgetown University)
    Abstract: This paper examines existence of Markov equilibria in the class of dynamic political games (DPGs). DPGs are dynamic games in which political institutions are endogenously determined each period. The process of change is both recursive and instrumental: the rules for political aggregation at date t+1 are decided by the rules at date t, and the resulting institutional choices do not affect payoffs or technology directly. Equilibrium existence in dynamic political games requires a resolution to a “political fixed point problem” in which a current political rule (e.g., majority voting) admits a solution only if all feasible political rules in the future admit solutions in all states. If the class of political rules is dynamically consistent, then DPGs are shown to admit political fixed points. This result is used to prove two equilibrium existence theorems, one of which implies that equilibrium strategies, public and private, are smooth functions of the economic state. We discuss practical applications that require existence of smooth equilibria.
    Keywords: Recursive, dynamic political games, political fixed points, dynamically consistent rules.
    JEL: C73 D72 D74
    Date: 2005–01–26
  15. By: Basak Bayramoglu (PSE and EUREQua); Jean-François Jacques (EURiSCO)
    Abstract: This paper analyses a transboundary pollution problem between two countries and studies the efficiency comparison of uniform versus differentiated abatement standards when there are imperfect transferts between countries. To achieve this goal, we use a negotiation game and the Nash bargaining solution as equilibrium. On the one hand, we remark that the argument of similarity of countries to defend the use of uniform standards is not appropriate, when there exists high level of fixed costs in abatement technology for symmetric countries. On the other hand, for asymmetric countries, according to the total welfare criteria, we notice first that differentiated standards with transfers are generally better than uniform standards with transfers. Secondly, differentiated standards without transfers always outperform uniform standards without transfers. Last, the numerical results show that the asymmetry on abatement benefits between the countries makes the uniform regime with imperfect transfers better than the differentiated regime without transfers, while an asymmetry on abatement costs gives the opposite result.
    Keywords: Transboundary pollution, cooperative games, bargaining, standards, transfers.
    JEL: Q50 C71
    Date: 2005–02
  16. By: Asheim , Geir B. (Dept. of Economics, University of Oslo); Claussen , Carl Andreas (Norges Bank); Nilssen, Tore (Dept. of Economics, University of Oslo)
    Abstract: We consider a situation where society decides, through majority voting in a secret ballot, between the alternatives of ‘reform’ and ‘status quo’. Reform is assumed to create a minority of winners, while being efficient in the Kaldor-Hicks sense. We explore the consequences of allowing binding transfers between voters conditional on the chosen alternative. In particular, we establish conditions under which the winners wish to compensate all losers, thus leading to unanimity for reform, rather than compensating some losers to form a non-maximal majority. The analysis employs concepts from cooperative game theory.
    Keywords: voting; reform; status quo; Kaldor-Hicks sense; chosen alternative; unanimity for reform; cooperative game theory
    JEL: C71 D72
    Date: 2005–01–07
  17. By: Toshiji Kawagoe (Future University - Hakodate); Hirokazu Takizawa (Research Institute of Economy, Trade & Industry)
    Abstract: We conduct experiments of a cheap-talk game with incomplete information in which one sender type has an incentive to misrepresent her type. Although that Sender type mostly lies in the experiments, the Receiver tends to believe the Sender's messages. This confirms ``truth bias'' reported in communication theory in a one-shot, anonymous environment without nonverbal cues. These results cannot be explained by existing refinement theories, while a bounded rationality model explains them under certain conditions. We claim that the theory for the evolution of language should address why truthful communication survives in the environment in which lying succeeds.
    Keywords: Cheap talk, Communication, Private information, Experiment, Equilibrium refinement, Bounded rationality, Truth bias
    JEL: C72 C92 D82
    Date: 2005–03–22
  18. By: Gustavo Bergantiños (Universidade de Vigo); Juan Vidal-Puga (Universidade de Vigo)
    Abstract: We study minimum cost spanning tree problems and define a cost sharing rule that satisfies many more properties than other rules in the literature. Furthermore, we provide an axiomatic characterization based on monotonicity properties.
    Keywords: minimum cost spanning tree, cost sharing
    JEL: C7 D8
    Date: 2005–04–04
  19. By: Mehlum, Halvor (Dept. of Economics, University of Oslo); Moene, Karl (Dept. of Economics, University of Oslo)
    Abstract: The fight for power is not only over immediate rents, but also over advantageous positions in future power struggles. When incumbency yields an extra fighting edge, current struggles involve high stakes as a victory today may guarantee the victory also tomorrow. Such an incumbency edge may stem from the control of the army, the police and other instruments reserved for the government. The conclusions drawn from static conflict models are turned on their head when the fight is also over the incumbency edge. A sharper incumbency edge increases the implicit prizes of winning. The fighting intensity may therefore rise when the strength of each side becomes more unequal. Unbalanced fights can last long and become particularly severe. This is in contrast to the standard result that equal strengths give the most intense fighting.
