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on Game Theory |
| By: | Ismail M.S. (GSBE) |
| Abstract: | We introduce a new concept which extends von Neumann and Morgensterns maximin strategy solution by incorporating individual rationality of the players. Maximin equilibrium, extending Nashs value approach, is based on the evaluation of the strategic uncertainty of the whole game. We show that maximin equilibrium is invariant under strictly increasing transformations of the payoffs. Notably, every finite game possesses a maximin equilibrium in pure strategies. Considering the games in von Neumann-Morgenstern mixed extension, we demonstrate that the maximin equilibrium value is precisely the maximin minimax value and it coincides with the maximin strategies in twoperson zerosum games. We also show that for every Nash equilibrium that is not a maximin equilibrium there exists a maximin equilibrium that Pareto dominates it. Hence, a strong Nash equilibrium is always a maximin equilibrium. In addition, a maximin equilibrium is never Pareto dominated by a Nash equilibrium. Finally, we discuss maximin equilibrium predictions in several games including the travelers dilemma. |
| Keywords: | Noncooperative Games; |
| JEL: | C72 |
| Date: | 2014 |
| URL: | http://d.repec.org/n?u=RePEc:unm:umagsb:2014037&r=gth |
| By: | Ulrich Faigle (Universität zu Köln - Mathematisches Institut); Michel Grabisch (Centre d'Economie de la Sorbonne - Paris School of Economics); Andres Jiménez-Losada (University of Seville - Escuela Superior de Ingenieros); Manuel Ordóñez (University of Seville - Escuela Superior de Ingenieros) |
| Abstract: | We introduce cooperative TU-games on concept lattices, where a concept is a pair (S,S') with S being a subset of players or objects, and S' a subset of attributes. Any such game induces a game on the set of players/objects, which appears to be a TU-game whose collection of feasible coalitions is a lattice closed under intersection, and a game on the set of attributes. We propose a Shapley value for each type of game, axiomatize it, and investigate the geometrical properties of the core (nonemptiness, boundedness, pointedness, extremal rays). |
| Keywords: | Cooperation game, restricted cooperation, concept lattice, core, Shapley value. |
| JEL: | C71 |
| Date: | 2014–10 |
| URL: | http://d.repec.org/n?u=RePEc:mse:cesdoc:14070&r=gth |
| By: | Khmelnitskaya, A.; Selçuk, O. (Tilburg University, Center For Economic Research); Talman, A.J.J. (Tilburg University, Center For Economic Research) |
| Abstract: | The Shapley value for directed graph (digraph) games, TU games with limited cooperation introduced by an arbitrary digraph prescribing the dominance relation among the players, is introduced. It is defined as the average of marginal contribution vectors corresponding to all permutations that do not violate the subordination of players. We assume that in order to cooperate players may join only coalitions containing no players dominating them. Properties of this solution are studied and a convexity type condition is provided that guarantees its stability with respect to an appropriately defined core concept. An axiomatization for cycle digraph games for which the digraphs are directed cycles is obtained. |
| Keywords: | TU game; Shapley value; directed graph; dominance structure; core; convexity |
| JEL: | C71 |
| Date: | 2014 |
| URL: | http://d.repec.org/n?u=RePEc:tiu:tiucen:86cd17d2-cbc2-43ed-a4af-728311063c05&r=gth |
| By: | Sergiu Hart |
| Abstract: | A Lotto game is a two-person zero-sum game where each player chooses a distribution on nonnegative real numbers with given expectation, so as to maximize the probability that his realized choice is higher than his opponent's. These games arise in various competitive allocation setups (e.g., contests, research and development races, political campaigns, Colonel Blotto games). A Captain Lotto game is a Lotto game with caps, which are upper bounds on the numbers that may be chosen. First, we solve the Captain Lotto games. Second, we show how to reduce all-pay auctions to simpler games—expenditure games—using the solution of the corresponding Lotto games. As a particular application we solve all-pay auctions with unequal caps, which yield a significant increase in the seller's revenue (or, the players' efforts). |
| Date: | 2014–11 |
| URL: | http://d.repec.org/n?u=RePEc:huj:dispap:dp670&r=gth |
| By: | Peleg, Bezalel (Institute of Mathematics and The Federmann Center for the Study of Rationality); Sudhölter, Peter (Department of Business and Economics) |
| Abstract: | We show that the Aumann-Davis-Maschler bargaining set and the Mas-Colell bargaining set of a non-leveled NTU game that is either ordinal convex or coalition merge convex coincides with the core of the game. Moreover, we show by means of an example that the foregoing statement may not be valid if the NTU game is marginal convex. |
| Keywords: | NTU game; Convex game; Bargaining set |
| JEL: | C71 |
| Date: | 2014–12–03 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:sdueko:2014_019&r=gth |
| By: | Wärneryd, Karl (Dept. of Economics) |
