|
on Game Theory |
|
Issue of 2012‒10‒13
sixteen papers chosen by Laszlo A. Koczy Hungarian Academy of Sciences and Obuda University |
| By: | Arantza Estevez-Fernandez (VU University Amsterdam); Hans Reijnierse (CentER, Tilburg University) |
| Abstract: | In this paper, we analyze cost sharing problems arising from a general service by explicitly taking into account the generated revenues. To this cost-revenue sharing problem, we associate a cooperative game with transferable utility, called cost-revenue game. By considering cooperation among the agents using the general service, the value of a coalition is defined as the maximum net profit that the coalition may obtain by means of cooperation. As a result, a coalition may profit from not allowing all its members to get the service that generates the revenues. We focus on the study of the core of cost-revenue games. Under the assumption that cooperation among the members of the grand coalition grants the use of the service under consideration to all its members, it is shown that a cost-revenue game has a non-empty core for any vector of revenues if, and only if, the dual game of the cost game has a large core. Using this result, we investigate minimum cost spanning tree games with revenues. We show that if every connection cost can take only two values (low or high cost), then, the corresponding minimum cost spanning tree game with revenues has a non-empty core. Furthermore, we provide an example of a minimum cost spanning tree game with revenues with an empty core where every connection cost can take only one of three values (low, medium, or high cost). |
| Keywords: | Cost-revenue allocation problem; cooperative game; core; minimum cost spanning tree problem |
| JEL: | C71 |
| Date: | 2012–09–27 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:20120101&r=gth |
| By: | M. Ali Khan (Department of Economics, Johns Hopkins University); Kali P. Rath (Department of Economics, University of Notre Dame); Yeneng Sun (Department of Economics, National University of Singapore); Haomiao Yu (Department of Economics, Ryerson University) |
| Abstract: | We present a comprehensive theory of large games in which players have names and determinate social-types and/or biological traits, and identify through four decisive examples, essentially based on a matching-pennies type game, pathologies arising from the use of a Lebesgue interval for player's names. In a sufficiently general context of traits and actions, we address this dissonance by showing a saturated probability space as being a necessary and sufficient name-space for the existence and upper hemi-continuity of pure-strategy Nash equilibria in large games with traits. We illustrate the idealized results by corresponding asymptotic results for an increasing sequence of finite games. |
| Keywords: | Large games, social-type, traits, idealized limit game, saturated probability space, pure-strategy Nash equilibrium, closed-graph property, upper hemi-continuity, asymptotic implementation |
| JEL: | C62 D50 D82 G13 |
| Date: | 2012–10 |
| URL: | http://d.repec.org/n?u=RePEc:rye:wpaper:wp035&r=gth |
| By: | Sofía Correa; Juan Pablo Torres-Martínez |
| Abstract: | We address essential stability properties of Cournot-Nash equilibria for generalized games with a continuum of players, where only a finite number of them are atomic. Given any set of generalized games continuously parameterized by a complete metric space, we analyze the robustness of equilibria to perturbations on parameters. As an application of our results, we show that essential stability can provide a rationale for electoral participation of politically engaged individuals. |
| Date: | 2012–09 |
| URL: | http://d.repec.org/n?u=RePEc:udc:wpaper:wp362&r=gth |
| By: | Irenaeus Wolff |
| Abstract: | Models of evolutionary game theory have shown that punishment may be an adaptive behaviour in environments characterised by a social-dilemma situation. Experimental evidence closely corresponds to this nding but questions the cooperation-enhancing eect of punishment if players are allowed to retaliate against their punishers. This study provides a theoretical explanation for the existence of retaliating behaviour in the context of repeated social dilemmas and analyses the role punishment can play in the evolution of cooperation under these conditions. We show a punishing strategy can pave the way for a partially-cooperative equilibrium of conditional cooperators and defecting types and, under positive mutation rates, foster the cooperation level in this equilibrium by prompting reluctant cooperators to cooperate. However, when rare mutations occur, it cannot sustain cooperation by itself as punishment costs favour the spread of non-punishing cooperators. |
| Keywords: | Public goods, Prisoner's Dilemma, Strong reciprocity, Counterpunishment |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:twi:respas:0077&r=gth |