    Keywords: Violent conflicts; Rent-seeking games; contests
    JEL: C70 D23 D74
    Date: 2005–01–15
  20. By: Alejandro Saporiti (Queen Mary, University of London)
    Abstract: This paper generalizes previous existence results on unidimensional electoral competition, by extending the traditional two-party electoral game to the case where parties have mixed motivations, in the sense that they are interested in winning the election, but also in the policy implemented after the contest. Although this game has discontinuous payoffs, it satisfies payoff security and reciprocally upper semi- continuity. However, conditional payoffs might violate quasi-concavity. Hence, our first result shows that the existence of a pure-strategy Nash equilibrium can be guaranteed only if parties' interests are symmetric. Instead, we prove that the mixed extension satisfies better reply security and, therefore, that a mixed-strategy equilibrium always exists. We also characterize the set of equilibria for a tractable version of the model. This shows that the interaction between the electoral uncertainty, the aggregate level of opportunism and its distribution among parties shape the equilibrium strategies. In particular, when the opportunism is large and asymmetrically distributed, the support of each mixed-strategy equilibrium is a closed interval located on one side of the median. Further, as the uncertainty increases, the probability distributions concentrate on the extremes of the support. And the mixed-strategy equilibrium vanishes above a critical level, over which each party plays a pure strategy in its own ideological side.
    Keywords: Electoral competition, mixed motivations, discontinuous games, Nash equilibrium.
    JEL: D70 D72 C72
    Date: 2005–04–11
  21. By: Américo Mendes (Portuguese Catholic University Porto - Faculty of Economics & Management)
    Abstract: In most of the land tenancy literature the type of contract is exogenous. Also even though these contracts vary a lot among farms, between regions and over time, the theoretical literature has not always acknowledged this idiosyncrasy. Building on the strategic bargaining theory initiated by Rubinstein, this model not only makes the type of contract endogenous, but also provides the surplus sharing rules and the conditions giving rise to each type of contract, showing how the type and terms of the contract are tailored to fit the characteristics of the parties and their economic environment. Pairwise bargaining is embedded into a market context by putting “competitive pressure” on the players through the opportunity they have to break up bargaining and look for alternative partners. Because of this threat of opting out, the outcome of the bargaining process depends not only on the characteristics of the players, but also on events outside their match and the information they have about them. The model departs from price-taking assumptions. Type and terms of the contract result from negotiation and are shaped by the “relative bargaining powers” of the players whose relevant components are identified in a precise way in the model.
    Keywords: land tenancy, contract choice, game theory
    JEL: C7 D8
    Date: 2005–03–13
  22. By: Matthew O. Jackson (Caltech); Alison Watts (Southern Illinois University)
    Abstract: We examine a new class of games, which we call social games, where players not only choose strategies but also choose with whom they play. A group of players who are dissatisfied with the play of their current partners can join together and play a new equilibrium. This imposes new refinements on equilibrium play, where play depends on the relative populations of players in different roles, among other things. We also examine finite repetitions of games where players may choose to rematch in any period. Some equilibria of fixed-player repeated games cannot be sustained as equilibria in a repeated social game. Conversely, the set of repeated matching (or social) equilibria also includes some plays that are not part of any subgame perfect equilibrium of the corresponding fixed-player repeated games. We explore existence under different equilibrium definitions, as well as the relationship to renegotiation-proof equilibrium. It is possible for repeated matching equilibria to be completely distinct from renegotiation-proof equilibria, and even to be Pareto inefficient.
    Keywords: Social Games, Matching, Games, Repeated Games, Renegotiation
    JEL: A14 C71 C72 C78 J41
    Date: 2005–03–14
  23. By: Matthew O. Jackson (Caltech); Brian W. Rogers (Caltech)
    Abstract: We examine a simple economic model of network formation where agents benefit from indirect relationships. We show that small-world features - -- short path lengths between nodes together with highly clustered link structures --- necessarily emerge for a wide set of parameters.
    Keywords: networks, small worlds
    JEL: A14 C72
    Date: 2005–03–14
  24. By: Matthew O. Jackson (Caltech); Brian W. Rogers (Caltech)
    Abstract: We present a model of network formation where entering nodes find other nodes to link to both completely at random and through search of the neighborhoods of these randomly met nodes. We show that this model exhibits the full spectrum of features that have been found to characterize large socially generated networks. Moreover, we derive the distribution of degree (number of links) across nodes, and show that while the upper tail of the distribution is approximately ``scale- free,'' the lower tail may exhibit substantial curvature, just as in observed networks. We then fit the model to data from six networks. Besides offering a close fit of these diverse networks, the model allows us to impute the relative importance of search versus random attachment in link formation. We find that the fitted ratio of random meetings to search-based meetings varies dramatically across these applications. Finally, we show that as this random/search ratio varies, the resulting degree distributions can be completely ordered in the sense of second order stochastic dominance. This allows us to infer how the relative randomness in the formation process affects average utility in the network.