| Abstract: | We consider rules (strategies, commitments, contracts, or computer programs) that make behavior contingent on an opponent’s rule. The set of perfectly observable rules is not well defined. Previous contributions avoid this problem by restricting the rules deemed admissible. We instead limit the information available about rules. Each player can only observe which class, out of a collection of classes smaller than the number of rules, the opponent’s rule belongs to. For any underlying 2-player, finite, normal-form game there is a game extended with coarsely observable strategies that has equilibria with payoffs arbitrarily close to any feasible, individually rational payoff profile. |
| Keywords: | Cooperation; reciprocity; transparency; commitment; contract |
| JEL: | C72 C78 D74 D86 |
| Date: | 2014–11–12 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:hastec:2014_002&r=gth |
| By: | Michael Trost (Max Planck Institute of Economics, Jena) |
| Abstract: | One central issue tackled in epistemic game theory is whether for a general class of strategic games the solution generated by iterated application of a choice rule gives exactly the strategy profiles that might be realized by players who follow this choice rule and commonly believe they follow this rule. For example, Brandenburger and Dekel (1987) and Tan and Werlang (1988) have established that this coincidence holds for the choice rule of strict undominance in mixtures in the class of finite strategic games, and Mariotti (2003) has established that this coincidence holds for Bernheim's (1984) choice rule of point rationality in the class of strategic games in which the strategy sets are compact Hausdorff and the payoff functions are continuous. In this paper, we aim at studying this coincidence in a general way. We seek to figure out general conditions of the choice rules ensuring it for a general class of strategic games. We state four substantial assumptions on choice rules. If the players' choices rules satisfy - besides the technical assumption of regularity - the properties of reflexivity, monotonicity, Aizerman's property, and the independence of payoff equivalent conditions, then this coincidence applies. This result proves to be strict in the following sense. None of the four substantial properties can be omitted without eliminating the coincidence. |
| Keywords: | Iterative deletion procedure, common belief, choice rule, epistemic game theory |
| JEL: | C72 D83 |
| Date: | 2014–11–25 |
| URL: | http://d.repec.org/n?u=RePEc:jrp:jrpwrp:2014-032&r=gth |
| By: | Erik Mohlin; Robert Ostling; Joseph Tao-yi Wang |
| Abstract: | We exploit a unique opportunity to study how a large population of players in the field learn to play a novel game with a complicated and non-intuitive mixed strategy equilibrium. We argue that standard models of belief-based learning and reinforcement learning are unable to explain the data, but that a simple model of similarity-based global cumulative imitation can do so. We corroborate our findings using laboratory data from a scaled-down version of the same game, as well as from three other games. The theoretical properties of the proposed learning model are studied by means of stochastic approximation. |
| Keywords: | Learning, imitation, behavioral game theory, evolutionary game theory, stochastic approximation, replicator dynamic, similarity-based reasoning, generalization, mixed equilibrium |
| JEL: | C72 C73 L83 |
| Date: | 2014–11–28 |
| URL: | http://d.repec.org/n?u=RePEc:oxf:wpaper:734&r=gth |
| By: | Kimmo Berg (Systems Analysis Laboratory, Aalto University School of Science); Mitri Kitti (Department of Economics, University of Turku) |
| Abstract: | This paper characterizes the subgame-perfect pure-strategy equilibrium paths in discounted supergames with perfect monitoring. It is shown that all the equilibrium paths are composed of fragments called elementary subpaths. This characterization result is complemented with an algorithm for finding the elementary subpaths. By using these subpaths it is possible to generate equilibrium paths and payoffs. When there are finitely many elementary subpaths, all the equilibrium paths can be represented by a directed graph. These graphs can be used in analyzing the complexity of equilibrium outcomes. In particular, it is shown that the size and the density of the equilibrium set can be measured by the asymptotic growth rate of equilibrium paths and the Hausdorff dimension of the payoff set. |
| Keywords: | repeated game, subgame-perfect equilibrium, equilibrium path, graph presentation of paths, complexity |
| JEL: | C72 C73 |
| Date: | 2014–12 |
| URL: | http://d.repec.org/n?u=RePEc:tkk:dpaper:dp96&r=gth |
| By: | Einy, Ezra; Haimanko, Ori; Orzach, Ram; Sela, Aner |
| Abstract: | We study two-player common-value all-pay auctions (contests) with asymmetric information under the assumption that one of the players has an information advantage over his opponent and both players are budget-constrained. We generalize the results for all-pay auctions with complete information, and show that in all-pay auctions with asymmetric information, sufficiently high (but still binding) bid caps do not change the players' expected total effort compared to the benchmark auction without any bid cap. Furthermore, we show that there are bid caps that increase the players' expected total effort compared to the benchmark. Finally, we demonstrate that there are bid caps which may have an unanticipated effect on the players' expected payoffs – one player's information advantage may turn into a disadvantage as far as his equilibrium payoff is concerned. |
