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on Game Theory |
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Issue of 2011‒09‒22
fifteen papers chosen by Laszlo A. Koczy Hungarian Academy of Sciences and Obuda University |
| By: | Suzuki, T.; Talman, A.J.J. (Tilburg University, Center for Economic Research) |
| Abstract: | We study transferable utility games with limited cooperation between the agents. The focus is on communication structures where the set of agents forms a circle, so that the possibilities of cooperation are represented by the connected sets of nodes of an undirected circular graph. Agents are able to cooperate in a coalition only if they can form a network in the graph. A single-valued solution which averages marginal contributions of each player is considered. We restrict the set of permutations, which induce marginal contributions to be averaged, to the ones in which every agent is connected to the agent that precedes this agent in the permutation. Staring at a given agent, there are two permutations which satisfy this restriction, one going clockwise and one going anticlockwise along the circle. For each such permutation a marginal vector is determined that gives every player his marginal contribution when joining the preceding agents. It turns out that the average of these marginal vectors coincides with the average tree solution. We also show that the same solution is obtained if we allow an agent to join if this agent is connected to some of the agents who is preceding him in the permutation, not necessarily being the last one. In this case the number of permutations and marginal vectors is much larger, because after the initial agent each time two agents can join instead of one, but the average of the corresponding marginal vectors is the same. We further give weak forms of convexity that are necessary and sufficient conditions for the core stability of all those marginal vectors and the solution. An axiomatization of the solution on the class of circular graph games is also given. |
| Keywords: | Cooperative game;graph structure;average tree solution;Myerson value;core stability;convexity. |
| JEL: | C71 |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:kubcen:2011100&r=gth |
| By: | Encarnacion Algaba (University of Sevilla); Jesus Mario Bilbao (University of Sevilla); Rene van den Brink (VU University Amsterdam); Jorge J. Lopez (University of Sevilla) |
| Abstract: | Cooperative games with partial cooperation cover a wider rank of real world situations than the classic model of cooperative games where every subset of a set of agents can form a coalition to execute the game. In this paper, the set of feasible coalitions which models the partial cooperation will be given by a union stable system. These systems contain, as particular cases, the communication situations and the permission structures, which are well-known both from a theoretical and applied point of view. Moreover, union stable systems are a natural framework for many other economic situations that arise in practice and which can not be modelled by these subsystems. In this paper, the goal is to make clear that there exists a close relationship between the Myerson value and the so-called conference game which player set consists of the supports of the union stable system. For that, we first analyze the relation between the restricted game and the conference game to establish later which effects a union stable system has on certain desirable properties of these games. Using the superfluous support property, defined through the conference game, new characterizations for the Myerson value are given in this context. |
| Keywords: | Conference game; restricted game; union stable system; Myerson value; superfluous support property |
| JEL: | C71 |
| Date: | 2011–09–08 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:20110127&r=gth |
| By: | Dan Kovenock; Brian Roberson |
| Abstract: | In the Colonel Blotto game, each of two players simultaneously allocates his fixed budget of a resource across a finite number n of battleelds. Within each battlefield, the player that allocates the higher level of the resource wins the battlefield. Each player's payoff is equal to the sum of the values of the battlefields he wins. In this paper we examine a multi-dimensional incomplete information version of the Colonel Blotto game in which each player's n-tuple of battlefield valuations is drawn from a common n-variate joint distribution function. |
| Keywords: | Colonel Blotto Game, Con ict, Multi-dimensional Incomplete Information, Multi-dimensional Action Space |
| JEL: | C72 D72 D74 |
| Date: | 2010–11 |
| URL: | http://d.repec.org/n?u=RePEc:pur:prukra:1262&r=gth |
| By: | Seierstad, Atle (Dept. of Economics, University of Oslo) |
| Abstract: | This paper yields sufficient conditions for Pareto inoptimality of controls forming Nash equilibria in differential games. In Appendix a result on existence of open loop Nash equilibria is added. |
| Keywords: | Differential games; Nash equilibria; Pareto improvements |
| JEL: | C73 |
| Date: | 2011–09–14 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:osloec:2011_019&r=gth |
| By: | Russo, Giuseppe; Senatore, Luigi |
| Abstract: | Decisions on joint funding of continuous public goods between two agents often involve heterogeneous targets. We introduce loss functions in a contribution game in order to study the effect of this conflict. Unlike Varian (1994), joint contribution occurs only if the players’ targets are sufficiently close and the sequential game reduces free riding problems, while total contribution is higher in the simultaneous game. |
