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on Game Theory |
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Issue of 2012‒11‒11
twenty-one papers chosen by Laszlo A. Koczy Hungarian Academy of Sciences and Obuda University |
| By: | Okada, Akira |
| Abstract: | We present a classification of all stationary subgame perfect equilibria of the random proposer model for a three-person cooperative game according to the level of efficiency. The efficiency level is characterized by the number of "central" players who join all equilibrium coalitions. The existence of a central player guarantees asymptotic efficiency. The marginal contributions of players to the grand coalition play a critical role in their expected equilibrium payoffs. |
| Keywords: | cooperative game, noncooperative bargaining, three-person game, random proposer, core, marginal contribution |
| JEL: | C71 C72 C78 |
| Date: | 2012–10 |
| URL: | http://d.repec.org/n?u=RePEc:hit:econdp:2012-06&r=gth |
| By: | Litan, Cristian M.; Marhuenda, Francisco |
| Abstract: | We show the generic finiteness of probability distributions induced on outcomes by the Nash equilibria in two player zero sum and common interest outcome games. |
| Keywords: | Generic finiteness; Outcome zero sum games; Outcome common interest games; |
| JEL: | C20 C70 |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:ner:carlos:info:hdl:10016/15801&r=gth |
| By: | Takuya Masuzawa (Faculty of Economics, Keio University) |
| Abstract: | In this article, we consider a many-to-one two-sided matching market and define a canonical strategic form game, in which any worker applies to the top k firms and is assigned to the most preferred firm that does not reject him/her. Under the substitute property of firms' preferences, the game satisfies the punishment-dominance condition. The deferred-acceptance algorithm by Gale and Shapley (Amer. Math. Monthly 69: 1962), which finds the maximum and minimum of stable matchings, is described as an instance of the algorithm by Masuzawa (Int. Jour. Game Theory 38: 2008), which determines the α-cores of the strategic form games with the punishment-dominance condition. |
| Date: | 2012–10 |
| URL: | http://d.repec.org/n?u=RePEc:kei:dpaper:2012-018&r=gth |
| By: | Habis , Helga (Department of Economics, Lund University); Csercsik, Dávid (Institute of Economics, Research Centre for Economic and Regional Studies, Hungarian Academy) |
| Abstract: | We introduce a new class of cooperative games where the worth of a coalition depends on the behavior of other players and on the state of nature as well. We allow for coalitions to form both before and after the resolution of uncertainty, hence agreements must be stable against both types of deviations. The appropriate extension of the classical core concept, the Sustainable Core, is defined for this new setup to test the stability of allocations in such a complex environment. A prominent application, a game of consumers and generators on an electrical energy transmission network is examined in details, where the power in- and outlets of the nodes have to be determined in a way, that if any line instantaneously fails, none of the remaining lines may be overloaded. We show that fulfilling this safety requirement in a mutually acceptable way can be achieved by choosing an element in the Sustainable Core. |
| Keywords: | partition function form games; uncertainty; core; sustainability |
| JEL: | C71 C73 D62 L14 L94 |
| Date: | 2012–10–08 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:lunewp:2012_027&r=gth |
| By: | M. Ali Khan (Department of Economics, Johns Hopkins University); Kali P. Rath (Department of Economics, University of Notre Dame); Haomiao Yu (Department of Economics, Ryerson University); Yongchao Zhang (School of Economics, Shanghai University of Finance and Economics) |
| Abstract: | A comprehensive theory of large strategic games with (socioeconomic and biological) traits (LSGT) has recently been presented in Khan et al. (2012 a and b), and in this paper, we present a reformulation pertaining to large distributional games with traits (LDGT). In addition to a generalization of work initiated and advocated by Mas-Colell (1984), we delineate the role of saturated spaces, as studied in Keisler-Sun (2009) in the reformulated theory, and consider questions pertaining to \lq\lq realizations" of equilibrium distributions that were not previously asked. |