| By: | Alexander Elbittar (Centro de Investigación y Docencia Económica (CIDE)); Andrei Gomberg (Centro de Investigacion Economica (CIE), Instituto Tecnologico Autonomo de Mexico (ITAM)) |
| Abstract: | In this paper we introduce communication into intergroup ultimatum bargaining in a lab. The responder groups vote whether to accept the proposals with unanimity required either for acceptance or for rejection. In contrast with the no-communication results reported in our previous study (Elbittar, Gomberg and Sour 2011), the group decision rule does affect the individual voting behavior when subjects are allowed to exchange messages before voting. In fact, when acceptance is the default, subjects become substantially more likely to vote to reject an offer. As a result, the formal group decision-making rule turns out to have little impact on group decisions, which follow the behavior of the more confronational subjects, as predicted by the "group discontinuity hypothesis" of the psychological literature. |
| Keywords: | Bargaining games, group decision making, communication and experiments |
| JEL: | C92 D44 D82 |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:cie:wpaper:1203&r=gth |
| By: | Arthur Lewbel (Boston College); Xun Tang (University of Pennsylvania) |
| Abstract: | The existing literature on binary games with incomplete information assumes that either payoff functions or the distribution of private information are finitely parameterized to obtain point identification. In contrast, we show that, given excluded regressors, payoff functions and the distribution of private information can both be nonparametrically point identified. An excluded regressor for player i is a sufficiently varying state variable that does not affect other players utility and is additively separable from other components in is payoff. We show how excluded regressors satisfying these conditions arise in contexts such as entry games between firms, as variation in observed components of fixed costs. Our identification proofs are constructive, so consistent nonparametric estimators can be readily based on them. For a semiparametric model with linear payoffs, we propose root-N consistent and asymptotically normal estimators for parameters in players payoffs. Finally, we extend our approach to accommodate the existence of multiple Bayesian Nash equilibria in the data-generating process without assuming equilibrium selection rules. |
| Keywords: | Games with Incomplete Information, Excluded Regressors, Nonparametric Identification, Semiparametric Estimation, Multiple Equilibria. |
| JEL: | C14 C51 D43 |
| Date: | 2012–08–21 |
| URL: | http://d.repec.org/n?u=RePEc:boc:bocoec:808&r=gth |
| By: | Breitmoser, Yves |
| Abstract: | A recent advance in our understanding of repeated PDs is the detection of a threshold d* at which laboratory subjects start to cooperate predictively. This threshold is substantially above the classic threshold "existence of Grim equilibrium" and has been characterized axiomatically by Blonski, Ockenfels, and Spagnolo (2011, BOS). In this paper, I derive its behavioral foundations. First, I show that the threshold is equivalent to existence of a "Semi-Grim" equilibrium s_cc>s_cd=s_dc>s_dd. It is cooperative (s_cc>0.5), non-reciprocal (s_cd=s_dc), and robust to imperfect monitoring ("belief-free"). Next, I show that the no-reciprocity condition s_cd=s_dc also follows from robustness to random-utility perturbations (logit equilibrium). Finally, I re-analyze strategies in four recent experiments and find that the majority of subjects indeed plays Semi-Grim when it is an equilibrium strategy, which explains d*'s predictive success. |
| Keywords: | Repeated Prisoner's Dilemma; experiment; equilibrium selection; cooperative behavior; reciprocity; belief-free equilibria; robustness |
| JEL: | C92 C73 C72 |
| Date: | 2012–10–04 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:41731&r=gth |
| By: | Brams, Steven J.; Kilgour, D. Marc |
| Abstract: | Assume it is known that one player in a 2 x 2 game can detect the strategy choice of its opponent with some probability before play commences. We formulate conditions under which the detector can, by credibly committing to a strategy of probabilistic tit-for-tat (based on its imperfect detector), induce an outcome favorable to itself. A non-Nash, Pareto-optimal outcome is inducible—that is, it can be stabilized via probabilistic tit-for-tat—in 20 of the 57 distinct 2 x 2 strict ordinal games without a mutually best outcome (35 percent). Sometimes the inducement is “weak,” but more often it is “strong.” As a case study, we consider the current conflict between Israel and Iran over Iran’s possible development of nuclear weapons and show that Israel’s credible commitment to probabilistic tit-for-tat can, with sufficiently accurate intelligence, induce a cooperative choice by Iran in one but not the other of two plausible games that model this conflict. |
