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on Game Theory |
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Issue of 2012‒07‒14
nineteen papers chosen by Laszlo A. Koczy Hungarian Academy of Sciences and Obuda University |
| By: | Philippe Bich (Centre d'Economie de la Sorbonne - Paris School of Economics); Rida Laraki (Ecole Polytechnique - Economics Department et IMJ - Equipe Combinatoire et Optimisation) |
| Abstract: | Several relaxations of Nash equilibrium are shown to exist in strategic games with discontinuous payoff functions. Those relaxations are used to extend and unify several recent results and link Reny's better-reply security condition [Reny, P.J. (1999). On the existence of Pure and Mixed Strategy Nash Equilibria in Discontinuous Games] to Simon-Zame's endogenous tie-breaking rules [Simon, L.K. and Zame, W.R. (1990). Discontinuous Games and Endogenous Sharing Rules]. |
| Keywords: | Discontinuous games, Nash equilibrium, Reny equilibrium, better-reply security, endogenous sharing rule, quasi equilibrium, finite deviation equilibrium, symmetric games. |
| JEL: | C02 C62 C72 |
| Date: | 2012–06 |
| URL: | http://d.repec.org/n?u=RePEc:mse:cesdoc:12040&r=gth |
| By: | Conrado Manuel (Universidad Complutense de Madrid); Enrique Gonzalez-Aranguena (Universidad Complutense de Madrid); Rene van den Brink| (VU University Amsterdam) |
| Abstract: | In this paper we provide new axiomatizations of the Shapley value for TU-games using axioms that are based on relational aspects in the interactions among players. Some of these relational aspects, in particular the economic or social interest of each player in cooperating with each other, can be found embedded in the characteristic function. We define a particular relation among the players that it is based on mutual indifference. The first new axiom expresses that the payoffs of two players who are not indifferent to each other are affected in the same way if they become enemies and do not cooperate with each other anymore. The second new axiom expresses that the payoff of a player is not affected if players to whom it is indifferent leave the game. We show that the Shapley value is characterized by these two axioms together with the well-known efficiency axiom. Further, we show that another axiomatization of the Shapley value is obtained if we replace t he second axiom and efficiency by the axiom which applies the efficiency condition to every class of indifferent players. Finally, we extend the previous results to the case of weighted Shapley values. |
| Keywords: | TU-game; Shapley value; axiomatization; indifferent players; weighted Shapley values |
| JEL: | C71 |
| Date: | 2012–04–11 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:20120036&r=gth |
| By: | Engwerda, J.C. (Tilburg University, Center for Economic Research) |
| Abstract: | Abstract: In this note we reconsider Nash equilibria for the linear quadratic differential game for an infinite planning horizon. We consider an open-loop information structure. In the standard literature this problem is solved under the assumption that every player can stabilize the system on his own. In this note we relax this assumption and provide both necessary and sufficient conditions for existence of Nash equilibria for this game under the assumption that the system as a whole is stabilizable. |
| Keywords: | linear-quadratic differential games;open-loop Nash equilibrium;solvability conditions;Riccati equations. |
| JEL: | C61 C72 C73 |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:kubcen:2012052&r=gth |
| By: | Jason Shachat; J. Todd Swarthout; Lijia Wei |
| Abstract: | We propose a statistical model to assess whether individuals strategically use mixed strategies in repeated games. We formulate a hidden Markov model in which the latent state space contains both pure and mixed strategies, and allows switching between these states. We apply the model to data from an experiment in which human subjects repeatedly play a normal form game against a computer that always follows its part of the unique mixed strategy Nash equilibrium profile. Estimated results show significant mixed strategy play and non-stationary dynamics. We also explore the ability of the model to forecast action choice. |
| Keywords: | Mixed Strategy, Nash Equilibrium, Experiment, Hidden Markov Model |
| JEL: | C92 C72 C10 |
| Date: | 2012–07 |
| URL: | http://d.repec.org/n?u=RePEc:exc:wpaper:2012-11&r=gth |
| By: | F. Javier Martinez de Albeniz; Carles Rafels (Universitat de Barcelona) |
| Abstract: | An assignment game is defined by a matrix A, where each row represents a buyer and each column a seller. If buyer i is matched with seller j, the market produces aij units of utility. We study Monge assignment games, that is bilateral cooperative assignment games where the assignment matrix satisfies the Monge property. These matrices can be characterized by the fact that in any submatrix of 2 2 an optimal matching is placed in its main diagonal. For square markets, we describe their cores by using only the central tridiagonal band of the elements of the matrix. We obtain a closed formula for the buyers-optimal and the sellers-optimal core allocations. Non- square markets are analyzed also by reducing them to appropriate square matrices. |