| Keywords: | Large game, strategic game, distributional game, traits, saturated probability space, realization, Nash equilibrium distribution |
| JEL: | C62 D50 D82 G13 |
| Date: | 2012–12 |
| URL: | http://d.repec.org/n?u=RePEc:rye:wpaper:wp037&r=gth |
| By: | Llerena Garrés, Francesc; Vilella Bach, Misericòrdia |
| Abstract: | In this paper we axiomatize the strong constrained egalitarian solution (Dutta and Ray, 1991) over the class of weak superadditive games using constrained egalitarianism, order-consistency, and converse order-consistency. JEL classification: C71, C78. Keywords: Cooperative TU-game, strong constrained egalitarian solution, axiomatization. |
| Keywords: | Jocs cooperatius, Negociacions -- Models matemàtics, 33 - Economia, |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:urv:wpaper:2072/203157&r=gth |
| By: | Abramsky, Samson; Winschel, Viktor |
| Abstract: | We present a novel coalgebraic formulation of infinite extensive games. We define both the game trees and the strategy profiles by possibly infinite systems of corecursive equations. Certain strategy profiles are proved to be subgame perfect equilibria using a novel proof principle of predicate coinduction which is shown to be sound by reducing it to Kozen’s metric coinduction. We characterize all subgame perfect equilibria for the dollar auction game. The economically interesting feature is that in order to prove these results we do not need to rely on continuity assumptions on the payoffs which amount to discounting the future. In particular, we prove a form of one-deviation principle without any such assumptions. This suggests that coalgebra supports a more adequate treatment of infinite-horizon models in game theory and economics. |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:mnh:wpaper:32525&r=gth |
| By: | Dirk Bergemann; Stephen Morris |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:cla:levarc:786969000000000601&r=gth |
| By: | Grabisch, Michel (Paris School of Economics); Sudhölter, Peter (Department of Business and Economics) |
| Abstract: | We consider TU-games with restricted cooperation, where the set of feasible coalitions is a distributive lattice, hence generated by a partial order on the set of players. In such a situation, the core may be unbounded, and one has to select a bounded part of the core as a solution concept. The restricted core is obtained by imposing equality constraints in the core for sets belonging to so-called normal collections, resulting (if nonempty) in the selection of a bounded face of the core. The bounded core proves to be the union of all bounded faces (restricted cores). The paper aims at investigating in depth the relation between the bounded core and restricted cores, as well as the properties and structures of the restricted cores and normal collections. In particular, it is found that a game is convex if and only if all restricted cores corresponding to the minimal nested normal collections are nonempty. Moreover, in this case the union of these restricted cores already covers the bounded core. |
| Keywords: | TU-game; restricted cooperation; distributive lattice; core; extremal rays; faces of the core |
| JEL: | C71 |
| Date: | 2012–10–31 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:sdueko:2012_022&r=gth |
| By: | Sonja Brangewitz (Department of Economics - University of Paderborn); Gaël Giraud (Centre d'Economie de la Sorbonne - Paris School of Economics) |
| Abstract: | We study the consequences of dropping the perfect competition assumption in a standard infinite horizon model with infinitely-lived traders and real collateralized assets, together with one additional ingredient : information among players is asymmetric and monitoring is incomplete. The key insight is that trading assets is not only a way to hedge oneself against uncertainty and to smooth consumption across time : it also enables learning information. Conversely, defaulting now becomes strategic : certain players may manipulate prices so as to provoke a default in order to prevent their opponents from learning. We focus on learning equilibria, at the end of which no player has incorrect beliefs — not because those players with heterogeneous beliefs were eliminated from the market (although default is possible at equilibrium) but because they have taken time to update their prior belief. We prove a partial Folk theorem à la Wiseman (2011) of the following form : for any function that maps each state of the world to a sequence of feasible and strongly individually rational allocations, and for any degree of precision, there is a perfect Bayesian equilibrium in which patient players learn the realized state with this degree of precision and achieve a payoff close to the one specified for each state. |
