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on Game Theory |
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Issue of 2011‒04‒16
seventeen papers chosen by Laszlo A. Koczy Hungarian Academy of Sciences and Obuda University |
| By: | Michel Grabisch (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I); Lijue Xie (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I) |
| Abstract: | Finding a solution concept is one of the central problems in cooperative game theory, and the notion of core is the most popular solution concept since it is based on some rationality condition. In many real situations, not all possible coalitions can form, so that classical TU-games cannot be used. An interesting case is when possible coalitions are defined through a partial ordering of the players (or hierarchy). Then feasible coalitions correspond to teams of players, that is, one or several players with all their subordinates. In these situations, the core in its usual formulation may be unbounded, making its use difficult in practice. We propose a new notion of core, called the restricted core, which imposes efficiency of the allocation at each level of the hierarchy, is always bounded, and answers the problem of sharing benefits in a hierarchy. We show that the core we defined has properties very close to the classical case, with respect to marginal vectors, the Weber set, and balancedness. |
| Keywords: | cooperative game, feasible coalition, core, hierarchy |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:hal:cesptp:halshs-00583868&r=gth |
| By: | Márkus, Judit; Pintér, Miklós; Radványi, Anna |
| Abstract: | In this paper cost sharing problems are considered. We focus on problems given by rooted trees, we call these problems cost-tree problems, and on the induced transferable utility cooperative games, called irrigation games. A formal notion of irrigation games is introduced, and the characterization of the class of these games is provided. The well-known class of airport games Littlechild and Thompson (1977) is a subclass of irrigation games. The Shapley value Shapley (1953) is probably the most popular solution concept for transferable utility cooperative games. Dubey (1982) and Moulin and Shenker (1992) show respectively, that Shapley's Shapley (1953) and Young (1985)'s axiomatizations of the Shapley value are valid on the class of airport games. In this paper we show that Dubey (1982)'s and Moulin and Shenker (1992)'s results can be proved by applying Shapley (1953)'s and Young (1985)'s proofs, that is those results are direct consequences of Shapley (1953)'s and Young (1985)'s results. Furthermore, we extend Dubey (1982)'s and Moulin and Shenker (1992)'s results to the class of irrigation games, that is we provide two characterizations of the Shapley value for cost sharing problems given by rooted trees. We also note that for irrigation games the Shapley value is always stable, that is it is always in the core Gillies (1959). |
| Keywords: | TU games; Shapley value; Axiomatization; Cost Sharing |
| JEL: | C71 |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:30031&r=gth |
| By: | Béal, Sylvain; Rémila, Eric; Solal, Philippe |
| Abstract: | This article shows that, for any transferable utility game in coalitional form with nonempty coalition structure core, the number of steps required to switch from a payoff configuration out of the coalition structure core to a payoff configuration in the coalition structure core is less than or equal to (n*n+4n)/4, where n is the cardinality of the player set. This number considerably improves the upper bound found so far by Koczy and Lauwers (2004). |
| Keywords: | coalition structure core; excess function; payoff configuration; outsider independent domination. |
| JEL: | C71 |
| Date: | 2011–03–22 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:29755&r=gth |
| By: | Ralph-C Bayer (School of Economics, University of Adelaide) |
| Abstract: | We investigate experimentally if endogenous partnership formation can improve efficiency in social dilemma situations. Subjects play multiple two-player public goods games, where they can break up with their current partner after every fourth game. Subjects without a partner provide rankings of the available other singles regarding their preferred subject to be matched with. A stable marriage mechanism determines the new matches. We vary the information subjects have when they express their preferences for their future matches and also if staying in a partnership leads to a cost or a bonus. We find that endogenous group formation can increase efficiency. Both the provision of contribution history at the time of re-matching and bonuses for staying in a partnership have positive effects. At least one of the two positive factors has to be present for an efficiency improvement. The presence of both leads to the best results. |