| Keywords: | core, sellers-optimal core allocation, assignment game, buyers-optimal core allocation, monge matrix |
| JEL: | C71 |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:bar:bedcje:2012282&r=gth |
| By: | Shachat, Jason; Swarthout, J. Todd; Wei, Lijia |
| Abstract: | We propose a statistical model to assess whether individuals strategically use mixed strategies in repeated games. We formulate a hidden Markov model in which the latent state space contains both pure and mixed strategies, and allows switching between these states. We apply the model to data from an experiment in which human subjects repeatedly play a normal form game against a computer that always follows its part of the unique mixed strategy Nash equilibrium profile. Estimated results show significant mixed strategy play and non-stationary dynamics. We also explore the ability of the model to forecast action choice. |
| Keywords: | Mixed Strategy; Experiment; Hidden Markov Model |
| JEL: | C92 C72 C11 |
| Date: | 2012–07–07 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:39896&r=gth |
| By: | Germán Coloma |
| Abstract: | This paper presents a model of the penalty-kick game between a soccer goalkeeper and a kicker, in which there is uncertainty about the kicker’s type (and there are two possible types of kicker). To find a solution for this game we use the concept of Bayesian equilibrium, and we find that, typically, one of the kicker’s types will play a mixed strategy while the other type will choose a pure strategy (or, sometimes, a “restricted mixed strategy”). The model has a simpler version in which the players can only choose between two strategies (right and left), and a more complex version in which they can also choose a third strategy (the center of the goal). Comparing the incomplete-information Bayesian equilibria with the corresponding complete-information Nash equilibria, we find that in all cases the expected scoring probability increases (so that, on average, the goalkeeper is worse off under incomplete information). The three-strategy model is also useful to explain why it could be optimal for a goal keeper never to choose the center of the goal (although at the same time there were some kickers who always chose to shoot to the center). |
| Keywords: | soccer penalty kicks, mixed strategies, Bayesian equilibrium, incomplete information |
| JEL: | C72 L83 |
| Date: | 2012–05 |
| URL: | http://d.repec.org/n?u=RePEc:cem:doctra:487&r=gth |
| By: | Jan-Peter Siedlarek (Department of Economics, European University Institute) |
| Abstract: | This paper studies bargaining and exchange in a networked market with intermediation. Possibilities to trade are restricted through a network of existing relationships and traders bargain over the division of available gains from trade along different feasible routes. Using a stochastic model of bargaining, I characterize stationary equilibrium payoffs as the fixed point of a set of intuitive value function equations and study efficiency and the relationship between network structure and payoffs. In equilibrium, trade is never unduly delayed but it may take place too early and in states where delay would be efficient. The inefficiency arises from a hold-up threat and the inability of bargaining parties credibly to commit to a split in a future period. The model also shows how with competing trade routes as trade frictions go to zero agents that are not essential to a trade opportunity receive a payoff of zero. |
| Keywords: | Stochastic Games, Bargaining, Random Matching, Middlemen, Network |
| JEL: | C73 C78 L14 |
| Date: | 2012–05 |
| URL: | http://d.repec.org/n?u=RePEc:fem:femwpa:2012.42&r=gth |
| By: | Yannick Viossat (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - CNRS : UMR7534 - Université Paris IX - Paris Dauphine); Andriy Zapechelnyuk (QMUL - School of Economics and Finance - Queen Mary, University of London) |
| Abstract: | Potential based no-regret dynamics are shown to be related to fictitious play. This allows to give alternative and sometimes much shorter proofs of known results on convergence of no-regret dynamics to the set of Nash equilibria. |
| Keywords: | Regret minimization; no-regret strategy; fictitious play; best reply dynamics; Nash equilibrium; Hannan set; curb set |
| Date: | 2012–07–02 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-00713871&r=gth |
| By: | Herbert Dawid (Bielefeld University); Tim Hellmann (Institute of Mathematical Economics, Bielefeld University) |
| Abstract: | In this paper, we study a standard Cournot model where rms are able to form bilateral collaboration agreements which lower marginal cost. While a static analysis of such a model can be found in Goyal and Joshi [5], we introduce an evolutionary model. Stable networks (in the static sense) exhibit the dominant group architecture and can be characterized with respect to the size of the group. However, in contrast to Goyal and Joshi [5], we nd that the group size of connected rms in stochastically stable networks is generically unique and monotonically decreasing in cost of link formation. Further, there exists a lower bound on the group size of connected rms such that a non-empty network can be stochastically stable. |
| Date: | 2012–06 |
| URL: | http://d.repec.org/n?u=RePEc:bie:wpaper:467&r=gth |
