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on Game Theory |
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Issue of 2012‒06‒13
sixteen papers chosen by Laszlo A. Koczy Hungarian Academy of Sciences and Obuda University |
| By: | Helga Habis (Institute of Economics, Hungarian Academy of Sciences Department of Microeconomics, Corvinus University of Budapest); P. Jean-Jacques Herings (Department of Economics, Universiteit Maastricht) |
| Abstract: | We study bankruptcy games where the estate and the claims have stochastic values. We use the Weak Sequential Core as the solution concept for such games.We test the stability of a number of well known division rules in this stochastic setting and find that most of them are unstable, except for the Constrained Equal Awards rule, which is the only one belonging to the Weak Sequential Core. |
| Keywords: | transferable utility games, uncertainty, weak sequential core, bankruptcy games |
| JEL: | C71 C73 |
| Date: | 2012–02 |
| URL: | http://d.repec.org/n?u=RePEc:has:discpr:1205&r=gth |
| By: | Peter Biro (Institute of Economics - Hungarian Academy of Sciences); Walter Kern (Faculty of Electrical Engineering, Mathematics and Computer Science, University of Twente, P.O.Box 217, NL-7500 AE Enschede); Daniel Paulusma (Department of Computer Science, University of Durham Science Laboratories, South Road, Durham DH1 3EY, England) |
| Abstract: | A matching game is a cooperative game (N; v) defined on a graph G = (N;E) with an edge weighting w : E ! R+. The player set is N and the value of a coalition S N is dened as the maximum weight of a matching in the subgraph induced by S. First we present an O(nm+n2 log n) algorithm that tests if the core of a matching game defined on a weighted graph with n vertices and m edges is nonempty and that computes a core member if the core is nonempty. This algorithm improves previous work based on the ellipsoid method and can also be used to compute stable solutions for instances of the stable roommates problem with payments. Second we show that the nucleolus of an n-player matching game with a nonempty core can be computed in O(n4) time. This generalizes the corresponding result of Solymosi and Raghavan for assignment games. Third we prove that is NP-hard to determine an imputation with minimum number of blocking pairs, even for matching games with unit edge weights, whereas the problem of determining an imputation with minimum total blocking value is shown to be polynomial-time solvable for general matching games. |
| Keywords: | matching game; nucleolus; cooperative game theory |
| JEL: | C61 C63 C71 C78 |
| Date: | 2011–12 |
| URL: | http://d.repec.org/n?u=RePEc:has:discpr:1142&r=gth |
| By: | Meier, Martin (IHS Vienna); Schipper, Burkhard C. (University of CA, Davis) |
| Abstract: | Applying unawareness belief structures introduced in Heifetz, Meier, and Schipper (2012), we develop Bayesian games with unawareness, define equilibrium, and prove existence. We show how equilibria are extended naturally from lower to higher awareness levels and restricted from higher to lower awareness levels. We apply Bayesian games with unawareness to investigate the robustness of equilibria to uncertainty about opponents' awareness of actions. We show that a Nash equilibrium of a strategic game is robust to unawareness of actions if and only if it is not weakly dominated. Finally, we discuss the relationship between standard Bayesian games and Bayesian games with unawareness. |
| JEL: | C70 C72 D80 D82 |
| Date: | 2012–05 |
| URL: | http://d.repec.org/n?u=RePEc:ecl:ucdeco:2012-09&r=gth |
| By: | Judit M rkus (Corvinus University of Budapest); Anna Radv nyi (Department of Mathematics, Corvinus University of Budapest); Mikl¢s Pint‚r (Department of Mathematics, Corvinus University of Budapest) |
| Abstract: | In this paper cost sharing problems are considered. We focus on problems on a rooted tree, we call these problems cost-tree problems, and on the induced transferable utility cooperative games, we call these games 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 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 on a rooted tree. In our characterization results we relate the TU games terminologies to the cost sharing terminologies, so we bridge between the two fields. |
| Keywords: | Cost sharing; Shapley value; Rooted tree; Axiomatization of the Shapley value |
