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on Game Theory |
| By: | Duygu Yengin (School of Economics, University of Adelaide) |
| Abstract: | Starting from her home, a service provider visits several customers, following a predetermined route, and returns home after all customers are visited. The problem is to ?nd a fair allocation of the total cost of this tour among the customers served. A transferable-utility cooperative game can be associated with this cost allocation problem. We intro- duce a new class of games, which we refer as the fixed-route traveling salesman games with appointments. We characterize the Shapley Value in this class using a property which requires that sponsors do not bene?t from mergers, or splitting into a set of sponsors. |
| Keywords: | Fixed-route travelling salesman games, routing games, appointment games, the Shapley value, the core, transferable-utility games, merging and splitting proofness, networks, cost allocation |
| JEL: | C71 |
| Date: | 2010–12 |
| URL: | http://d.repec.org/n?u=RePEc:adl:wpaper:2010-32&r=gth |
| By: | Aymeric Lardon (GATE Lyon Saint-Etienne - Groupe d'analyse et de théorie économique - CNRS : UMR5824 - Université Lumière - Lyon II - Ecole Normale Supérieure Lettres et Sciences Humaines) |
| Abstract: | The purpose of this article is to analyze a class of voting games in which externalities are present. We consider a society in which coalitions can be formed and where a finite number of voters have to choose among a set of alternatives. A coalition is winning if it can veto any proposed alternative. In our model, the veto power of a coalition is dependent on the coalition formation of the outsiders. We show that whether or not the core is non-empty depends crucially on the expectations of each coalition regarding outsiders' behavior when it wishes to veto an alternative. On the one hand, if each coalition has pessimistic expectations, then the core is non-empty if and only if the dimension of the set of alternatives is equal to one. On the other hand, if each coalition has optimistic expectations, the non-emptiness of the core is not ensured. |
| Keywords: | voting games; externalities; core |
| Date: | 2010 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:halshs-00544034_v1&r=gth |
| By: | Michel Grabisch (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: | The core of a cooperative game on a set of players N is one of the most popular concept of solution. When cooperation is restricted (feasible coalitions form a subcollection F of 2N), the core may become unbounded, which makes it usage questionable in practice. Our proposal is to make the core bounded by turning some of the inequalities defining the core into equalities (additional efficiency constraints). We address the following mathematical problem : can we find a minimal set of inequalities in the core such that, if turned into equalities, the core becomes bounded ? The new core obtained is called the restricted core. We completely solve the question when F is a distributive lattice, introducing also the notion of restricted Weber set. We show that the case of regular set systems amounts more or less to the case of distributive lattices. We also study the case of weakly union-closed systems and give some results for the general case. |
| Keywords: | Cooperative game, core, restricted cooperation, bounded core, Weber set. |
| Date: | 2010–11 |
| URL: | http://d.repec.org/n?u=RePEc:hal:cesptp:halshs-00544134_v1&r=gth |
| By: | Michel Grabisch (Centre d'Economie de la Sorbonne - Paris School of Economics) |
| Abstract: | The core of a cooperative game on a set of players N is one of the most popular concept of solution. When cooperation is restricted (feasible coalitions form a subcollection F of 2N), the core may become unbounded, which makes it usage questionable in practice. Our proposal is to make the core bounded by turning some of the inequalities defining the core into equalities (additional efficiency constraints). We address the following mathematical problem : can we find a minimal set of inequalities in the core such that, if turned into equalities, the core becomes bounded ? The new core obtained is called the restricted core. We completely solve the question when F is a distributive lattice, introducing also the notion of restricted Weber set. We show that the case of regular set systems amounts more or less to the case of distributive lattices. We also study the case of weakly union-closed systems and give some results for the general case. |
| Keywords: | Cooperative game, core, restricted cooperation, bounded core, Weber set. |
| JEL: | C7 D7 |
| Date: | 2010–11 |
| URL: | http://d.repec.org/n?u=RePEc:mse:cesdoc:10093&r=gth |
| By: | Aymeric Lardon (GATE Lyon Saint-Etienne - Groupe d'analyse et de théorie économique - CNRS : UMR5824 - Université Lumière - Lyon II - Ecole Normale Supérieure Lettres et Sciences Humaines) |