| Keywords: | 2 x 2 games; tit-for-tat; inducubility; Israel-Iran conflict; nuclear weapons |
| JEL: | C78 D74 C72 |
| Date: | 2012–10 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:41773&r=gth |
| By: | Jeannette Brosig-Koch; Timo Heinrich; Christoph Helbach |
| Abstract: | We investigate learning and the development of the capability to backward induct in children and young adults aged 6 to 23 under controlled laboratory conditions. The experimental design employs a modified version of the race game. As in the original game (see Burks et al., 2009, Dufwenberg et al., 2010, Gneezy et al., 2010, and Levitt et al., 2011), subjects need to apply backward induction in order to solve the games. We find that subjects’ capability to backward induct improves with age, but that this process systematically diff ers across gender. Our repetition of the games provides insights into differences in learning between age groups and across gender. |
| Keywords: | Backward induction; learning; age effects; experimental economics; children |
| JEL: | C72 J13 C91 |
| Date: | 2012–07 |
| URL: | http://d.repec.org/n?u=RePEc:rwi:repape:0360&r=gth |
| By: | Amegashie, J. Atsu |
| Abstract: | I present a two-player nested contest which is a convex combination of two widely studied contests: the Tullock (lottery) contest and the all-pay auction. A Nash equilibrium exists for all parameters of the nested contest. If and only if the contest is sufficiently asymmetric, then there is an equilibrium in pure strategies. In this equilibrium, individual and aggregate efforts are lower relative to the efforts in a Tullock contest. This leads to the surprising result that if aggregate efforts in the all-pay auction are higher than the aggregate efforts in the Tullock contest, then aggregate efforts in the nested contest may not lie between aggregate efforts in the all-pay auction and aggregate efforts in the Tullock contest. When the contest is symmetric or asymmetric, I find a mixed-strategy equilibrium and describe some properties of the equilibrium distribution function; I also find the equilibrium payoffs and expected bids. When the weight on the all-pay auction component of this nested contest lies in an intermediate range, then there exist multiple non-payoff-equivalent equilibria such that there is an all-pay auction equilibrium as defined in Alcade and Dahm (2010) and another equilibrium which is not an all-pay auction equilibrium; these equilibria cannot be ranked using the Pareto criterion. If the goal of a contest-designer is to reduce aggregate effort (i.e., wasteful rent-seeking efforts), then this nested contest may be better than both the Tullock contest and the all-pay auction. |
| Keywords: | all-pay auction; discontinuous games; mixed strategy; pure strategy; Tullock contest |
| JEL: | B21 D44 D72 C72 |
| Date: | 2012–06–19 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:41654&r=gth |
| By: | Jakub Steiner (Northwestern University); Laurent Mathevet (University of Texas at Austin) |
| Abstract: | We study the impact of frictions on the prevalence of systemic crises. Agents privately learn about a fixed payoff parameter, and repeatedly adjust their investments while facing transaction costs in a dynamic global game. The model has a rich structure of externalities: payoffs may depend on the volume of aggregate investment, on the concentration of investment, or on its volatility. We examine how small frictions, including those similar to the Tobin tax, affect the equilibrium. We identify conditions under which frictions discourage harmful behavior without compromising investment volume. The analysis is driven by a robust invariance result: the volume of aggregate investment (measured in a pivotal contingency) is invariant to a large family of frictions. |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:red:sed012:123&r=gth |
| By: | Peter Cramton (Economics Department, University of Maryland); Steven Stoft |
| Abstract: | The international game of cap and trade begins when countries choose their quantity targets, which are largely selected according to self interest. The analogous public-goods game, in which countries choose their abatement levels, has an uncooperative outcome. Compared to that, the Nash equilibrium of the cap-and-trade game shows that abatement can increase but that trade provides opportunities for uncooperative behavior. By contrast, a game in which all countries vote for a global quantity target or a global price target can lead to a highly cooperative choice of target. However, the assignment of responsibilities for a global quantity target stymies implementation of a global cap. The global-price-target game largely overcomes this barrier because a uniform global price provides a focal point for cooperation. However low-emission countries apparently prefer a much lower global-price than more prosperous countries unless a Green Fund is implemented. A game that couples such a fund to the global price target can largely overcome this barrier to cooperation. We describe such a game along with its equilibrium outcome, which promises to be inexpensive and cooperative. |