| Keywords: | Public Goods; Intergovernmental Relations |
| JEL: | H77 H41 C72 |
| Date: | 2011–08 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:33423&r=gth |
| By: | Julian Romero |
| Abstract: | One of the fundamental problems in both economics and organization is to understand how individuals coordinate. The widely used minimum-effort coordination game has been used as a simplied model to better understand this problem. This paper rst presents some theoretical results that give conditions under which the minimum-effort coordination game exhibits hysteresis. Using these theoretical results, some experimental hypotheses are developed and then conrmed using human subjects in the laboratory. The main insight is that play in a given game is heavily dependent on the history of parameters leading up to that game. For example, the experiments show when cost c = 0:5 in the minimum-effort coordination game, there is signicantly more high effort if the cost has increased to c = 0:5 compared to when the cost has decreased to c = 0:5. One implication of this is that a temporary change in parameters may be able move the economic system from a bad equilibrium to a good equilibrium. |
| Keywords: | Hysteresis, Minimum-effort Coordination Game, Logit Equilibrium, Experimental Economics, Equilibrium Selection |
| JEL: | C72 C92 M53 |
| Date: | 2011–09 |
| URL: | http://d.repec.org/n?u=RePEc:pur:prukra:1265&r=gth |
| By: | Indrajit Ray; Sonali Sen Gupta |
| Abstract: | For duopoly models, we consider the notion of weak correlation using simple symmetric devices that the players choose to commit to in equilibrium. In a linear duopoly game, we prove that Nashcentric devices involving a sunspot structure are simple symmetric weak correlated equilibria. Any small perturbation from such a structure fails to be an equilibrium. |
| Keywords: | Duopoly, weak Correlation, Simple device, Sunspots |
| JEL: | C72 |
| Date: | 2011–09 |
| URL: | http://d.repec.org/n?u=RePEc:bir:birmec:11-14&r=gth |
| By: | Michalis Drouvelis; Alejandro Saporiti; Nicolaas J Vriend |
| Abstract: | We study both theoretically and experimentally the complete set of Nash equilibria of a classical one-dimensional, majority rule election game with two candidates, who might be interested in power as well as in ideology, but not necessarily in the same way. Apart from obtaining the well known median voter result and the two-sided policy differentiation outcome, the paper uncovers the existence of two new equilibrium configurations, called 'one-sided' and probabilistic' policy differentiation, respectively. Our analysis shows how these equilibrium configurations depend on the relative interests in power (resp., ideology) and the uncertainty about voters' preferences. The theoretical predictions are supported by the data collected from a series of laboratory experiments, as we observe convergence to the Nash equilibrium values at the aggregate as well as the individual levels in all treatments, and the comparative statics effects across treatments are as prediced by the theory. |
| Keywords: | Electoral competition, Power, Ideology, Uncertainty, Nash equilibrium |
| JEL: | C72 C90 D7 |
| Date: | 2011–08 |
| URL: | http://d.repec.org/n?u=RePEc:bir:birmec:11-15&r=gth |
| By: | Fabrice Valognes, Université de Caen Basse-Normandie, CREM-CNRS UMR 6211; Hélène Ferrer, Université de Caen Basse-Normandie, CREM-CNRS UMR 6211; Guillermo Owen, Dept. of Mathematics, Naval Postgraduate School, Monterey, USA. |
| Abstract: | We consider a situation in which members of an oligopoly have different technologies, which allow them to produce at different costs. Members may license their technology to other members. Using the Aumann-Drèze modification of the Shapley value, we compute fair prices for these licenses. We also study the problem of stability for these ``licensing coalitions.'' |
| Keywords: | Cooperative Game Theory, Technology Transfers, Modified Shapley Value |
| JEL: | C71 L13 L24 |
| Date: | 2011–04 |
| URL: | http://d.repec.org/n?u=RePEc:tut:cremwp:201109&r=gth |
| By: | Stephen Kinsella (Department of Economics, Kemmy School of Business, University of Limerick); David M. Ramsey (Department of Mathematics and Statistics, University of Limerick) |
| Abstract: | We present a model of partnership formation based on two discrete character traits. There are two classes of individual. Each individual observes a sequence of potential partners from the other class. The traits are referred to as attractiveness and character, respectively. All individuals prefer partners of high attractiveness and similar character. Attractiveness can be measured instantly. However, in order to observe the character of an individual, a costly interview (or date) is required. On observing the attractiveness of a prospective partner, an individual must decide whether he/she wishes to proceed to the interview stage. During the interview phase, the prospective pair observe each other's character and then decide whether they wish to form a pair. Mutual acceptance is required for both an interview to occur and a pair to form. An individual stops searching on nding a partner. A set of criteria based on the concept of a subgame perfect Nash equilibrium is used to define an equilibrium of this game. It is argued that under such a general formulation there may be multiple equilibria. For this reason, we define a specific formulation of the game, the so called symmetric version, which has a unique symmetric equilibrium. The form of this equilibrium has some similarities to the block separating equilibrium derived for classical models of two-sided mate choice and job search problems, but is essentially different. |
