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on Game Theory |
| By: | Ceparano, Maria Carmela; Quartieri, Federico |
| Abstract: | We prove the existence of a unique pure-strategy Nash equilibrium in nice games with isotone chain-concave best replies and compact strategy sets. We establish a preliminary fixpoint uniqueness argument, thus showing sufficient assumptions on the best replies of a nice game that guarantee the existence of exactly one Nash equilibrium. Then, by means of a comparative statics analysis, we examine the necessity and sufficiency of the conditions on marginal utility functions for such assumptions to be satisfied; in particular, we find necessary and sufficient conditions for the isotonicity and chain-concavity of best replies. We extend the results on Nash equilibrium uniqueness to nice games with upper unbounded strategy sets and we present "dual" results for games with isotone chain-convex best replies. A final application to Bayesian games is exhibited. |
| Keywords: | Nash equilibrium uniqueness; Chain-concave best reply; Nice game; Comparative statics; Strategic complementarity. |
| JEL: | C61 C72 |
| Date: | 2015–10–05 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:69010&r=gth |
| By: | Stéphane Gonzalez (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, Université Jean Monnet - Saint-Etienne); Michel Grabisch (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics) |
| Abstract: | In cooperative games, the core is one of the most popular solution concept since it ensures coalitional rationality. For non-balanced games however, the core is empty, and other solution concepts have to be found. We propose the use of general solutions, that is, to distribute the total worth of the game among groups rather than among individuals. In particular, the k-additive core proposed by Grabisch and Miranda is a general solution preserving coalitional rationality which distributes among coalitions of size at most k, and is never empty for k ≥ 2. The extended core of Bejan and Gomez can also be viewed as a general solution, since it implies to give an amount to the grand coalition. The k-additive core being an unbounded set and therefore difficult to use in practice, we propose a subset of it called the minimal negotiation set. The idea is to select elements of the k-additive core mimimizing the total amount given to coalitions of size greater than 1. Thus the minimum negotiation set naturally reduces to the core for balanced games. We study this set, giving properties and axiomatizations, as well as its relation to the extended core of Bejan and Gomez. We give a method of computing the minimum bargaining set, and lastly indicate how to eventually get classical solutions from general ones. |
| Keywords: | general solution,core,balancedness,cooperative game |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:hal:cesptp:halshs-01235625&r=gth |
| By: | Katerina Sherstyuk (University of Hawaii); Nina Karmanskaya (Novosibirsk State Technical University); Pavel Teslia (Novosibirsk State Technical University) |
| Abstract: | We study, theoretically and experimentally, alternative mechanisms to allocate assets when the future value of the asset is unknown at the time of allocation because of strategic uncertainty. We compare auctions, or bidding with money, for the right to play the minimum effort coordination game, with bidding with action (effort) proposals, where bidders with the highest proposed actions are selected as winners. Provided that the bidders commit to their proposals, bidding with action proposals eliminates strategic uncertainly and is characterized by the unique fully efficient Nash equilibrium. Allowing to revise action proposals after the assets are allocated admits both informative fully efficient, and uninformative babbling equilibria. In the experiment, bidding with action proposals with commitment consistently leads to the efficient outcome, whereas without commitment, both fully efficient and inefficient outcomes are observed. Auctioning off the right to play leads to higher actions than under random allocation, but is characterized by significant overbidding and winner losses. We further experimentally compare the mechanisms in their ability to train the players to achieve and sustain efficient coordination even after the allocation mechanism changes. |
| Keywords: | economic experiments; minimum effort coordination game; selection mechanisms |
| JEL: | C90 C72 |
| Date: | 2016–02 |
| URL: | http://d.repec.org/n?u=RePEc:hai:wpaper:201603&r=gth |
| By: | WU, JIABIN |
| Abstract: | This paper experimentally examines why communication may matter for inducing cooperation in strategic interactions involving intermediaries. We consider a three-player centipede game in which the first and the third players do not interact sequentially, but only through the second player. We posit that the third player's decision to cooperate depends on his indirect higher order belief, that is, his belief about what the first player believes the second player would choose. The evidence demonstrates that communication between the first and the third player can effectively induce cooperation from the third player through shaping his indirect higher order belief. |
| Keywords: | indirect higher order beliefs, communication, psychological game theory, guilt aversion, sequential reciprocity, social preferences, behavioral economics, experimental economics |