| JEL: | C71 |
| Date: | 2012–02 |
| URL: | http://d.repec.org/n?u=RePEc:has:discpr:1207&r=gth |
| By: | P‚ter Bir¢ (Institute of Economics Research Centre for Economic and Regional Studies Hungarian Academy of Sciences); Matthijs Bomhoff (Faculty of Electrical Engineering, Mathematics and Computer Science, University of Twente); Walter Kern (Faculty of Electrical Engineering, Mathematics and Computer Science, University of Twente); Petr A. Golovach (School of Engineering and Computing Sciences, Durham University, Science Laboratories); Dani‰l Paulusma (School of Engineering and Computing Sciences, Durham University, Science Laboratories) |
| Abstract: | The stable roommates problem with payments has as input a graph G(E,V) with an edge weighting w:E_ùR+ and the problem is to find a stable solution. A solution is a matching M with a vector p.RV that satisfies pu+pv=w(uv) for all uv.M and pu=0 for all u unmatched in M. A solution is stable if it prevents blocking pairs, i.e., pairs of adjacent vertices u and v with pu+pv<w(uv). By pinpointing a relationship to the accessibility of the coalition structure core of matching games, we give a simple constructive proof for showing that every yes-instance of the stable roommates problem with payments allows a path of linear length that starts in an arbitrary unstable solution and that ends in a stable solution. This result generalizes a result of Chen, Fujishige and Yang for bipartite instances to general instances. We also show that the problems Blocking Pairs and Blocking Value, which are to find a solution with a minimum number of blocking pairs or a minimum total blocking value, respectively, are NP-complete. Finally, we prove that the first problem is NP-complete also when a matching is prescribed, whereas this variant of the second problem becomes polynomial-time solvable. |
| Keywords: | roommates problem, matching game, cooperative game theory |
| JEL: | C61 C63 C71 C78 |
| Date: | 2012–03 |
| URL: | http://d.repec.org/n?u=RePEc:has:discpr:1211&r=gth |
| By: | Yehuda (John) Levy |
| Abstract: | We present an example of a discounted stochastic game with a continuum of states, finitely many players and actions, and deterministic transitions, that possesses no measurable stationary equilibria, or even stationary approximate equilibria. The example is robust to perturbations of the payoffs, the transitions, and the discount factor, and hence gives a strong nonexistence result for stationary equilibria. The example is a game of perfect information, and hence it also does not possess stationary extensive-form correlated equilibrium. Markovian equilibria are also shown not to exist in appropriate perturbations of our example. |
| Keywords: | Stochastic Game, Discounting, Stationary Equilibrium |
| Date: | 2012–01–11 |
| URL: | http://d.repec.org/n?u=RePEc:huj:dispap:dp596r&r=gth |
| By: | Kleppe, J.; Borm, P.E.M.; Hendrickx, R.L.P. (Tilburg University, Center for Economic Research) |
| Abstract: | Abstract: In this paper we provide a characterisation of the set of fall back equilibria for 2 x n bimatrix games. Furthermore, for this type of games we discuss the relation between the set of fall back equilibria and the sets of perfect, proper and strictly perfect equilibria. In order to do this we reformulate the existing characterizations for these three equilibrium concepts by the use of refinement-specific subgames. |
| Keywords: | game theory;fall back equilibrium;2 x n bimatrix game;equilibrium refinement. |
| JEL: | C72 |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:kubcen:2012044&r=gth |
| By: | Aldo Rustichini (Department of Economics, University of Minnesota - University of Minnesota); Marie-Claire Villeval (GATE Lyon Saint-Etienne - Groupe d'analyse et de théorie économique - CNRS : UMR5824 - Université Lumière - Lyon II - École Normale Supérieure - Lyon) |