| By: | Itzhak Gilboa (Tel Aviv University - Tel Aviv University, GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC - GROUPE HEC - CNRS : UMR2959); Larry Samuelson (Department of Economics - Yale University) |
| Abstract: | This paper examines circumstances under which subjectivity enhances the effectiveness of inductive reasoning. We consider a game in which Fate chooses a data generating process and agents are characterized by inference rules that may be purely objective (or data-based) or may incorporate subjective considerations. The basic intuition is that agents who invoke no subjective considerations are doomed to "overfit" the data and therefore engage in ineffective learning. The analysis places no computational or memory limitations on the agents -- the role for subjectivity emerges in the presence of unlimited reasoning powers. |
| Keywords: | induction; simplicity; Bayesian learning; prediction |
| Date: | 2012–05 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:hal-00489433&r=gth |
| By: | Nicola Dimitri (Department of Economics and Statistics, University of Sienna, and Research Fellow, Maastricht School of Management) |
| Abstract: | In the Italian Football League rights to a player’s performance could be co-owned by two clubs for one year. Co-ownership must then be resolved and if the clubs fail finding an agreement they are asked by the League to participate to an auction, where each of them submits a price offer for the missing half of the rights. The player offering the highest price obtains the missing half of the rights paying that price to the opponent. In the paper we characterize the auction equilibrium structure with both complete and incomplete information. Due to its features, a main finding in such auction is that “losers” can obtain a higher payoff than “winners”, and in this sense be the real winners. Then, by considering the auction as a more general mechanism for co-ownership resolution, we extend the model to any finite number of players and argue how some of the results with two players do not necessarily generalize. In particular, while with two players the equilibrium expected payoffs can never be negative this may not be so with a higher number of players. Finally, also with incomplete information the symmetric bidding equilibrium function with any finite number of players is in the “winning losers” spirit. Indeed, bids range between one’s value and twice of it, and increase with the number of players since it becomes more likely that some opponent will have a higher value. |
| Date: | 2012–07 |
| URL: | http://d.repec.org/n?u=RePEc:msm:wpaper:2012/08&r=gth |
| By: | Zenou, Yves |
| Abstract: | We provide an overview on networks in economics. We first look at the theoretical aspects of network economics using a game-theoretical approach. We derive some results on games on networks and network formation. We also study what happens when agents choose both links and actions. We then examine how these models can be used to address some applied and empirical-relevant questions by mainly focusing on labor-market networks and crime networks. We provide some empirical evidence on these two types of networks and address some policy implications of the models. |
| Keywords: | criminal networks; games on networks; labor networks; network formation; Social networks |
| JEL: | A14 C72 D85 |
| Date: | 2012–06 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:9021&r=gth |
| By: | Timothy Shields (Argyros School of Business and Economics, Chapman University, USA); Baohua Xin (Rotman School of Management, University of Toronto, Canada) |
| Abstract: | We examine the role of higher order beliefs in asset markets where coordination between a buyer and seller can lead to gains to trade. The scenarios are modeled such that trader’s strategies do not only depend upon their beliefs of underlying economic phenomena, but also upon the others’ beliefs regarding the beliefs of themselves. Under certain parameters the breakdown of coordination is predicted–even when both traders are certain the underlying phenomena dictates trade is advantageous. We demonstrate the equilibrium predictions can be constructed via a small number of iterated thought exercises. The experimental design allows us to control for various behavioral phenomena and examine subjects’ decisions across different accounting regimes as to tease out strategic uncertainty due solely to information asymmetry. In this setting we find evidence supporting higher order beliefs. An implication is that the lack of uniformity leads to lack of common knowledge of the beliefs of others, which in turn leads to the spreading of inefficient outcomes. |
| Keywords: | information asymmetry; experiment; strategic uncertainty; higher-order beliefs; iterative reasoning |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:chu:wpaper:12-18&r=gth |
| By: | Efthymios Athanasiou (Dep. of Philosophy, CMU); Santanu Dey (ISYE, Georgia Tech); Giacomo Valleta (Dep. of Economics, Maastricht) |
| Abstract: | We put forward a model of private goods with externalities. Agents derive benefit from communicating with each other. In order to communicate they need to have a language in common. Learning languages is costly. In this setting no individually rational and feasible Groves mechanism exists. We characterize the best-in-class feasible Groves mechanism and the best-in-class individually rational Groves mechanism. |