| JEL: | C72 C9 C91 D03 D83 |
| Date: | 2016–02–18 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:69600&r=gth |
| By: | Giacomo Bonanno (Department of Economics, University of California Davis) |
| Abstract: | We discuss the issues that arise in modeling the notion of common belief of rationality in epistemic models of dynamic games, in particular at the level of interpretation of strategies. A strategy in a dynamic game is defined as a function that associates with every information set a choice at that information set. Implicit in this definition is a set of counterfactual statements concerning what a player would do at information sets that are not reached, or a belief revision policy concerning behavior at information sets that are ruled out by the initial beliefs. We discuss the role of both objective and subjective counterfactuals in attempting to flesh out the interpretation of strategies in epistemic models of dynamic games. |
| Keywords: | Extensive-form game, strategy, counterfactual, belief revision, Kripke frame, modal logic |
| JEL: | C7 |
| Date: | 2014–03–12 |
| URL: | http://d.repec.org/n?u=RePEc:cda:wpaper:14-9&r=gth |
| By: | Frank Page |
| Abstract: | For a discounted stochastic game with an uncountable state space and compact metric action spaces, we show that if the measurable-selection-valued, Nash payoff selection correspondence of the underlying one-shot game contains a sub-correspondence having the K-limit property (i.e., if the Nash payoff selection sub-correspondence contains its K-limits and therefore is a K correspondence), then the discounted stochastic game has a stationary Markov equilibrium. Our key result is a new fixed point theorem for measurable-selection-valued correspondences having the K-limit property. We also show that if the discounted stochastic game is noisy (Duggan, 2012), or if the underlying probability space satisfies the G-nonatomic condition of Rokhlin (1949) and Dynkin and Evstigneev (1976) (and therefore satisfies the coaser transition kernel condition of He and Sun, 2014), then the Nash payoff selection correspondence contains a sub-correspondence having the K-limit property. |
| Keywords: | approximate Caratheodory selections; fixed points of nonconvex valued correspondences; measurable selection valued correspondences; Komlos limits; Komlos’ Theorem; weak star convergence; discounted stochastic games; stationary Markov equilibria. |
| JEL: | C7 |
| Date: | 2015–09 |
| URL: | http://d.repec.org/n?u=RePEc:ehl:lserod:65103&r=gth |
| By: | Csóka P.; Herings P.J.J. (GSBE) |
| Abstract: | We consider a situation in which agents have mutual claims on each other, summarized in a liability matrix. Agents assets might be insufficient to satisfy their liabilities leading to defaults. We assume the primitives to be denoted in some unit of account. In case of default, bankruptcy rules are used to specify the way agents are going to be rationed. We present a convenient representation of bankruptcy rules. A clearing payment matrix is a payment matrix consistent with the prevailingbankruptcy rules that satisfies limited liability and priority of creditors. Both clearing payment matrices and the corresponding values of equity are not uniquely determined. We provide bounds on the possible levels equity can take. We analyze decentralized clearing processes and show the convergence of any such process in finitely many steps to the least clearing payment matrix. When the unit of account is sufficiently small, all decentralized clearing processes lead essentially to the same value of equity as a centralized clearing procedure. As a policy implication, it is not necessary to collect and process all the sensitive data of all the agents simultaneously and run a centralized clearing procedure. |
| Keywords: | Cooperative Games; General Financial Markets: General (includes Measurement and Data); |
| JEL: | C71 G10 |
| Date: | 2016 |
| URL: | http://d.repec.org/n?u=RePEc:unm:umagsb:2016005&r=gth |
| By: | Andrej Angelowski (LUISS Guido Carli, Rome); Daniela Di Cagno (LUISS Guido Carli, Rome); Werner Güth (Luiss Guido Carli, Rome; Frankfurt School of Finance and Management, Frankfurt; Max Planck Institute on Collective Goods, Bonn); Francesca Marazzi (Università degli Studi di Roma Tor Vergata); Luca Panaccione (Università degli Studi di Roma Tor Vergata) |
| Abstract: | In a circular neighborhood with each member having a left and a right neighbor, individuals choose two contribution levels, one each for the public good shared with the left, respectively right, neighbor. This allows for general free riders, who do not contribute at all, and general cooperators, who contribute to both local public goods, as well as for differentiating contributors who contribute in a discriminatory way. Although the two-person local public good games are structurally independent, we investigate whether intra- as well as interpersonal spillover effects arise. We find that participants do not behave as if they are playing two separate public good games, hence that both inter-personal and intrapersonal behavioral spillovers occur. To investigate more clearly motives for voluntary cooperation via analyzing individual adaptations in playing two structurally independent games, we design treatments differing in cooperation incentives (i.e. different MPCR) and structural (a)symmetry of local public goods. We find that when the MPCR is asymmetric, free-riding occurs less, and contributions are more stable over time. We also find that contributions in the asymmetric treatment when MPCR is low are higher than contributions in symmetric treatments with higher MPCR. |