| Keywords: | asymmetric information; bid caps; common-value all-pay auctions; information advantage |
| JEL: | C72 D44 |
| Date: | 2014–09 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:10173&r=gth |
| By: | Ahmet Ozkardas (Turgut Özal Üniversitesi et Centre d'Economie de la Sorbonne); Agnieszka Rusinowska (Centre d'Economie de la Sorbonne - Paris School of Economics) |
| Abstract: | We consider a union-firm wage bargaining in which the preferences of the union and the firm are expressed by sequences of discount rates varying in time. The contribution of the paper is twofold. First, we consider a model in which the union must choose between strike and holdout in case of disagreement. We show that there exist inefficient subgame perfect equilibria in the model where the union engages in several periods of strikes prior to reaching a final agreement. Furthermore, we analyze a wage bargaining in which the firm is allowed to engage in lockouts. We consider a game in which only lockouts are feasible, i.e., strikes are not allowed. We prove that under certain assumptions there is a subgame perfect equilibrium for this game and it leads to an immediate agreement which yields the union a wage contract smaller that the statuts quo contract. Under this equilibrium the firm always locks out the union after its own offer is rejected and holds out after rejecting an offer of the union. |
| Keywords: | Union, firm bargaining, varying discount rates, subgame perfect equilibrium, inefficient equilibria, strike, lockouts. |
| JEL: | J52 C78 |
| Date: | 2014–09 |
| URL: | http://d.repec.org/n?u=RePEc:mse:cesdoc:14073&r=gth |
| By: | Andersson, T.; Gudmundsson, J.; Talman, A.J.J. (Tilburg University, Center For Economic Research); Yang, Z. |
| Abstract: | A group of heterogenous agents may form partnerships in pairs. All single agents as well as all partnerships generate values. If two agents choose to cooperate, they need to specify how to split their joint value among one another. In equilibrium, which may or may not exist, no agents have incentives to break up or form new partnerships. This paper proposes a dynamic competitive adjustment process that always either finds an equilibrium or exclusively disproves the existence of any equilibrium in finitely many steps. When an equilibrium exists, partnership and revenue distribution will be automatically and endogenously determined by the process. Moreover, several fundamental properties of the equilibrium solution and the model are derived. |
| Keywords: | Partnership formation; adjustment process; equilibrium; assignment market |
| JEL: | C62 C72 D02 |
| Date: | 2013 |
| URL: | http://d.repec.org/n?u=RePEc:tiu:tiucen:b5dd75eb-d5be-4788-97b4-fd233c48babc&r=gth |
| By: | Krumer, Alex; Megidish, Reut; Sela, Aner |
| Abstract: | We study round-robin tournaments with one prize and four symmetric players. There are three rounds, each of which includes two sequential matches where each player plays against a different opponent in every round. Each pair-wise match is modelled as an all-pay auction. We characterize the sub-game perfect equilibrium and show that a player who plays in the first match of each of the first two rounds has a first-mover advantage as reflected by a significantly higher winning probability as well as a significantly higher expected payoff than his opponents. Therefore, if the contest designer wishes to sustain the fair play principle he has to schedule all the matches in each round at the same time in order to obstruct a meaningful advantage to one of the players. |
| Keywords: | all-pay contests; round-robin tournaments |
| JEL: | D44 O31 |
| Date: | 2014–11 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:10274&r=gth |
| By: | Deimen, Inga; Szalay, Dezso |
| Abstract: | We study strategic information transmission in a Sender-Receiver game where players' optimal actions depend on the realization of multiple signals but the players disagree on the relative importance of each piece of news. We characterize a statistical environment - featuring symmetric loss functions and elliptically distributed parameters - in which the Sender's expected utility depends only on the first moment of his posterior. Despite disagreement about the use of underlying signals, we demonstrate the existence of equilibria in differentiable strategies in which the Sender can credibly communicate posterior means. The existence of smooth communication equilibria depends on the relative usefulness of the signal structure to Sender and Receiver, respectively. We characterize extensive forms in which the quality of information is optimally designed of equal importance to Sender and Receiver so that the best equilibrium in terms of ex ante expected payoffs is a smooth communication equilibrium. The quality of smooth equilibrium communication is entirely determined by the correlation of interests. Senders with better aligned preferences are endogenously endowed with better information and therefore give more accurate advice. |
| Keywords: | elliptical distribution; endogenous information; monotone strategies; multi-dimensional cheap talk; strategic information transmission |
| JEL: | D82 |
| Date: | 2014–10 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:10190&r=gth |