| Keywords: | Groves Mechanisms, Externality, Budget Surplus or Deficit, Pareto Undominated Mechanisms |
| JEL: | D70 D62 C60 |
| Date: | 2012–05 |
| URL: | http://d.repec.org/n?u=RePEc:fem:femwpa:2012.41&r=gth |
| By: | Andersson, Tommy (Department of Economics, Lund University); Svensson, Lars-Gunnar (Department of Economics, Lund University) |
| Abstract: | In many real-life house allocation problems, rents are bounded from above by price ceilings imposed by the government or a local administration. This is known as rent control. Because some price equilibria may be disqualified given such restrictions, a weaker equilibrium concept is suggested. Given the weaker notion, this paper defines an allocation mechanism, tailored to capture the specific features of housing markets with rent control, which always selects a weak price equilibrium. The main results demonstrate the existence of a weak price equilibrium and that the introduced allocation mechanism is efficient and non-manipulable for any given price ceiling. In its two bounding cases, the mechanism reduces to the weak version of the serial dictatorship mechanism (Svensson, 1994) and the competitive price mechanism (Demange and Gale, 1985), respectively. In this sense, the housing market with rent control, investigated in this paper, integrates two of the predominant models in the two-sided matching literature into a more general framework. |
| Keywords: | House allocation; rent control; rationing; weak price equilibrium; priority efficiency; non-manipulability |
| JEL: | C71 C78 D63 D71 D78 |
| Date: | 2012–06–28 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:lunewp:2012_018&r=gth |
| By: | Hougaard, Jens Leth (University of Copenhagen); Moreno-Ternero, Juan D. (Universidad Pablo de Olavide, and CORE, Univeristé catholique de Louvain); Østerdal, Lars Peter (Department of Business and Economics) |
| Abstract: | We consider the problem of assigning agents to a facility, represented by slots on a line, where only one agent can be served at a time. There is a finite number of agents, and each one wants to be served as close as possible to his preferred slot. We first consider deterministic assignment of agents to slots. We characterize (Pareto) efficiency in such setting and provide an algorithm for testing if a given deterministic assignment is efficient. We also characterize utilitarianism (minimization of the total gap between preferred and assigned slots) and provide a quick algorithm for testing if a given deterministic assignment is utilitarian. We then consider probabilistic assignment of agents to slots. In such framework, we characterize, making use of the previous algorithms, a method which is ordinally efficient and utilitarian. |
| Keywords: | Random assignment; ordinal efficiency; ex post efficiency; congested facility; utilitarianism |
| JEL: | C78 D61 D63 |
| Date: | 2012–07–01 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:sdueko:2012_011&r=gth |
| By: | Gabrielle Gayer (Department of Economics [Israël] - Bar-Ilan University); Itzhak Gilboa (GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC - GROUPE HEC - CNRS : UMR2959, Tel-Aviv University - Tel-Aviv University) |
| Abstract: | We consider the dynamics of reasoning by general rules (theories) and specific cases (analogies). When an agent faces an exogenous process, we show that, under mild conditions, if reality happens to be simple, the agent will converge to adopt a theory and discard analogical thinking. If, however, reality is complex, the agent may rely on analogies more than on theories. By contrast, when the process is generated by agents' predictions, convergence to a theory is much more likely, as in the emergence of norms in a coordination game. Mixed cases, involving noisy endogenous processes are likely to give rise to complex dynamics of reasoning, switching between theories and analogies. |
| Keywords: | analogies, theories, simplicity, norms |
| Date: | 2012–06–28 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-00712917&r=gth |
| By: | Itai Ashlagi; David Gamarnik; Michael A. Rees; Alvin E. Roth |
| Abstract: | It has been previously shown that for sufficiently large pools of patient-donor pairs, (almost) efficient kidney exchange can be achieved by using at most 3-way cycles, i.e. by using cycles among no more than 3 patient-donor pairs. However, as kidney exchange has grown in practice, cycles among n>3 pairs have proved useful, and long chains initiated by non-directed, altruistic donors have proven to be very effective. We explore why this is the case, both empirically and theoretically. We provide an analytical model of exchange when there are many highly sensitized patients, and show that large cycles of exchange or long chains can significantly increase efficiency when the opportunities for exchange are sparse. As very large cycles of exchange cannot be used in practice, long non-simultaneous chains initiated by non-directed donors significantly increase efficiency in patient pools of the size and composition that presently exist. Most importantly, long chains benefit highly sensitized patients without harming low-sensitized patients. |
| JEL: | C78 D02 I11 |
| Date: | 2012–07 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:18202&r=gth |