| Keywords: | global warming, climate change, climate treaty, cap and trade, carbon tax, carbon price, public goods |
| JEL: | Q54 Q56 Q58 H41 D78 |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:pcc:pccumd:12csgcg&r=gth |
| By: | A.K.S. Chand (Department of Economics, University Of Venice Ca’ Foscari) |
| Abstract: | In this paper, I discuss a Cheap Talk model that arises during the allocation of a limited budget to multiple Senders by a Receiver with private communication. The Receiver's utility is the sum of the utilities of the Senders. Considering quadratic utility functions, I show that there is no fully revealing equilibrium with budget constraint. I also show that a higher budget facilitates information transmission to the Receiver in terms of ex-ante expected utility by considering (1) an equilibrium where only one Sender reveals truthfully, (2) a symmetric equilibrium with two intervals and (3) a commitment strategy by the Receiver where only one Sender receives his desired amount. The commitment strategy is doing better than the other two types of equilibria for budget more than a particular value. This requires us to look for equilibria with higher number of intervals which does better than the commitment strategy. |
| Keywords: | Cheap Talk, Multiple Senders, Budget Constraint |
| JEL: | C72 D82 D83 |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:ven:wpaper:2012_19&r=gth |
| By: | Caterina Cruciani (Department of Economics, Università Ca' Foscari Venezia); Anna Moretti (Department of Management, Università Ca' Foscari Venezia); Paolo Pellizzari (Department of Economics, Università Ca' Foscari Venezia) |
| Abstract: | This paper studies the profile of cooperation emerging in a context in which agents may choose to join one of two groups or stay on their own, in a world where similarity across peers matters. In particular, we investigate the role of heterogeneity in individual contributions, of the level of information and of in-group processes of convergence in values (sense making) in fostering higher levels of cooperation, assessed through higher participation rates to groups. Starting from the result that more heterogeneity reduces participation, we show that increasing the level of information available to subjects and activating sense-making dynamics are able to support higher cooperation levels, which, however, come at the cost of increased radicalization of agent types within group. |
| Keywords: | Similarity, Sense making, Cooperation, Groups |
| JEL: | B41 D74 D85 |
| Date: | 2012–09 |
| URL: | http://d.repec.org/n?u=RePEc:vnm:wpdman:27&r=gth |
| By: | Frank Huettner (Universität Leipzig, Institut für Empirische Wirtschaftsforschung); Marco Sunder (Universität Leipzig, Institut für Empirische Wirtschaftsforschung) |
| Abstract: | Decomposition of the goodness of fit to (groups of) regressor variables can be a useful diagnostic tool to quickly assess “relative importanceâ€. Owen and Shapley values, two closely related solutional concepts in cooperative game theory, provide unique solutions to the decomposition exercise on the basis of a sound set of assumptions. At this stage, the new command rego implements decomposition of R-squared in OLS regression, based on the covariance matrix of the data for fast computation in the Mata environment. It also allows for bootstrapping the outcomes. Inclusion of other measures of fit and classes of models is planned for future extensions. |
| Date: | 2012–09–22 |
| URL: | http://d.repec.org/n?u=RePEc:boc:usug12:17&r=gth |
| By: | Lawrence M. Ausubel (Economics Department, University of Maryland); Peter Cramton (Economics Department, University of Maryland) |
| Abstract: | The best sites for offshore wind farms on the US Outer Continental Shelf are scarce. To make the best use of this scarce resource, it is necessary to implement a fair and efficient mechanism to assign wind rights to companies that are most likely to develop off-shore wind energy projects. Coastal states, particularly along the eastern seaboard, are taking aggressive actions to spur the growth of an offshore wind sector in their states to help meet their renewable portfolio targets while nurturing the supporting on-shore infrastructure. This paper discusses the design of auctions for wind rights in which price is the sole factor of competition. A second paper, Ausubel and Cramton (2011), extends the analysis to auctions in which multiple factors are used in bid evaluation. This may be especially useful in settings where states (and potential bidders) have already taken actions to foster offshore wind development. |
| Keywords: | Auctions, clock auctions, spectrum auctions, market design, wind rights auctions |
| JEL: | D44 C78 L96 |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:pcc:pccumd:11acadw&r=gth |