| Keywords: | Social Dilemma, Endogenous Group Formation, Public Goods |
| JEL: | D83 H41 |
| Date: | 2011–04 |
| URL: | http://d.repec.org/n?u=RePEc:adl:wpaper:2011-22&r=gth |
| By: | Herings P. Jean-Jacques; Predtetchinski Arkadi (METEOR) |
| Abstract: | We study the implications of procedural fairness on income taxation. We formulateprocedural fairness as a particular non-cooperative bargaining game and examine thestationary subgame perfect equilibria of the game. The equilibrium outcome is called tax equilibrium and is shown to be unique. The procedurally fair tax rate is defined as the tax rate that results in the limit of tax equilibria when the probability that negotiations break down converges to zero. The procedurally fair tax rate is shown to be unique. We also provide a characterization of the procedurally fair tax rate that involves the probability mass of below average income citizens and a particular measure of the citizens'' boldness. This characterization is then used to show that in a number of interesting cases the procedurally fair tax rate equals the probability mass of below average income citizens. |
| Keywords: | public economics ; |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:umamet:2011024&r=gth |
| By: | Tsakas Elias (METEOR) |
| Abstract: | In this paper, we consider a finite set of agents with commonly known full-support priors on the fundamental space of uncertainty. Then, we show that if the hierarchies of conditional beliefs á la Battigalli and Siniscalchi (1999) are derived from these priors, then all types of the same agent yield the same hierarchy. We also show that the previous result does not necessarily hold when the priors are not full-support. Moreover, if the collections of conditioning events does not cover the underlying space of uncertainty, there are always commonly known (non-full-support) priors such that every agent''s conditional belief hierarchies are derived from these priors. |
| Keywords: | mathematical economics; |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:umamet:2011021&r=gth |
| By: | Michel Grabisch (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I); Agnieszka Rusinowska (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I) |
| Abstract: | We study and compare two frameworks: a model of influence, and command games. In the influence model, in which players are to make a certain acceptance/rejection decision, due to influence of other players, the decision of a player may be different from his inclination. We study a relation between two central concepts of this model: influence function, and follower function. We deliver sufficient and necessary conditions for a function to be a follower function, and we describe the structure of the set of all influence functions that lead to a given follower function. In the command structure introduced by Hu and Shapley, for each player a simple game called the command game is built. One of the central concepts of this model is the concept of command function. We deliver sufficient and necessary conditions for a function to be a command function, and describe the minimal sets generating a normal command game. We also study the relation between command games and influence functions. A sufficient and necessary condition for the equivalence between an influence function and a normal command game is delivered. |
| Keywords: | influence function, follower function, lower and upper inverses, kernel, command game, command function, minimal sets generating a command game |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:hal:cesptp:halshs-00583867&r=gth |
| By: | Tremewan, James |
| Abstract: | This paper is an experimental study on the effect of group identity on the formation of coalitions and the resulting distribution of resources. After inducing group identity based on preferences over paintings, subjects play symmetric three-player _divide the dollar_ games with a majority rule decision process. The main finding is that where two players are from one group and one from the other, those in the minority earn significantly less than majority players. This is largely a result of a two-way split between majority players occurring more frequently, either because of the increased salience of this outcome, or a shift in social preferences. |
| Date: | 2010–06 |
| URL: | http://d.repec.org/n?u=RePEc:cpm:docweb:1020&r=gth |
| By: | Wu, Haoyang |
