Game Theory
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Game Theory2015-07-04László Á. KóczyA new basis and the Shapley value
http://d.repec.org/n?u=RePEc:wap:wpaper:1418&r=gth
The purpose of this paper is to introduce a new basis of the set of all TU games. Shapley (1953) introduced the unanimity game in which cooperation of all players in a given coalition yields payoff. We introduce the commander game in which only one player in a given coalition yields payoff. The set of the commander games forms a basis and has two properties. First, when we express a game by a linear combination of the basis, the coefficients related to singletons coincide with the Shapley value. Second, the basis induces the null space of the Shapley value.Koji Yokote, Yukihiko Funaki, Yoshio Kamijo2015-01TU game; Shapley value; Basis; Null spaceDichotomous multi-type games: Shapley-Shubik and Banzhaf-Coleman power indices
http://d.repec.org/n?u=RePEc:ema:worpap:2015-05&r=gth
This work focuses on multi-type games in which there are a number of nonordered types in the input, while the output consists of a single real value. When considering the dichotomous case, we extend the Shapley-Shubik and Banzhaf- Coleman indices. We also provide a full characterization of both extensions. Our results generalize the literature on classical cooperative games.Sebastien Courtin, Zephirin Nganmeni, Bertrand Tchantcho2015Game theory,Multi-type games, Simple games, Shapley-Shubik index, Banzhaf-Coleman indexSimple and three-valued simple minimum coloring games
http://d.repec.org/n?u=RePEc:tiu:tiucen:425c90bb-c6c6-4561-ad44-111883cd7bc4&r=gth
In this paper minimum coloring games are considered. We characterize the type<br/>of conflict graphs inducing simple or three-valued simple minimum coloring games. We provide an upper bound on the number of maximum cliques of conflict graphs inducing such games. Moreover, a characterization of the core is provided in terms of the underlying conflict graph. In particular, in case of a perfect conflict graph the core of an induced three-valued simple minimum coloring game equals the vital core.Musegaas, Marieke, Borm, Peter, Quant, Marieke2015Minimum coloring game; three-valued simple gamesAxiomatic characterizations under players nullification
http://d.repec.org/n?u=RePEc:crb:wpaper:2015-06&r=gth
Many axiomatic characterizations of values for cooperative games invoke axioms which evaluate the consequences of removing an arbitrary player. Balanced contributions (Myerson, 1980) and balanced cycle contributions (Kamijo and Kongo, 2010) are two well-known examples of such axioms. We revisit these characterizations by nullifying a player instead of deleting her/him from a game. The nullification (Béal et al., 2014) of a player is obtained by transforming a game into a new one in which this player is a null player, i.e. the worth of the coalitions containing this player is now identical to that of the same coalition without this player. The degree with which our results are close to the original results in the literature is connected to the fact that the targeted value satisfies the null player out axiom (Derks and Haller, 1999).Sylvain Béal, Sylvain Ferrières, Eric Rémila, Philippe Solal2015-06Player nullification, balanced contributions, Shapley value, equal allocation of non-separable costs, potential.Weak Surplus Mononicity characterizes convex combination of egalitarian Shapley value and Consensus value
http://d.repec.org/n?u=RePEc:wap:wpaper:1504&r=gth
We deal with the problem of striking a balance between marginal- ism and egalitarianism in the class of TU cooperative games. We introduce a new axiom, Weak Surplus Monotonicity. It states that if the marginal contribution of a player increases, the worth of the grand coalition increases and the cooperative surplus increases, then the pay- off of the player should also increase. We show that a solution satisfies Efficiency, Symmetry and Weak Surplus Monotonicity if and only if it is a convex combination of the Shapley value, the Equal division and the CIS value. By replacing the new axiom with a stronger axiom and taking the dual, we obtain 11 characterizations of solutions, including the results of Young (1985) or Casajus and Huettner (2014).Koji Yokote, Yukihiko Funaki2015-06TU game; Shapley value; Monotonicity; AxiomatizationLying in public good games with and without punishment
http://d.repec.org/n?u=RePEc:cgr:cgsser:06-02&r=gth