| Abstract: | In this article we consider Bertrand oligopoly TU-games with differentiated products. We assume that the demand system is Shubik's (1980) and that firms operate at a constant and identical marginal and average cost. First, we show that the alpha and beta- characteristic functions (Aumann 1959) lead to the same class of Bertrand oligopoly TU-games and we prove that the convexity property holds for this class of games. Then, following Chander and Tulkens (1997) we consider the gamma-characteristic function where firms react to a deviating coalition by choosing individual best reply strategies. For this class of games, we show that the Equal Division Solution belongs to the core and we provide a sufficient condition under which such games are convex. |
| Keywords: | Bertrand oligopoly TU-games; Core; Convexity; Equal Division Solution |
| Date: | 2010 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:halshs-00544056_v1&r=gth |
| By: | Brian Roberson (Krannert School of Management, Economics Department, Purdue University); Dmitriy Kvasov (School of Economics, University of Adelaide) |
| Abstract: | The Colonel Blotto game is a two-player constant-sum game in which each player simultaneously distributes his fixed level of resources across a set of contests. In the traditional formulation of the Colonel Blotto game, the players' resources are ''use it or lose it'' in the sense that any resources which are not allocated to one of the contests are forfeited. This article examines a non-constant-sum version of the Colonel Blotto game which relaxes this use it or lose it feature. We find that if the level of asymmetry between the players' budgets is below a threshold, then there exists a one-to-one mapping from the unique set of equilibrium univariate marginal distribution functions in the constant-sum game to those in the non-constant-sum game. Once the asymmetry of the players' budgets exceeds the threshold this relationship breaks down and we construct a new equilibrium. |
| Keywords: | Colonel Blotto Game; all-pay auction; contests; mixed strategies |
| JEL: | C72 D7 |
| Date: | 2010–12 |
| URL: | http://d.repec.org/n?u=RePEc:adl:wpaper:2010-31&r=gth |
| By: | Aymeric Lardon (GATE Lyon Saint-Etienne - Groupe d'analyse et de théorie économique - CNRS : UMR5824 - Université Lumière - Lyon II - Ecole Normale Supérieure Lettres et Sciences Humaines) |
| Abstract: | In this paper we consider cooperative Cournot oligopoly games. Following Chander and Tulkens (1997) we assume that firms react to a deviating coalition by choosing individual best reply strategies. Lardon (2009) shows that if the inverse demand function is not differentiable, it is not always possible to define a Cournot oligopoly TU(Transferable Utility)-game. In this paper, we prove that we can always specify a Cournot oligopoly interval game. Furthermore, we deal with the problem of the non-emptiness of two induced cores: the interval gamma-core and the standard gamma-core. To this end, we use a decision theory criterion, the Hurwicz criterion (Hurwicz 1951), that consists in combining, for any coalition, the worst and the better worths that it can obtain in its worth interval. The first result states that the interval gamma-core is non-empty if and only if the oligopoly TU-game associated with the better worth of every coalition in its worth interval admits a non-empty gamma-core. However, we show that even for a very simple oligopoly situation, this condition fails to be satisfied. The second result states that the standard gamma-core is non-empty if and only if the oligopoly TU- game associated with the worst worth of every coalition in its worth interval admits a nonempty gamma-core. Moreover, we give some properties on every individual profit function and every cost function under which this condition always holds, what substantially extends the gamma-core existence results in Lardon (2009). |
| Keywords: | Cournot oligopoly interval game; Interval gamma-core; Standard gamma-core; Hurwicz criterion; |
| Date: | 2010 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:halshs-00544044_v1&r=gth |
| By: | Ingela Alger (Department of Economics, Carleton University); Jörgen W. Weibull (Department of Economics, Stockholm School of Economics) |
| Abstract: | We extend the domain of evolutionary stability from strategies in symmetric two- player games played in asexually reproducing in?nite populations under uniform ran- dom matching to abstract heritable traits in symmetric pairwise interactions in ?nite or in?nite populations under more general random matching schemes, including inter- actions between relatives in sexually reproducing populations. We examine in detail interactions where the traits are ?behavioral inclinations? that may be more or less altruistic or spiteful. By a behavioral inclination we mean a rule that speci?es what strategy to use, depending on the nature of the interaction at hand and on the strategy used by the other individual (which, in turn, depends on that individual?s behavioral inclination). We show that evolutionary stability of such behavioral inclinations agrees with Hamilton?s rule at the abstract level of behavioral inclinations but not always at the level of strategies. In particular, in social dilemmas with decreasing returns to scale in the production of a public good, there is less (more) co-operation than predicted by Hamilton?s rule, as applied directly to strategies, if contributions are substitutes (complements). |