| Keywords: | mutual mate choice, game theory, common preferences, homotypic preferences, subgame perfect equilibrium |
| Date: | 2011–09–13 |
| URL: | http://d.repec.org/n?u=RePEc:ucd:wpaper:201119&r=gth |
| By: | Norovsambuu Tumennasan (School of Economics and Management, Aarhus University, Denmark) |
| Abstract: | Economists perceive moral hazard as an undesirable problem because it undermines efficiency. Carefully designed contracts can mitigate the moral hazard problem, but this assumes that a team is already formed. This paper demonstrates that these contracts are sometimes the reason why teams do not form. Formally, we study the team formation problem in which the agents’ efforts are not verifiable and the size of teams does not exceed quota r. We show that if the team members can make only balanced transfers, then moral hazard affects stability adversely. However, if the team members cannot make transfers, then moral hazard affects stability positively in a large class of games. For example, a stable team structure exists if teams produce public goods or if the quota is two. However, these existence results no longer hold if efforts are verifiable. |
| Keywords: | team formation, hedonic game, moral hazard, assortative partition |
| JEL: | C71 C78 |
| Date: | 2011–09–12 |
| URL: | http://d.repec.org/n?u=RePEc:aah:aarhec:2011-12&r=gth |
| By: | Ana Espinola-Arredondo; Felix Munoz-Garcia (School of Economic Sciences, Washington State University) |
| Abstract: | This paper investigates the effect of monopoly subsidies on entry deterrence. We consider a potential entrant who observes two signals: the subsidy set by the regulator and the output level produced by the incumbent firm. We show that not only an informative equilibrium can be supported, where information about the incumbent's costs is conveyed to the entrant, but also an uninformative equilibrium, where the actions of regulator and incumbent conceal the monopolist's type, thus deterring entry. While the regulator?s role can support entry-deterrence practices, we demonstrate that his presence is nonetheless welfare improving. Furthermore, we compare equilibrium welfare relative to two benchmarks: complete information environments, and standard entry-deterrence games where the regulator is absent. |
| Keywords: | Entry deterrence; Signaling; Monopoly subsidies |
| JEL: | D82 H23 L12 Q5 |
| Date: | 2011–09 |
| URL: | http://d.repec.org/n?u=RePEc:wsu:wpaper:espinola-10&r=gth |
| By: | Elvio Accinelli (Facultad de Economía, Universidad Autónoma de san Luis Potosí. Departamento de Economía, Facultad de Ciencias Sociales, Universidad de la República); Leobardo Plata (Facultad de Economía, Universidad Autónoma de san Luis Potosí.); Joss Sánchez (Facultad de Economía, Universidad Autónoma de san Luis Potosí.) |
| Abstract: | This paper provides an analysis of solutions to bankruptcy problems from an axiomatic point of view. In particular, we provide characterizations of certain classes of solutions involving the properties of linearity, symmetry and efficiency. Furthermore, we show that there is a unique solution satisfying the previous axioms and inessentiality. |
| Keywords: | Bankruptcy problems, axiomatic solutions. |
| JEL: | A12 C71 C02 |
| Date: | 2011–08 |
| URL: | http://d.repec.org/n?u=RePEc:ude:wpaper:1911&r=gth |
| By: | Anna Conte (Max Planck Institute of Economics, Jena, and University of Westminster, EQM Department, London); M. Vittoria Levati (Max Planck Institute of Economics, Jena, and University of Verona, Department of Economics) |
| Abstract: | In a series of one-shot linear public goods game, we ask subjects to report their contributions, their contribution plans for the next period, and their first-order beliefs about their present and future partner. We estimate subjects' preferences from plans data by a finite mixture approach and compare the results with those obtained from contribution data. Our results indicate that preferences are heterogeneous, and that most subjects exhibit conditionally cooperative inclinations. Controlling for beliefs, which incorporate the information about the other's decisions, we are able to show that plans convey accurate information about subjects' preferences and, consequently, are good predictors of their future behavior. |
| Keywords: | Public goods games, Experiments, Social preferences, Mixture models |
| JEL: | C35 C51 C72 H41 |
| Date: | 2011–09–13 |
| URL: | http://d.repec.org/n?u=RePEc:jrp:jrpwrp:2011-039&r=gth |
| By: | Hammond, Peter J (Department of Economics, University of Warwick) |
| Abstract: | The subjective expected utility (SEU) criterion is formulated for a particular four-person “laboratory game” that a Bayesian rational decision maker plays with Nature, Chance, and an Experimenter who influences what quantum behaviour is observable by choosing an orthonormal basis in a separable complex Hilbert space of latent variables. Nature chooses a state in this basis, along with an observed data series governing Chance's random choice of consequence. When Gleason's theorem holds, imposing quantum equivalence implies that the expected likelihood of any data series w.r.t. prior beliefs equals the trace of the product of appropriate subjective density and likelihood operators. |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:wrk:warwec:969&r=gth |