We experimentally study a frequently observed public good setting where accurate contribution feedback is not available and group members can send non-verifiable cheap talk messages about their contributions. As feedback, subjects receive only announced contributions or the announced or actual contribution with 50% probability. In this setting, we explore both information transmission and reception as well as the effectiveness of costly peer punishment. Overall, we find that cooperation breaks down in all announcement treatments except when actual contribution feedback is provided some of the time and punishment is available. We identify various constraints to full cooperation relative to the standard public good game. First, subjects make errors in adjusting their beliefs for the announcements of others and, on average, adjust their beliefs downward for a given announcement. Second, we find that significantly more punishment is assigned to high contributors compared to the standard public good game. Furthermore, punishment for low contributors appears to have a smaller disciplining effect. When actual contribution information is provided some of the time we find that these constraints are less severe compared to the setting where only announcements are available.Bernd Irlenbusch, Janna Ter Meer2015-05-21public goods, punishment, lying, credibility, communicationStable Biased Sampling
http://d.repec.org/n?u=RePEc:bsl:wpaper:2015/03&r=gth
This paper presents a model in which sampling biases are evolutionary stable. We consider the sampling best response dynamics for a two-strategy population game having a unique equilibrium that is in mixed strategies. Allowing players to use differingsampling procedures, we model evolutionary competition between such procedures witha variant of the replicator dynamics that discriminates on the basis of average fitnessamong players with the same procedure. Using results on slow-fast systems, we findthat the sampling bias in stable procedures is generically non-zero, that the size of thebias is the more extreme the closer the mixed equilibrium is to the boundary of (0,1),and that, if sample size increases, then the bias eventually decreases. Based on theseobservations, we argue that the presence of biases can be explained by an evolutionarysecond-best effect correcting for suboptimal choices induced by playing best responseto small samples.Samuel Häfner2015Sampling Best Response Dynamics, Sampling Bias, Evolutionary Second-Best, Two-Speed DynamicsDuality in Dynamic Discrete Choice Models
http://d.repec.org/n?u=RePEc:spo:wpmain:info:hdl:2441/7svo6civd6959qvmn4965cth1d&r=gth
Using results from convex analysis, we characterize the identification and estimation of dynamic discrete-choice models based on the random utility framework. We show that the conditional choice probabilities and the choice specific payoffs in these models are related in the sense of conjugate duality. Based on this, we propose a new two-step estimator for these models; interestingly, the first step of our estimator involves solving a linear program which is identical to the classic assignment (two-sided matching) game of Shapley and Shubik (1971). The application of convex-analytic tools to dynamic discrete choice models, and the connection with two-sided matching models, is new in the literature.Khai Chiong, Alfred Galichon, Matt Shum2015-05Discret choice model; Mass Transport Approach (MTA); Conjugate dualityOrdinal and cardinal solution concepts for two-sided matching
http://d.repec.org/n?u=RePEc:spo:wpmain:info:hdl:2441/5k6c74nfqf91aa74v72q2ca5tm&r=gth
We characterize solutions for two-sided matching, both in the transferable - and in the nontransferable - utility frameworks, using a cardinal formulation. Our approach makes the comparison of the matching models with and without transfers particularly transparent. We introduce the concept of a no-trade matching to study the role of transfers in matching. A no-trade matching is one in which the availability of transfers do not affect the outcome.Federico Echenique, Alfred Galichon2014-04Matching; Stability; EfficiencyAn Approximate Auction
http://d.repec.org/n?u=RePEc:hhs:lunewp:2015_019&r=gth
This paper presents an auction procedure which is of particular interest when short execution times are of importance. It is based on a method for approximating the bidders' preferences over two types of items when complementarity between the two may exist. In particular, linear approximations of the bidders' indifference curves are made. The resulting approximated preference relation is shown to be complete and transitive at any given price vector. It is shown that an approximated Walrasian equilibrium always exists if the approximated preferences of the bidders comply with the gross substitutes condition. Said condition also ensures that the set of approximated equilibrium prices forms a complete lattice. A process is proposed which is shown to always reach the smallest approximated Walrasian price vector.Ingebretsen Carlson, Jim2015-06-11Approximate auction; one-round auction; non-quasi-linear preferences; approximated preferencesIntegrating Affective Responses into Game Theory: A Dual Selves Model
http://d.repec.org/n?u=RePEc:mar:magkse:201517&r=gth