| By: | Hubert János Kiss (‘Momentum’ Game Theory Research Group, Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences and Eötvös Loránd University - Department of Economics); Ismael Rodriguez-Lara (Middlesex University London - Business School and LUISS Guido Carli University, Rome); Alfonso Rosa-García (Facultad de Ciencias Juridicas y de la Empresa, Universidad Catolica San Antonio) |
| Abstract: | We assess the impact of cognitive abilities on withdrawal decisions in a bank-run game. In our setup, depositors choose sequentially between withdrawing or keeping their funds deposited in a common bank. They may observe previous decisions depending on the information structure. Theoretically, the last depositor in the sequence of decisions has a dominant strategy and should always keep the funds deposited, regardless of what she observes (if anything). Recognizing the dominant strategy, however, is not always straightforward. If there exists strategic uncertainty (e.g., the last depositor has no information about predecessors’ decisions) the identification of the dominant strategy requires harder thinking than when there is not strategic uncertainty (e.g., the last depositor is informed about all previous decisions). We find that cognitive abilities, as measured by the Cognitive Reflection Test (CRT), predict withdrawals in the presence of strategic uncertainty (participants with higher abilities tend to identify the dominant strategy more easily) but the CRT does not predict behavior when there is no strategic uncertainty. |
| Keywords: | bank runs, coordination game, observability of actions, cognitive abilities, strate-gic uncertainty |
| JEL: | C91 D03 D8 G02 J16 |
| Date: | 2014–11 |
| URL: | http://d.repec.org/n?u=RePEc:has:discpr:1428&r=gth |
| By: | Hidir, Sinem |
| Abstract: | This paper studies a buyer-seller game with pre-trade communication of private horizontal taste from the buyer followed by a take it or leave it offer by the seller. The amount of information transmitted improves the gains from trade, but also determines how this surplus will be shared between the two. Lack of commitment to a price creates a hold-up problem and a trade off between efficiency and rent extraction. In this setting, coarse information arises due to the concerns on the terms of the transaction. As the preferences get less important, information transmission becomes less precise. It is shown that in the buyer optimal equilibria of the static and dynamic games, the messages sent are just informative enough to ensure trade. In the dynamic game, the buyer is always better off sending infor- mative messages only at the first period, implying no gains from gradual revelation of information. |
| Keywords: | information; cheap-talk; bargaining; buyer-seller relation |
| JEL: | C72 D83 |
| Date: | 2014–11 |
| URL: | http://d.repec.org/n?u=RePEc:tse:wpaper:28788&r=gth |
| By: | Maria Vittoria Levati (Department of Economics (University of Verona)); Stefan Napel (University of Bayreuth); Ivan Soraperra (Department of Economics (University of Verona)) |
| Keywords: | Ambiguity aversion, majority voting, dictatorship |
| JEL: | C91 C92 D71 D81 |
| Date: | 2014–08 |
| URL: | http://d.repec.org/n?u=RePEc:ver:wpaper:13/2014&r=gth |
| By: | Drugov, Mikhail |
| Abstract: | This paper studies a dynamic bargaining model with informational externalities between bargaining pairs. Two principals bargain with their respective agents about the price they will pay for their work while its cost is agents' private information and correlated between them. The principals benchmark their agents against each other by making the same offers in the equilibrium even if this involves delaying or advancing the agreement compared to the autarky. When principals compete in complements this pattern is reinforced while under competition in substitutes the principals trade off the benefits of differentiation in the product market against the cost of the agents' rent. |
| Keywords: | adverse selection; bargaining; competition; delay; externalities; information |
| JEL: | C78 D82 D83 L10 |
| Date: | 2014–06 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:10021&r=gth |
| By: | Hakimov, Rustamdjan; Kesten, Onur |
| Abstract: | A particular adaptation of Gale's top trading cycles procedure to school choice, the so-called TTC mechanism, has attracted much attention both in theory and practice due to its superior efficiency and incentive features. We discuss and introduce alternative adaptations of Gale's original procedure that can offer improvements over TTC in terms of equity along with various other distributional considerations. Instead of giving all the trading power to those students with the highest priority for a school, we argue for the distribution of the trading rights of all slots of each school among those who are entitled to a slot at that school, allowing them to trade in a thick market where additional constraints can be accommodated. We propose a particular mechanism of this kind, the Equitable Top Trading Cycles (ETTC) mechanism, which is also Pareto efficient and strategy-proof just like TTC and eliminates justified envy due to pairwise exchanges. Both in simulations and in the lab, ETTC generates significantly fewer number of justified envy situations than TTC. |
| Keywords: | school choice,stability,top trading cycles |
| JEL: | C78 C79 D61 D78 I20 |
| Date: | 2014 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:wzbmbh:spii2014210&r=gth |