| Keywords: | Public goods, experiments, voluntary contribution mechanism |
| JEL: | C91 C72 H41 |
| Date: | 2015–12 |
| URL: | http://d.repec.org/n?u=RePEc:lui:cesare:1509&r=gth |
| By: | Vincent Iehlé (LEDa - Laboratoire d'Economie de Dauphine - Université Paris IX - Paris Dauphine, CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris IX - Paris Dauphine - CNRS - Centre National de la Recherche Scientifique) |
| Abstract: | For any TU game and any ranking of players, the set of all preimputations compat- ible with the ranking, equipped with the Lorenz order, is a bounded join semi-lattice. Furthermore the set admits as sublattice the S-Lorenz core intersected with the region compatible with the ranking. This result uncovers a new property about the structure of the S-Lorenz core. As immediate corollaries we obtain complementary results to the findings of Dutta and Ray, Games Econ. Behav., 3(4) p. 403-422 (1991), by showing that any S-constrained egalitarian allocation is the (unique) Lorenz greatest element of the S-Lorenz core on the rank-preserving region the allocation belongs to. Besides, our results suggest that the comparison between W- and S-constrained egalitarian allocations is more puzzling than what is usually admitted in the literature. |
| Keywords: | constrained egalitarian allocation,cooperative game,Lorenz criterion,Lorenz core,lattice |
| Date: | 2015–01 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:halshs-00846826&r=gth |
| By: | Hiroki Ozono (Faculty of Law, Economics and Humanities, Kagoshima University); Yoshio Kamijo (Department of Management, Kochi University of Technology); Kazumi Shimizu (School of Political Science and Economics, Waseda University) |
| Abstract: | In this paper, we propose a new mechanism to achieve cooperation in public goods provision. The mechanism is named GEM, which stands for gradualism, endogeneity, and modification, its important properties. In a public goods game with GEM, spread over 20 periods, a target contribution is presented to the players in each period. The target is gradually increased when all members reach it. If players contribute less than the target in a certain period, the minimum contribution will be treated as the next period’s target. In the experiment, the GEM mechanism achieved a high level of cooperation when the participants’contributions were restricted to the target. However, when participants were allowed to contribute more than the target, cooperation was not achieved because of the presence of“excessive altruists”—participants who contributed more than the target.This is because excessive cooperation facilitated free riding by other members. Finally,we discuss the limitation and possibilities of the GEM mechanism. |
| Keywords: | cooperation, public goods game, altruist, experiment |
| JEL: | C72 C91 C92 M54 |
| Date: | 2014–08 |
| URL: | http://d.repec.org/n?u=RePEc:wap:wpaper:1408&r=gth |
| By: | Aurora García-Gallego (LEE-Ec. Dpt., U. Jaume I (Spain)); Nikolaos Georgantzís (Agriculture Policy and Development, University of Reading (UK) &LEE & Economics Dept., Universitat Jaume I, Castellón (Spain)); Ainhoa Jaramillo-Gutiérrez (Department of Economic Theory and Economic History, University of Granada.) |
| Abstract: | We present an experiment on the Heaven game, a generalization of the dictator game. The heavendictator player chooses between increasing, decreasing and maintaining the earnings of the passive player, without incurring any cost or profit. Thus, we avoid the experimenter demand effect. Based on the psychological literature on music as mood inductor and on the effects of mood on helping behavior, we also study the effect of exposure to different types of music on the heaven-dictator choices. We find that the overwhelming majority of subjects choose to increase their partners’ earnings and no general effect of music over the heaven-dictator choices, except for classical music that seems to foster helping-indifference behavior. |
| Keywords: | experimental economics, behavioural economics, other-regarding preferences, musicinduced mood, dictator game |
| JEL: | C72 C91 |
| Date: | 2015–12–07 |
| URL: | http://d.repec.org/n?u=RePEc:gra:wpaper:15/07&r=gth |
| By: | Kristóf Madarász |
| Abstract: | People exaggerate the extent to which their private information is shared with others. This paper introduces this phenomenon portably into Bayesian games where people wrongly think that if they can condition their strategy on an event others can do as well. I apply the model to a variety of settings. In the context of social investment people misattribute the uncertainty they face about others preferences to others having antagonistic motives. Even if all parties prefer mutual investment, none invests, yet all come to believe that others prefer not to invest. In the context of communication with costly state veri…cation, the model predicts credulity: persuasion by advisors, who are known to have an incentive to exaggerate the quality of an asset, will nevertheless induce uniformly exaggerated average posteriors for receivers. When endogenizing the con‡ict of interest between senders and receivers, I show that such credulous belief-bubbles rise discontinuously as the size of the market or the complexity of the asset increases. Further implications to auctions, common value trade and zero-sum games are explored. |