| Keywords: | Strategic market games, infinite horizon, incomplete markets, collateral, incomplete information, learning, adverse selection. |
| JEL: | C72 D43 D52 G12 G14 G18 |
| Date: | 2012–09 |
| URL: | http://d.repec.org/n?u=RePEc:mse:cesdoc:12062&r=gth |
| By: | Antoine Mandel (Centre d'Economie de la Sorbonne); Herbert Gintis (Santa Fe Institute and Central European University) |
| Abstract: | We present a mathematical model for the analysis of the bargaining games based on private prices used by Gintis to simulate the dynamics of prices in exchange economies, see [Gintis 2007]. We then characterize, in the Scarf economy, a class of dynamics for which the Walrasian equilibrium is the only stochastically stable state. Hence, we provide dynamic foundations for general equilibrium for one of the best-known example of instability of the tâtonement process. |
| Date: | 2012–10 |
| URL: | http://d.repec.org/n?u=RePEc:mse:cesdoc:12066&r=gth |
| By: | Barreira da Silva Rocha, André; Laruelle, Annick |
| Abstract: | Differently from previous studies of tag-based cooperation, we assume that individuals fail to recognize their own tag. Due to such incomplete information, the action taken against the opponent cannot be based on similarity, although it is still motivated by the tag displayed by the opponent. We present stability conditions for the case when individuals play unconditional cooperation, unconditional defection or conditional cooperation. We then consider the removal of one or two strategies. Results show that conditional cooperators are the most resilient agents against extinction and that the removal of unconditional cooperators may lead to the extinction of unconditional defectors. |
| Keywords: | evolution, similarity, cooperation, snowdrift game, replicator dynamics |
| Date: | 2012–09–19 |
| URL: | http://d.repec.org/n?u=RePEc:ehu:ikerla:201262&r=gth |
| By: | Osório Costa, Antonio Miguel |
| Abstract: | This paper studies the limits of discrete time repeated games with public monitoring. We solve and characterize the Abreu, Milgrom and Pearce (1991) problem. We found that for the "bad" ("good") news model the lower (higher) magnitude events suggest cooperation, i.e., zero punishment probability, while the highrt (lower) magnitude events suggest defection, i.e., punishment with probability one. Public correlation is used to connect these two sets of signals and to make the enforceability to bind. The dynamic and limit behavior of the punishment probabilities for variations in ... (the discount rate) and ... (the time interval) are characterized, as well as the limit payo¤s for all these scenarios (We also introduce uncertainty in the time domain). The obtained ... limits are to the best of my knowledge, new. The obtained ... limits coincide with Fudenberg and Levine (2007) and Fudenberg and Olszewski (2011), with the exception that we clearly state the precise informational conditions that cause the limit to converge from above, to converge from below or to degenerate. JEL: C73, D82, D86. KEYWORDS: Repeated Games, Frequent Monitoring, Random Pub- lic Monitoring, Moral Hazard, Stochastic Processes. |
| Keywords: | Teoria de jocs, Incertesa -- Models matemàtics, Contractes -- Aspectes econòmics, 33 - Economia, |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:urv:wpaper:2072/203171&r=gth |
| By: | Jiménez Gómez, José M. (José Manuel); Vilella Bach, Misericòrdia |
| Abstract: | In this note, we consider claims problems with indivisible goods. Specifically, by applying recursively the P-rights lower bound (Jiménez-Gómez and Marco-Gil (2008)), we ensure the fulfillment of Weak Order Preservation, considered by many authors as a minimal requirement of fairness. Moreover, we retrieve the Discrete Constrained Equal Losses and the Discrete Constrained Equal Awards rules (Herrero and MartÃınez (2008)). Finally, by the recursive double imposition of a lower and an upper bound, we obtain the average between them. Keywords: Claims problems, Indivisibilities, Order Preservation, Constrained Egalitarian rules, Midpoint. JEL classification: C71, D63, D71. |