| Abstract: | [Moore and Repullo, \emph{Econometrica} \textbf{58} (1990) 1083-1099] and [Dutta and Sen, \emph{Rev. Econom. Stud.} \textbf{58} (1991) 121-128] are two fundamental papers on two-agent Nash implementation. Both of them are based on Maskin's classic paper [Maskin, \emph{Rev. Econom. Stud.} \textbf{66} (1999) 23-38]. A recent work [Wu, http://arxiv.org/abs/1002.4294, \emph{Inter. J. Quantum Information}, 2010 (accepted)] shows that when an additional condition is satisfied, the Maskin's theorem will no longer hold by using a quantum mechanism. Furthermore, this result holds in the macro world by using an algorithmic mechanism. In this paper, we will investigate two-agent Nash implementation by virtue of the algorithmic mechanism. The main result is: The sufficient and necessary conditions for Nash implementation with two agents shall be amended, not only in the quantum world, but also in the macro world. |
| Keywords: | Quantum game theory; Mechanism design; Nash implementation. |
| JEL: | D71 |
| Date: | 2011–04–05 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:30068&r=gth |
| By: | Wu, Haoyang |
| Abstract: | The Prisoner's Dilemma is a simple model that captures the essential contradiction between individual rationality and global rationality. Although the single-shot Prisoner's Dilemma is usually viewed simple, in this paper we will propose an algorithmic model and a non-binding scheme to help non-cooperative agents obtain Pareto-efficient payoffs self-enforcingly. The scheme stems from quantum game theory, but is applicable to the macro world immediately. |
| Keywords: | Quantum game theory; Prisoner's Dilemma. |
| JEL: | C72 |
| Date: | 2011–04–05 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:30070&r=gth |
| By: | Wu, Haoyang |
| Abstract: | Bayesian implementation concerns decision making problems when agents have incomplete information. This paper proposes that the traditional sufficient conditions for Bayesian implementation shall be amended by virtue of a quantum Bayesian mechanism. Furthermore, by using an algorithmic Bayesian mechanism, this amendment holds in the macro world too. |
| Keywords: | Bayesian implementation; Quantum game theory; Mechanism design |
| JEL: | D71 |
| Date: | 2011–04–05 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:30072&r=gth |
| By: | Saran Rene; Tumennasan Norovsambuu (METEOR) |
| Abstract: | The mechanism used in Nash implementation is a form of direct democracy, taking everyone''s opinion into account. We augment this mechanism with a political process that selects the opinions of a subset of the individuals. We study three such processes -- oligarchy, oligarchic democracy and random sampling -- and compare the social choice rules (SCRs) that can be implemented using each of these processes with those that can be Nash implemented. In oligarchy, only the opinions of a fixed subset of the individuals -- the oligarchs -- determine the implemented alternative. We obtain a negative result for oligarchies: there exist Nash implementable SCRs that cannot be implemented by any oligarchy. Oligarchic democracy is a perturbation of oligarchy, in which the opinions of the oligarchs “almost always” determine the implemented alternative but sometimes, everyone''s opinions are considered. In a sharp contrast to the negative result for oligarchies, we show that in economic environments, every Nash implementable SCR can be implemented by an oligarchic democracy in which any three individuals act as oligarchs. In random sampling, opinions of a fixed number of individuals are selected randomly, which then determine the implemented alternative. We show that in economic environments, every Nash implementable SCR can be implemented by randomly sampling opinions of four individuals. |
| Keywords: | microeconomics ; |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:umamet:2011019&r=gth |
| By: | Werner Güth (Max Planck Institute of Economics, Strategic Interaction Group) |
| Abstract: | Different evaluators typically disagree how to rank different candidates since they care more or less for the various qualities of the candidates. It is assumed that all evaluators submit vector bids assigning a monetary bid for each possible rank order. The rules must specify for all possible vectors of such vector bids the collectively binding rank order of candidates and the "payments" for this bid vector and its implied rank order. Three axioms uniquely define the "procedurally fair" ranking rules. We finally discuss how our approach can be adjusted to situations where one wants to rank only acceptable candidates. |
| Keywords: | social ranking, fairness, fair game forms, objective equality, mechanism desig,, committee decision making |
| JEL: | C70 C72 D63 D71 |
| Date: | 2011–04–07 |
| URL: | http://d.repec.org/n?u=RePEc:jrp:jrpwrp:2011-020&r=gth |
| By: | Olga Bogach (Department of Economics, University of Hawaii at Manoa); Andreas Leibbrandt (Department of Economics, University of Chicago) |