| Keywords: | Projection, Social Investment, Pluralistic Ignorance, Persuasion Belief-Bubbles. |
| JEL: | D03 C7 |
| Date: | 2015–01 |
| URL: | http://d.repec.org/n?u=RePEc:cep:stitep:/2015/566&r=gth |
| By: | Bernard De Meyer (Paris School of Economics - Centre d'Economie de la Sorbonne); Gaëtan Fournier (Centre d'Economie de la Sorbonne) |
| Abstract: | A market with asymmetric information can be viewed as a repeated exchange game between an informed sector and an uniformed sector. The case where all agents in the market are risk neutral was analyzed in De Meyer [2010]. The main result of that paper was that the price process in this risk neutral environment should be a particular kind o Brownian martingale called CMMV. This type of dynamics is due to the strategic use of their private information by the informed agents. In this paper, we generalize this analysis to the case of a risk averse market. Our main result is that the price process is still a CMMV under a martingale equivalent measure |
| Keywords: | Asymmetric information; Price dynamics; Martingales of maximal variation; Repeated games; Martingale equivalent measure; Risk aversion |
| JEL: | G14 C72 C73 D44 |
| Date: | 2015–06 |
| URL: | http://d.repec.org/n?u=RePEc:mse:cesdoc:15054&r=gth |
| By: | Achim Hagen (University of Oldenburg, Department of Economics); Leonhard Kaehler (University of Oldenburg, Department of Economics); Klaus Eisenack (University of Oldenburg, Department of Economics) |
| Abstract: | This paper explores transnational environmental agreements on climate change. As the Paris agreement of 2015 contains no binding emission reduction targets for nation states, understanding other forms of cooperation as complements to the United Nations Framework Convention on Climate Change (UNFCCC) process becomes increasingly important. We thus aim to identify directions for further research on agreements with heterogeneous contracting parties. By building on empirical examples of emerging transnational environmental agreements, and on insights from the global governance literature, we discuss the scope and limits of the current economic literature on international environmental agreements. We argue that further game theoretical research would benefit from extending the analysis (i) to consider actors that are not nation state governments, and (ii) to consider multiple environmental agreements that are in force at the same time. We underpin this claim by suggesting two proposals for economic models that analyze climate clubs and city alliances. The results show that transnational environmental agreements can be individually rational and can improve the effectiveness of climate policies. |
| Keywords: | heterogeneous actors, international environmental agreements, transnational agreements |
| JEL: | C72 Q54 |
| Date: | 2016–01 |
| URL: | http://d.repec.org/n?u=RePEc:old:dpaper:387&r=gth |
| By: | Javier de Frutos (IMUVA, Universidad de Valladolid); Guiomar Martín-Herrán (IMUVA, Universidad de Valladolid) |
| Abstract: | We analyze a differential game model where pollution control is spatially distributed among a number, possibly large, of agents with predetermined spatial relationships. The analysis emphasizes the effects of the different geographical relationships among decision makers. The game has one state variable (pollution stock) distributed among one large region divided in subregions which control their own emissions of pollutants. The emissions are also represented as distributed variables. The dynamics of the state variable is defined by a parabolic PDE. We numerically characterize the feedback Nash equilibrium of a discrete-space model that still captures the spatial interactions among agents. |
| Keywords: | Spatially Distributed Controls; Spatial Dynamics; Parabolic Differential Equations; Differential Games; Transboundary Pollution. |
| JEL: | R12 Q5 C73 C61 |
| Date: | 2016–01 |
| URL: | http://d.repec.org/n?u=RePEc:cst:wpaper:201601&r=gth |
| By: | Cristián Troncoso-Valverde (School of Business and Economics, Universidad del Desarrollo) |
| Abstract: | This paper studies the incentives faced by competing auctioneers who can release information to prospective bidders before bidders choose trading partners. I provide sufficient conditions that ensure the existence of a unique equilibrium in which both sellers release all available information. Contrary to previous findings in the literature, the existence of this equilibrium holds true even if there are only two bidders in the market. Thus, the findings of this paper provides support to the idea that competition among sellers improves informational efficiency relatively to monopoly |
| Keywords: | Competing Auctions, Information Structures, Private Provision of Information |
| Date: | 2015–04 |
| URL: | http://d.repec.org/n?u=RePEc:dsr:wpaper:15&r=gth |
| By: | Bergantiños, Gustavo; Valencia-Toledo, Alfredo; Vidal-Puga, Juan |
| Abstract: | The program evaluation review technique (PERT) is a tool used to schedule and coordinate activities in a complex project. In assigning the cost of a potential delay, we characterize the Shapley rule as the only rule that satisfies consistency and other desirable properties. |
| Keywords: | PERT problem; consistency; delay |
| JEL: | B4 C0 C6 C7 |
| Date: | 2016 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:68973&r=gth |