This paper develops a method to integrate affective reponses into game theoretical models. We illustrate our method in a team production framework. The model analyzes how concave and convex status preferences for esteem solve the problem of team production under complete and incomplete information about workers’ abilities. Using a dual selves model, we model the choice of effort as a deliberative decision and the expression of esteem as an affective response. Modeling an individual’s affective system as a seperate player allows us to apply standard game-theoretic solution concepts to analyze affective responses.Matthias Greiff2015Matching in Closed-Form: Equilibrium, identification, and comparative statics
http://d.repec.org/n?u=RePEc:spo:wpmain:info:hdl:2441/34a8d5vcod96oo2cch2e7gs4v6&r=gth
This paper provides closed-form formulas for a multidimensional two-sided matching problem with transferable utility and heterogeneity in tastes. When the matching surplus is quadratic, the marginal distributions of the characteristics are normal, and when the heterogeneity in tastes is of the continuous logit type, as in Choo and Siow (2006), we show that the optimal matching distribution is also jointly normal and can be computed in closed form from the model primitives. Conversely, the quadratic surplus function can be identiﬁed from the optimal matching distribution, also in closed-form. The analytical formulas make it computationally easy to solve problems with even a very large number of matches and allow for quantitative predictions about the evolution of the solution as the technology and the characteristics of the matching populations change.Raicho Bolijov, Alfred Galichon2014-10Matching; Marriage; AssignmentTwo-sided Altruism and Signaling
http://d.repec.org/n?u=RePEc:nbr:nberwo:21309&r=gth
This paper shows that when donors and recipients care about each other --two-sided altruism -- the presence of asymmetry of information about the donor's income leads very naturally to a signaling game. A donor who cares about the recipient's welfare has incentives to appear richer than he is when the recipient cares about him. Similarly, asymmetry of information regarding the donor's income generates a signaling game in the presence of two-sided altruism. These signaling games put upward pressure on transfers and this pressure increases with the altruism of the recipient.Garance Genicot2015-06On the importance of the probabilistic model in identifying the most decisive game in a tournament
http://d.repec.org/n?u=RePEc:cte:wsrepe:ws1514&r=gth
Identifying the important matches in international football tournaments is of great relevance for a variety of decision makers such as organizers, team coaches and/or media managers. This paper addresses this issue by analyzing the role of the statistical approach used to estimate the outcome of the game on the identification of decisive matches on international tournaments for national football teams. We extend the measure of decisiveness proposed by Geenens (2014) in order to allow us to predict or evaluate match importance before, during and after of a particular game on the tournament. Using information from the 2014 FIFA World Cup, our results suggest that Poisson and Kernel regressions significantly outperform the forecasts of ordered probit models. Moreover, we find that the identification of the key, but not most important, matches depends on the model considered. We also apply this methodology to identify the favorite teams and to predict the most important matches in 2015 Copa America before the start of the competition.Francisco Corona, Juan de Dios Tena, Michael P. Wiper2015-06Game importance , Ordered probit model , Entropy , Poisson model , Kernel regressionLeniency and Damages
http://d.repec.org/n?u=RePEc:cpr:ceprdp:10682&r=gth
Damage actions may reduce the attractiveness of leniency programs for cartel participants if their cooperation with the competition authority increases the chance that the cartel’s victims will bring a successful suit. A long legal debate culminated in an EU directive, adopted in November 2014, which seeks a balance between public and private enforcement. It protects the effectiveness of a leniency program by preventing the use of leniency statements in subsequent actions for damages. Our analysis shows such compromise is not required: limiting the cartel victims’ ability to recover their loss is not necessary to preserve the effectiveness of a leniency program and may be counterproductive. We show that damage actions will actually improve its effectiveness, through a legal regime in which the civil liability of the immunity recipient is minimized and full access to all evidence collected by the competition authority, is granted to claimants, like in the US.Buccirossi, Paolo, Marvão, Catarina, Spagnolo, Giancarlo2015-06cartels; competition policy; Leniency Program; private and public enforcement