| JEL: | C73 D64 |
| Date: | 2010–12–03 |
| URL: | http://d.repec.org/n?u=RePEc:car:carecp:10-11&r=gth |
| By: | Rabia Nessah (IÉSEG School of Management, LEM-CNRS (UMR 8179),) |
| Keywords: | n-Person Game, Multiple objectives Game, Strong Equilibrium, Absolute Optimal Solution |
| Date: | 2010–08 |
| URL: | http://d.repec.org/n?u=RePEc:ies:wpaper:e201007&r=gth |
| By: | Christian Hilbe |
| Abstract: | Experimental economics has repeatedly demonstrated that the Nash equilibrium makes inaccurate predictions for a vast set of games. Instead, several alternative theoretical concepts predict behavior that is much more in tune with observed data, with the quantal response equilibrium as the most prominent example. However, here we show that this equilibrium notion itself, like any other concept that varies smoothly with the payoffs, is necessarily subject to framing effects: If the same economic problem is represented in a different but equivalent way, the predicted results will differ. As a consequence, we argue that tools and methods that are successful in explaining human behavior in laboratory experiments may be unsuitable for doing theory. |
| Date: | 2010–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1012.1188&r=gth |
| By: | M. Beatrice Lignola (Università di Napoli Federico II); Jacqueline Morgan (Università di Napoli Federico II and CSEf) |
| Abstract: | We consider quasi-variational problems (variational problems having constraint sets depending on their own solutions) which appear in concrete economic models such as social and economic networks, financial derivative models, transportation network congestion and traffic equilibrium. First, using an extension of the classical Minty lemma, we show that new upper stability results can be obtained for parametric quasi-variational and linearized quasi-variational problems, while lower stability, which plays a fundamental role in the investigation of hierarchical problems, cannot be achieved in general, even on very restrictive conditions. Then, regularized problems are considered allowing to introduce approximate solutions for the above problems and to investigate their lower and upper stability properties. We stress that the class of quasi-variational problems include social Nash equilibrium problems in abstract economies, so results about approximate Nash equilibria can be easily deduced. |
| Keywords: | quasi-variational, social Nash equilibria, approximate solution, closed map, lower semicontinuous map, upper stability, lower stability |
| Date: | 2010–12–11 |
| URL: | http://d.repec.org/n?u=RePEc:sef:csefwp:268&r=gth |
| By: | Michalis Drouvelis |
| Abstract: | Experimental evidence from public good games with punishment suggests that punishment works when subjects assign it fairly by sanctioning non-cooperators. This paper reports an experiment in which punishment is assigned unfairly in the sense that it is not linked to individual behaviour and is melted out to all group members (irrespective of their prior behaviour). We test whether unfair punishment generates different contribution and punishment behaviour relative to the standard punishment game. Our findings suggest different dynamics of average contributions in the presence of unfair punishment relative to the standard punishment game. Contribution levels are significantly different only when subjects have obtained experience from both games. We also find that, although the assignment of punishment is unaffected after the experience of an environment with unfair punishment, a history of unfair punishment makes a difference regarding reactions to alleviation, reward and punishment received. |
| Keywords: | Recriprocity, Unfair punishment, Public good experiments |
| JEL: | C92 H41 |
| Date: | 2010–11 |
| URL: | http://d.repec.org/n?u=RePEc:bir:birmec:10-34&r=gth |
| By: | Shakun D. Mago (Department of Economics, Robins School of Business, University of Richmond); Roman Sheremeta (Argyros School of Business and Economics, Chapman University); Andrew Yates (Department of Economics, Robins School of Business, University of Richmond) |