| Abstract: | We show with a laboratory experiment that individuals adjust their moral principles to the situation and to their actions, just as much as they adjust their actions to their principles. We first elicit the individuals' principles regarding the fairness and unfairness of allocations in three different scenarios (a Dictator game, an Ultimatum game, and a Trust game). One week later, the same individuals are invited to play those same games with monetary compensation. Finally in the same session we elicit again their principles regarding the fairness and unfairness of allocations in the same three scenarios. Our results show that individuals adjust abstract norms to fit the game, their role and the choices they made. First, norms that appear abstract and universal take into account the bargaining power of the two sides. The strong side bends the norm in its favor and the weak side agrees : Stated fairness is a compromise with power. Second, in most situations, individuals adjust the range of fair shares after playing the game for real money compared with their initial statement. Third, the discrepancy between hypothetical and real behavior is larger in games where real choices have no strategic consequence (Dictator game and second mover in Trust game) than in those where they do (Ultimatum game). Finally the adjustment of principles to actions is mainly the fact of individuals who behave more selfishly and who have a stronger bargaining power. The moral hypocrisy displayed (measured by the discrepancy between statements and actions chosen followed by an adjustment of principles to actions) appears produced by the attempt, not necessarily conscious, to strike a balance between self-image and immediate convenience. |
| Keywords: | Moral hypocrisy; fairness; social preferences; power; self-deception |
| Date: | 2012–05–30 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:halshs-00702578&r=gth |
| By: | Bonanno, Giacomo (University of CA, Davis) |
| Abstract: | This is the first draft of a chapter for the forthcoming Handbook of Epistemic Logic, edited by Hans van Ditmarsch, Joe Halpern, Wiebe van der Hoek and Barteld Kooi (College Publications). Contents: 1. Introduction 2. Epistemic Models of Strategic-Form Games 3. Semantic Analysis of Common Belief of Rationality 4. Syntactic Characterization of Common Belief of Rationality 5. Common Belief versus Common Knowledge 6. Probabilistic Beliefs and von Neumann- Morgenstern Payoffs 7. Dynamic Games with Perfect Information 8. The Semantics of Belief Revision 9. Common Belief of Rationality in Perfect-Information Games 10. Literature Review. |
| Date: | 2012–05 |
| URL: | http://d.repec.org/n?u=RePEc:ecl:ucdeco:2012-11&r=gth |
| By: | Grundel, S.; Ciftci, B.B.; Borm, P.E.M.; Hamers, H.J.M. (Tilburg University, Center for Economic Research) |
| Abstract: | To analyze the allocation problem of the maximal cost savings of the whole group of jobs, we define and analyze a so-called corresponding cooperative family sequencing game which explicitly takes into account the maximal cost savings for any coalition of jobs. Using nonstandard techniques we prove that each family sequencing game has a non-empty core by showing that a particular marginal vector belongs to the core. Finally, we specifically analyze the case in which the initial order is family ordered. |
| Keywords: | Single-machine scheduling;Family scheduling model;Setup times;Cooperative Game;Core;Marginal Vector. |
| JEL: | C71 |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:kubcen:2012040&r=gth |
| By: | Francesco Guala; Luigi Mittone; Matteo Ploner |
| Abstract: | Group membership increases cooperation in social dilemma games, altruistic donation in dictator games, and fair offers in ultimatum games. While the empirical study of group action has grown rapidly over the years, there is little agreement at the theoretical level on exactly why and how group membership changes individual behaviour. According to some theorists, the effect of group framing is channelled primarily via the beliefs of group members, while others identify changes in preference as the key explanatory mechanism. We report an experiment using the minimal group paradigm and a prisoner’s dilemma with multiple actions, in which we manipulate players’ beliefs and show that common knowledge of group affiliation is necessary for group action. We also observe puzzling variations in behaviour when knowledge of group membership is asymmetric, which may be interpreted as cognitive dissonance generated by a normative cue administered in a highly unusual situation. |
| Keywords: | group identity, team preferences, social dilemmas, experimental economics |
| JEL: | C72 C92 H41 |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:trn:utwpce:1203&r=gth |
| By: | Kesternich, Martin; Lange, Andreas; Sturm, Bodo |
