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on Game Theory |
| By: | Igal Milchtaich (Department of Economics, Bar-Ilan University) |
| Abstract: | In a correlated equilibrium, the players’ choice of actions is affected by random, correlated messages that they receive from an outside source, or mechanism. This allows for more equilibrium outcomes than without such messages (pure-strategy equilibrium) or with statistically independent ones (mixed-strategy equilibrium). In an incomplete information game, the messages may also convey information about the types of the other players, either because they reflect extraneous events that affect the types (correlated equilibrium) or because the players themselves report their types to the mechanism (communication equilibrium). Thus, mechanisms can be classified by the connections between the messages that the players receive and their own and the other players’ types, the dependence or independence of the messages, and whether randomness is involved. These properties may affect the achievable equilibrium outcomes, i.e., the payoffs and joint distributions of type and action profiles. Whereas for complete information games there are only three classes of equilibrium outcomes, with incomplete information the number is 14–15 for correlated equilibria and 15–17 for communication equilibria. Each class is characterized by the properties of the mechanisms that implement its members. The majority of these classes have not been described before. |
| Keywords: | Correlated equilibrium, Communication equilibrium, Incomplete information, Bayesian games, Mechanism, Correlation device, Implementation |
| Date: | 2009–11 |
| URL: | http://d.repec.org/n?u=RePEc:biu:wpaper:2009-27&r=gth |
| By: | Kathleen L. McGinn (Harvard Business School, Negotiation, Organizations & Markets Unit); Katherine L. Milkman (Wharton School, University of Pennsylvania); Markus Nöth (Universität Hamburg,) |
| Abstract: | We study the framing effects of communication in multiparty bargaining. Communication has been shown to be more truthful and revealing than predicted in equilibrium. Because talk is preference-revealing, it may effectively frame bargaining around a logic of fairness or competition, moving parties on a path toward or away from equal-division agreements. These endogenous framing effects may outweigh any overall social utility effects due to the mere presence of communication. In two experiments, we find that non-binding talk of fairness within a three-party, complete-information game leads toward off-equilibrium, equal division payoffs, while non-binding talk focusing on competitive reasoning moves parties away from equal divisions. Our two studies allow us to demonstrate that spontaneous within-game dialogue and manipulated pre-game talk lead to the same results. |
| Keywords: | communication, fairness, bargaining |
| JEL: | C72 C78 D74 |
| Date: | 2009–11 |
| URL: | http://d.repec.org/n?u=RePEc:hbs:wpaper:10-039&r=gth |
| By: | Lee, J.; Sabourian, H. |
| Abstract: | This paper examines repeated implementation of a social choice function (SCF) with infinitely-lived agents whose preferences are determined randomly in each period. An SCF is repeated-implementable in (Bayesian) Nash equilibrium if there exists a sequence of (possibly history-dependent) mechanisms such that (i) its equilibrium set is non-empty and (ii) every equilibrium outcome corresponds to the desired social choice at every possible history of past play and realizations of uncer- tainty. We first show, with minor qualifications, that in the complete information environment an SCF is repeated-implementable if and only if it is effcient. We then extend this result to the incomplete information setup. In particular, it is shown that in this case efficiency is sufficient to ensure the characterization part of repeated implementation. For the existence part, incentive compatibility is sufficient but not necessary. In the case of interdependent values, existence can also be established with an intuitive condition stipulating that deviations can be detected by at least one agent other than the deviator. Our incomplete information analysis can be extended to incorporate the notion of ex post equilibrium. |
| Keywords: | Repeated implementation, Nash implementation, Bayesian implementation, Ex post implementation, Efficiency, Incentive compatibility, Identifiability |
| JEL: | A13 C72 C73 D78 |
| Date: | 2009–11–13 |
| URL: | http://d.repec.org/n?u=RePEc:cam:camdae:0948&r=gth |
| By: | Pelosse, Yohan |
| Abstract: | This paper examines the foundations of arbitrary contest success functions (CSFs) in two distinct types of contests – unmediated and mediated contests. In an unmediated contest, CSFs arise as the (interim) players’ equilibrium beliefs of a two-stage game – the gun-butter game – in which players choose an activity (appropriative vs. productive) in the first stage, and apply effort to their activity in the second stage. In this view a CSF is rationalizable if a contest is induced on the equilibrium path of the gun-butter game. In the second approach, a CSF is the result of the optimal design of an administrator. Here, the designer seeks to maximize his utility by implementing a probability distribution on the set of contestants. However, he is curbed by a disutility term which represents the underlying institutional constraints or the designer’s preferences. Both approaches provide foundations for arbitrary CSFs with no restrictions on the number of contestants. |
| Keywords: | Induced contests; Gun-butter game; Control costs |
| JEL: | C72 |
| Date: | 2009–10 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:18664&r=gth |
| By: | Dutta, Bhaskar (Department of Economics, University of Warwick); Sen, Arunava (Planning Unit, Indian Statistical Institute) |
| Abstract: | We investigate the problem of Nash implementation in the presence of "partially honest" individuals. A partially honest player is one who has a strict preference for revealing the true state over lying when truthtelling does not lead to a worse outcome (according to preferences in the true state) than that which obtains when lying. We show that when there are at least three individuals, the presence of even a single partially honest individual (whose identity is not known to the planner) can lead to a dramatic increase in the class of Nash implementable social choice correspondences. In particular, all social choice correspondences satisfying No Veto Power can be implemented. We also provide necessary and sufficient conditions for implementation in the two-person case when there is exactly one partially honest individual and when both individuals are partially honest. We describe some implications of the characterization conditions for the two-person case. Finally, we extend our three or more individual result to the case where there is an individual with an arbitrary small but strictly positive probability of being partially honest. |
| Date: | 2009 |
| URL: | http://d.repec.org/n?u=RePEc:wrk:warwec:920&r=gth |
| By: | Chirantan Ganguly; Indrajit Ray |
| Abstract: | In the Crawford-Sobel (uniform, quadratic utility) cheap-talk model, we consider a simple mediation scheme (a communication device) in which the informed agent reports one of N possible elements of a partition to the mediator and then the mediator suggests one of N actions to the uninformed decision-maker according to the probability distribution of the device. We show that such a simple mediated equilibrium cannot improve upon the unmediated N-partition Crawford-Sobel equilibrium when the preference divergence parameter (bias) is small. |
| Keywords: | Cheap Talk, Mediated Equilibrium; Cheap Talk, Mediated Equilibrium |
| JEL: | C72 |
| Date: | 2009–11 |
| URL: | http://d.repec.org/n?u=RePEc:bir:birmec:05-08r&r=gth |
| By: | Luca Anderlini; Daniele Terlizzese |
| Date: | 2009–11–05 |
| URL: | http://d.repec.org/n?u=RePEc:cla:levarc:814577000000000379&r=gth |
| By: | Stefano Vannucci |
| Abstract: | The choice functions that are consistent with selections of VNM-stable sets of an underlying revealed dominance digraph are characterized both under VNM-perfection of the latter and in the general case. |
| Keywords: | VNM-stable sets, kernel-perfect digraphs, choice func-tions 1 |
| JEL: | C70 C71 D01 |
| Date: | 2009–10 |
| URL: | http://d.repec.org/n?u=RePEc:usi:wpaper:576&r=gth |