    Keywords: Networks, Network Formation, Power Laws, Scale-Free Networks, Small Worlds, Search
    JEL: A14 C71 C72
    Date: 2005–03–14
  25. By: Yaron Azrieli (Tel Aviv University); Ehud Lehrer (Tel Aviv University)
    Abstract: The model of a cooperative fuzzy game is interpreted as both a population game and a cooperative investment game. Three types of core- like solutions induced by these interpretations are introduced and investigated. The interpretation of a game as a population game allows us to define sub-games. We show that, unlike the well-known Shapley- Shubik theorem on market games (Shapley-Shubik) there might be a population game such that each of its sub-games has a non-empty core and, nevertheless, it is not a market game. It turns out that, in order to be a market game, a population game needs to be also homogeneous. We also discuss some special classes of population games such as convex games, exact games, homogeneousgames and additive games.
    Keywords: investment game, population game, fuzzy game, core-like solution, market game
    JEL: C7 D8
    Date: 2005–03–16
  26. By: Ludovic Renou (University of Adelaide, School of Economics)
    Abstract: A social game is a generalization of a strategic-form game, in which not only the payoff of each player depends upon the strategies chosen by their opponents, but also their set of admissible strategies. Debreu (1952) proves the existence of a Nash equilibrium in social games with continuous strategy spaces. Recently, Polowczuk and Radzik (2004) have proposed a discrete counterpart of Debreu's theorem for two-person social games satisfying some ``convexity properties'. In this note, we define the class of supermodular social games and give an existence theorem for this class of games.
    Keywords: Strategic-form games, social games, supermodularity, Nash equilibrium, existence.
    JEL: C7 D8
    Date: 2005–02–03
  27. By: Zaier Aouani (CERMSEM)
    Abstract: We are interested in this work, in capacities which are deformations of probability i.e. v = f o P, we characterize respectively balanced, totally balanced, exact and convex capacities by properties concerning the probability transformation function f. And we give the explicit expression, in the case of a convex capacity v = f o P, of a probability in the core of v which coincides with v on a given finite chain of elements of the algebra A. We end this work by two notions of increase in risk recently studied in [4] and connected with star-shaped functions and with an application to the optimality of the deductible insurance studied in [14]
    Keywords: Cooperative game, capacity, balanced, exact, core, increase in risk
    JEL: C71 D80
    Date: 2004–12
  28. By: Ulrich Berger (Vienna Univrsity of Economics)
    Abstract: What modern game theorists describe as 'fictitious play' is not the learning process George W. Brown defined in his 1951 paper. His original version differs in a subtle detail, namely the order of belief updating. In this note we revive Brown's original fictitious play process and demonstrate that this seemingly innocent detail allows for an extremely simple and intuitive proof of convergence in an interesting and large class of games: nondegenerate ordinal potential games.
    Keywords: Fictitious Play, Learning Process, Ordinal Potential Games
    JEL: C72
    Date: 2005–03–21
  29. By: Teck-Hua Ho (University of California, Berkeley); Keith Weigelt (University of Pennsylvania)
    Abstract: The trust building process is basic to social science. We investigate it in a laboratory setting using a novel multi-stage trust game where social gains are achieved if players trust each other in each stage. And in each stage, players have an opportunity to appropriate these gains or be trustworthy by sharing them. Players are strangers because they do not know the identity of others and they will not play them again in the future. Thus there is no prospect of future interaction to induce trusting behavior. So, we study the trust building process where there is little scope for social relations and networks. Standard game theory, which assumes all players are opportunistic, untrustworthy, and should have zero trust for others is used to construct a null hypothesis. We test whether people are trusting or trustworthy and examine how inferring the intentions of those who trust affects trustworthiness. We also investigate the effect of stake on trust, and study the evolution of trust. Results show subjects exhibit some degree of trusting behavior though a majority of them are not trustworthy and claim the entire social gain. Players are more reluctant to trust in later stages than in earlier ones and are more trustworthy if they are certain of the trustee’s intention. Surprisingly, subjects are more trusting and trustworthy when the stake size increases. Finally, we find the sub- population who invests in initiating the trust building process modifies its trusting behavior based on the relative fitness of trust.
    Keywords: Experimental Economics, Behavioral Economics
    JEL: C79 C91 D64
    Date: 2005–04–14

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