| Abstract: | We conduct an experimental analysis of a best-of-three Tullock contest. Intermediate prizes lead to higher efforts, while increasing the role of luck (as opposed to effort) leads to lower efforts. Both intermediate prizes and luck reduce the probability of contest ending in two rounds. The patterns of players? efforts and the probability that a contest ends in two rounds is consistent with „strategic momentum?, i.e. momentum generated due to strategic incentives inherent in the contest. We do not find evidence for „psychological momentum?, i.e. momentum which emerges when winning affects players? confidence. Similar to previous studies of contests, we find significantly higher efforts than predicted and strong heterogeneity in effort between subjects. |
| Keywords: | best-of-three contest, experiments, strategic momentum, psychological momentum |
| JEL: | C72 C91 D72 |
| Date: | 2010 |
| URL: | http://d.repec.org/n?u=RePEc:chu:wpaper:10-24&r=gth |
| By: | Juan D. Moreno-Ternero (Department of Economic Theory, Universidad de Málaga) |
| Abstract: | We provide a general coalitional procedure that characterizes a family of rules for bankruptcy problems inspired by the Talmud. |
| Keywords: | bankruptcy, coalitions, claims, Talmud |
| JEL: | C71 |
| Date: | 2010–12 |
| URL: | http://d.repec.org/n?u=RePEc:mal:wpaper:2010-11&r=gth |
| By: | Harris, D.; Herrmann, B.; Kontoleon, A. |
| Abstract: | In-group favouritism behaviour is observed everywhere around the world and previous research has shown that this behaviour is also easily triggered in a laboratory in various contexts. However, little is known about why different magnitudes of in-group favouritism are observed across societies. In this paper, we use a new allocation experiment to examine the nature of social norms within the context of in-group favouritism behaviour. In this experiment, a decision-maker has to decide only once how to allocate a fixed amount of resource between each of the three members of her own group and each of the three members of the out-group, whilst the decision- maker's own payo is not aected by her decision. Three treatments are implemented: in the first treatment, only the members of the in-group can punish the decision-maker. In the second treatment, only the members of the out-group can punish the decision-maker. Finally, in the third treatment, only an independent third-party observer can punish the decision-maker. The aim of these treatments is to test whether there is a prevailing social norm which dominates the behavioural standard within the context of in-group favouritism and whether this mechanism varies across dierent subject pools, namely Thailand and the UK.<br><br> Compared to a baseline treatment with no punishment opportunity, we observed that among the Thai subjects in-group favouritism significantly increased once the in-group members were given the opportunity to punish the decision-maker. The threat of punishment from a third-party punisher also increased in-group favouritism in Thailand. However, when only the out-group members had the opportunity to punish, no change in in-group favouritism behaviour was observed. On the contrary, within the British subject pool, when the out-group members had the opportunity to punish the decision-maker, we observed a decline in in-group favouritism as well as a marked shift towards an equitable outcome. The threats of punishments from the in-group members and the third-party, on the other hand, did not have any impact on in-group favouritism behaviour in the UK. The results suggest that within the Thai subject pool, there appears to be a prevailing `in-group bias norm' which is strongly enforced within and outside the group. Within the UK subject pool, however, it is less clear what the prevailing norm is. Whilst the threat of punishment from the out-group members who directly lose out from favouritism behaviour appeared to significantly reduce this behaviour, an uninvolved third-party was not willing to incur a cost to punish this behaviour. This interesting result indicates two possible explanations: first, in-group favouritism, in contrast to selfish or opportunistic behaviour, may not considered as a strong enough violation of a social norm; and second, the norm of egalitarianism within the context of favouritism may still be `evolving'. |
| Keywords: | Social Norms, In-group Favouritism, Group Behaviour, In-group Punishment, Out-group Punishment, Third-party Punishment, Experimental Design |
| JEL: | D73 C92 |
| Date: | 2010–12–13 |
| URL: | http://d.repec.org/n?u=RePEc:cam:camdae:1062&r=gth |
| By: | Asen Ivanov (Department of Economics, VCU School of Business); Dan Levin (Department of Economics, The Ohio State University); James Peck (Department of Economics, The Ohio State University) |
| Abstract: | We experimentally test an endogenous-timing herding model in which subjects observe their cost of investing and a signal correlated with the common investment return. Investment exceeds the Nash benchmark in all of our treatments, reminiscent of Keynes’ notion of “animal spirits.” The effect of overinvestment on best-response profits due to the informational externality can be positive or negative, depending on the environment. Subjects are highly heterogeneous in their propensities to invest. Initial overinvestment is followed by underinvestment with the tendency towards overinvestment dominating. |