| Keywords: | Jocs cooperatius, Economia del benestar -- Models matemàtics, Elecció social, 33 - Economia, |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:urv:wpaper:2072/203160&r=gth |
| By: | Pradeep Dubey (Department of Economics, Stony Brook University); Rahul Garg (Opera Solutions, INDIA); Bernard De Meyer (Cermsem, Univesit´e Paris 1, Paris, FRANCE) |
| Abstract: | There are many situations in which a customer’s proclivity to buy the product of any firm depends not only on the classical attributes of the product such as its price and quality, but also on who else is buying the same product. Under quite general circumstances, it turns out that customers’ influence on each other dynamically converges to a steady state. Thus we can model these situations as games in which firms compete for customers located in a “social network”. A canonical example is provided by competition for advertisement on the web. Nash Equilibrium (NE) in pure strategies exist in general. In the quasi-linear version of the model, NE turn out to be unique and can be precisely characterized. If there are no a priori biases between customers and firms, then there is a cut-off level above which high cost firms are blockaded at an NE, while the rest compete uniformly throughout the network. Otherwise there is a tendency towards regionalization, with firms dominating disjoint territories. We also explore the relation between the connectivity of a customer and the money firms spend on him. This relation becomes particularly transparent when externalities are dominant: NE can be characterized in terms of the invariant measures on the recurrent classes of the Markov chain underlying the social network. Finally we consider convex (instead of linear) cost functions for the firms. Here NE need not be unique as we show via an example. But uniqueness is restored if there is enough competition between firms or if their valuations of clients are anonymous. |
| Date: | 2012–09 |
| URL: | http://d.repec.org/n?u=RePEc:nys:sunysb:12-10&r=gth |
| By: | Christophe Dutang (SAF - Laboratoire de Sciences Actuarielle et Financière - Université Claude Bernard - Lyon I : EA2429, IRMA - Institut de Recherche Mathématique Avancée - CNRS : UMR7501 - Université de Strasbourg); Hansjoerg Albrecher (UNIL - Université de Lausanne - Université de Lausanne); Stéphane Loisel (SAF - Laboratoire de Sciences Actuarielle et Financière - Université Claude Bernard - Lyon I : EA2429) |
| Abstract: | In this paper, we formulate a noncooperative game to model a non-life insurance market. The aim is to analyze the e ects of competition between insurers through di erent indicators: the market premium, the solvency level, the market share and the underwriting results. Resulting premium Nash equilibria are discussed and numerically illustrated. |
| Date: | 2012–05 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-00746245&r=gth |
| By: | Jens Leth Hougaard (Institute of Food and Resource Economics, University of Copenhagen); Hervé Moulin (Department of Economics, Rice University) |
| Abstract: | We ask how to share the cost of finitely many public goods (items) among users with different needs: some smaller subsets of items are enough to serve the needs of each user, yet the cost of all items must be covered, even if this entails inefficiently paying for redundant items. Typical examples are network connectivity problems when an existing (possibly inefficient) network must be maintained. We axiomatize a family of simple usage indices, one for each agent and for each item, measuring the relative worth of this item across agents, and generating cost sharing rules additive in costs. |
| Keywords: | Cost sharing; Redundant costs; Connection networks; Connectivity |
| JEL: | C71 D30 D85 M41 |
| Date: | 2012–09 |
| URL: | http://d.repec.org/n?u=RePEc:foi:msapwp:06_2012&r=gth |
| By: | Fairley, Kim; Sanfey, Alan; Vyrastekova, Jana; Weitzel, Utz |