| Abstract: | This paper uses an experimental approach to study whether nationality serves as a focal point. We let subjects from Japan, Korea, and China play stag-hunt coordination games in which we vary information about their partner. The results show that subjects are more likely to try to coordinate on the payoff-dominant equilibrium if the only piece of information they have about their partner is that they have the same nationality. However, if subjects receive additional information about their partner, subjects are not more likely to try to coordinate on the payoff dominant equilibrium. We also do not find that subjects are less likely to try to coordinate on the payoff-dominant equilibrium when their partner has a different nationality as compared to when the partner’s nationality is unknown. In addition, we observe that giving subjects information about their partner in general increases the risk of miscoordination. Thus, our findings suggest that nationality can serve as a coordination device but also that the scope of this device is limited. |
| Keywords: | Coordination, Focal points, Cultural economics, Inter-cultural lab experiments, In-group behavior. |
| JEL: | C91 C92 Z1 Z13 |
| Date: | 2011–04–01 |
| URL: | http://d.repec.org/n?u=RePEc:hai:wpaper:201104&r=gth |
| By: | Harmsen-van Hout Marjolein J.W.; Herings P. Jean-Jacques; Dellaert Benedict G.C. (METEOR) |
| Abstract: | We propose a model on strategic formation of communication networks with (i) link specificity: the more direct links somebody maintains, the less she can specify her attention per link, the lower her links’ value, while this negative externality was previously ignored in the communication context, and (ii) value transferability via indirect links for informational but not for social value from communication, while this positive externality was modeled uniformly before. Assuming only social value to isolate the impact of link specificity, the pairwise stable set includes many nonstandard networks under high or particular combinations of fully connected components under low link specificity. Allowing for social and informational value, the joint effect of link specificity and value transferability reduces the stable set to certain fragmented networks under high or the complete network under low link specificity. These extremes are beneficial for efficiency, whereas quite inefficient networks may arise for intermediate link specificity. |
| Keywords: | microeconomics ; |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:umamet:2011022&r=gth |
| By: | Paulo Brito; Bipasa Datta; Huw Dixon |
| Abstract: | This paper adopts an evolutionary perspective on the rent-extraction model with conjectural variations (CV). We analyze the global dynamics of the model with three CVs under the replicator equation. We find that the end points of the evolutionary dynamics include the pure-strategy consistent CVs. However, there are also mixed-strategy equilibria that occur. These are on the boundaries between the basins of attraction of the pure-strategy sinks. We develop a more general notion of consistency which applies to mixed-strategy equilibria. In a three conjecture example, we find that in contrast to the pure-strategy equilibria, the mixed-strategy equilibria are not ESS: under the replicator dynamics, there are three or four mixed equilibria that may either be totally unstable, or saddle-stable. There also exist heteroclinic orbits that link equilibria together. |
| Keywords: | Rent-extraction, evolutionary dynamics, consistent conjectures, global dynamics, mixed-strategy. |
| JEL: | L15 H0 |
| Date: | 2011–04 |
| URL: | http://d.repec.org/n?u=RePEc:yor:yorken:11/06&r=gth |
| By: | Jean Guillaume Forand (Department of Economics, University of Waterloo) |
| Abstract: | This paper studies the Markov perfect equilibrium outcomes of a dynamic game of electoral competition between two policy-motivated parties. I model incumbent policy persistence: parties commit to implement a policy for their full tenure in office, and hence in any election only the opposition party renews its platform. In equilibrium, parties alternate in power and policies converge to symmetric alternations about the median voter's ideal policy. Parties' disutility from opponents' policies leads to alterna- tions that display bounded extremism; alternations far from the median are never limits of equilibrium dynamics. Under a natural restriction on strategies, I find that robust long-run outcomes display bounded moderation; alternations close to the median are reached in equilibrium only if policy dynamics start there. I show that these results are robust to voters being forward-looking, the introduction of term limits, costly policy adjustments for incumbents, and office benefits. |
| JEL: | C73 D72 D78 |
| Date: | 2010–11 |
| URL: | http://d.repec.org/n?u=RePEc:wat:wpaper:1011&r=gth |