| Date: | 2010–10 |
| URL: | http://d.repec.org/n?u=RePEc:vcu:wpaper:1004&r=gth |
| By: | Michel Grabisch (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); Agnieszka Rusinowska (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 generalize a yes-no model of influence in a social network with a single step of mutual influence to a framework with iterated influence. Each agent makes an acceptance- rejection decision and has an inclination to say either ‘yes' or ‘no'. Due to influence by others, an agent's decision may be different from his original inclination. Such a transformation from the inclinations to the decisions is represented by an influence function. We analyze the decision process in which the mutual influence does not stop after one step but iterates. Any classical influence function can be coded by a stochastic matrix, and a generalization leads to stochastic influence functions. We apply Markov chains theory to the analysis of stochastic binary influence functions. We deliver a general analysis of the convergence of an influence function and then study the convergence of particular influence functions. This model is compared with the Asavathiratham model of influence. We also investigate models based on aggregation functions. In this context, we give a complete description of terminal classes, and show that the only terminal states are the consensus states if all players are weakly essential. |
| Keywords: | Social network, influence, stochastic influence function, convergence, terminal class, Markov chains, aggregation functions. |
| Date: | 2010–11 |
| URL: | http://d.repec.org/n?u=RePEc:hal:cesptp:halshs-00543840_v1&r=gth |
| By: | Lind, Jo Thori (Dept. of Economics, University of Oslo) |
| Abstract: | I consider a society with heterogeneous individuals who can form organizations for the production of a differentiated service. An arrangement of organizations is said to be split up stable when there is no majority to split any of the organizations. Unlike other equilibrium concepts in the literature, the largest number of organizations that is split up stable corresponds to the socially optimal number of organizations, with a possibility of over provision of one organization. The analysis is extended to a case with endogeneous membership, where it is shown that the results remain the same. |
| Keywords: | Organizations; public goods; split up stability; efficiency; endogneous membership |
| JEL: | D71 D73 H49 L31 |
| Date: | 2010–05–27 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:osloec:2010_008&r=gth |
| By: | Itaya, Jun-ichi; Okamura, Makoto; Yamaguchi, Chikara |
| Abstract: | This paper investigates the conditions under which partial harmonization for capital taxation is sustained in a repeated interactions model of tax competition when there are three heterogenous countries with respect to their capital endowments. We show that regardless of the structure of the coalition (i.e., any group of countries), whether partial tax harmonization is sustainable or not crucially depends on the capital endowment of the median country relative to those of the large and small countries. The most noteworthy finding is that the closer the capital endowment of the median country to the average capital endowment of the large and small countries, the less likely is the tax harmonization including the median country to prevail and the more likely is the partial tax harmonization excluding the median country to prevail. |
| Keywords: | Tax coordination, Asymmetric countries, Repeated game, Tax competition, |
| JEL: | H73 F59 F21 |
| Date: | 2010–11 |
| URL: | http://d.repec.org/n?u=RePEc:hok:dpaper:229&r=gth |
| By: | Antonio Cabrales (Universidad Carlos III de Madrid); Olivier Gossner (Paris School of Economics and LSE); Roberto Serrano (Brown University and IMDEA Social Sciences Institute) |
| Abstract: | Consider any investor who fears ruin facing any set of investments that satisfy no-arbitrage. Before investing, he can purchase information about the state of nature in the form of an information structure. Given his prior, information structure alpha is more informative than information structure beta if whenever he rejects alpha at some price, he also rejects beta at that price. We show that this complete informativeness ordering is represented by the decrease in entropy of his beliefs, regardless of his preferences, initial wealth or investment problem. It is also shown that no prior-independent informativeness ordering based on similar premises exists. |
| Keywords: | informativeness; information structures; entropy; decision under uncertainty; investment; Blackwell ordering |
| JEL: | C00 C43 D00 D80 D81 G00 G11 |
| Date: | 2010–12–06 |
| URL: | http://d.repec.org/n?u=RePEc:imd:wpaper:wp2010-23&r=gth |