| Abstract: | Despite intensive research there is no clear evidence for a link between lottery risk preferences and risk involved in trusting others. We argue that this is partially due to a misalignment of the underlying sources of risk. Trusting is giving up control to a human source of risk while lottery risk has a mechanistic source. We propose a risky trust game that experimentally elicits social risk preferences that pertain to the same underlying human source. Our results show that transfers in the classic trust game are indeed best explained by social risk preferences and not by lottery risk preferences with an underlying mechanistic source. In addition, we argue that the type of uncertainty also plays a role. In the absence of objectively known probabilities of trustworthiness, trust also has an ambiguous component. We therefore decompose uncertainty in the trust game into social risk and an ambiguous component. Our results provide evidence that, when accounting for social risk, subjects who score high on ambiguity tolerance explain some of the remainder of trusting behavior. |
| Keywords: | Trust; trust game; decision making under uncertainty; risk; ambiguity; source of uncertainty |
| JEL: | C9 C7 D8 |
| Date: | 2012–10–29 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:42302&r=gth |
| By: | José M. Jiménez Gómez (Universidad Politécnica de Cartagena); Josep Enric Peris Ferrando (Universidad de Alicante) |
| Abstract: | How should scholarships be distributed among the (public) higher education students? We raise thissituation as a redistribution problem. Following the approach developed in Fleurbaey (1994) andBossert (1995), redistribution should be based on the notion of solidarity and it re-allocates resourcestaking into account only agents' relevant characteristics. We also follow Luttens (2010a), whoconsiders that compensation of relevant characteristics must be based on a lower bound on whatevery individual deserves. In doing so, we use the so-called fair bound (Moulin 2002) to define anegalitarian redistribution mechanism and characterize it in terms of non-negativity, priority in lowerbound and solidarity. Finally, we apply our approach to the scholarships redistribution problem. |
| Keywords: | Redistribution mechanism, Lower bounds, Scholarship, Solidarity. |
| JEL: | C71 D63 D71 |
| Date: | 2012–10 |
| URL: | http://d.repec.org/n?u=RePEc:ivi:wpasad:2012-18&r=gth |
| By: | Gabriel E. Kreindler; H. Peyton Young |
| Abstract: | The diffusion of an innovation can be represented by a stochastic process in which agents choose noisy best responses to what their neighbors are currently doing. Diffusion is said to be fast if the expected time until a majority of agents play the stochastically stable (risk-dominant) equilibrium scales with the size of the network. Previous work has identified specific topological properties of networks that result in fast diffusion. Here we derive topology-free bounds such that diffusion is fast in any network with a given degree distribution (and no restriction on the topology), so long as the payoff gain from the innovation is sufficiently high and the response function is moderately noisy. In particular for the logit response function it suffices that the error rate be on the order of 5% and the payoff gain on the order of 80% to achieve fast diffusion in any regular network. |
| Keywords: | Innovation diffusion, Convergence time, Local Interaction |
| JEL: | C72 C73 |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:oxf:wpaper:626&r=gth |
| By: | Herweg, Fabian; Schmidt, Klaus M. |
| Abstract: | We propose a theory of ex post inefficient renegotiation that is based on loss aversion. When two parties write a long-term contract that has to be renegotiated after the realization of the state of the world, they take the initial contract as a reference point to which they compare gains and losses of the renegotiated transaction. We show that loss aversion makes the renegotiated outcome sticky and materially inefficient. The theory has important implications for the optimal design of long-term contracts. First, it explains why parties often abstain from writing a beneficial long-term contract or why some contracts specify transactions that are never ex post efficient. Second, it shows under what conditions parties should rely on the allocation of ownership rights to protect relationshipspecific investments rather than writing a specific performance contract. Third, it shows that employment contracts can be strictly optimal even if parties are free to renegotiate. |
| Keywords: | Renegotiation; Incomplete Contracts; Reference Points; Employment Contracts; Behavioral Contract Theory |
| JEL: | C78 D03 D86 |
| Date: | 2012–10 |
| URL: | http://d.repec.org/n?u=RePEc:lmu:muenec:14191&r=gth |