| Abstract: | We investigate how burden sharing rules may impact the voluntary provision of a public good which generates heterogeneous benefits to agents. We compare different rule-based contribution schemes that are based on the principle of the smallest common denominator: all agents can suggest a minimum provision level of the public good that is allocated across agents according to some predetermined rule. We find that rule-based contribution schemes significantly increase payoff levels relative to the VCM. Important differences exist between the rules. Contrary to theory predictions, the equal-payoff rule Pareto-dominates all other rules. This also holds relative to a scheme where different types of players separately can determine their minimum contribution levels. Our results lend insights into the efficient institutional design for voluntary private provision of public goods, and how burden sharing rules interact with efficiency when agents are heterogeneous. -- |
| Keywords: | public goods,institutions,minimum contribution rules,cooperation,heterogeneity |
| JEL: | C72 C92 H41 |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:zewdip:12033&r=gth |
| By: | Wu, Haoyang |
| Abstract: | The Maskin's theorem is a fundamental work in the theory of mechanism design. In this paper, we propose that if agents report messages to the designer through channels (\emph{e.g.}, Internet), agents can construct a self-enforcing agreement such that any Pareto-inefficient social choice rule satisfying monotonicity and no-veto will not be Nash implementable when an additional condition is satisfied. The key points are: 1) The agreement is unobservable to the designer, and the designer cannot prevent the agents from constructing such agreement; 2) The agents act non-cooperatively, and the Maskin mechanism remain unchanged from the designer's perspective. |
| Keywords: | Mechanism design; Nash implementation; Social choice |
| JEL: | C70 |
| Date: | 2012–06–06 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:39268&r=gth |
| By: | Kenju Kamei; Louis Putterman |
| Abstract: | The expectation that non-cooperators will be punished can help to sustain cooperation, but there are competing claims about whether opportunities to engage in higher-order punishment (punishing punishment or failure to punish) help or undermine cooperation in social dilemmas. In a set of experimental treatments, we find that availability of higher-order punishment increases cooperation and efficiency when subjects have full information on the pattern of punishing, including its past history, and opportunities to punish are unrestricted. Availability of higher-order punishment reduces cooperation and efficiency if it is restricted to counter-punishing alone, if past history is unavailable, and if there is a dedicated counter-punishment stage. |
| Keywords: | collective action, social dilemma, voluntary contribution, public goods, punishment, counter-punishment, higher-order punishment. |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:bro:econwp:2012-3&r=gth |
| By: | Musolino, Francesco; Carfì, David |
| Abstract: | The aim of this paper is to propose a methodology to stabilize the currency markets by adopting Game Theory. Our idea is to save the Euro from the speculative attacks (due the crisis of the Euro-area States), and this goal is reached by the introduction, by the normative authority, of a financial transactions tax. Specifically, we focus on two economic operators: a real economic subject (as for example the Ferrari S.p.A., our first player), and a financial institute of investment (the Unicredit Bank, our second player). The unique solution which allows both players to win something, and therefore the only one collectively desirable, is represented by an agreement between the two subjects. So the Ferrari artificially causes an inconsistency between currency spot and futures markets, and the Unicredit takes the opportunity to win the maximum possible collective sum, which later will be divided with the Ferrari by contract. |
| Keywords: | Currency Markets; Financial Risk; Financial Crisis; Game Theory; Speculation |
| JEL: | G1 D53 C7 E44 |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:39240&r=gth |
| By: | Stephan Lauermann; Georg Nöldeke (University of Basel) |
| Keywords: | Marriage Market, Stable Matchings, Random Matchings, Serarch Frictions |
| JEL: | C78 D83 |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:bsl:wpaper:2012/10&r=gth |