118,661 research outputs found
Jere Nash Interview with Crymes G. Pittman
No full textInterview conducted by author Jere Nash with attorney Crymes G. Pittman in the process of writing Mississippi Politics: The Struggle for Power, 1976-2006. Topic is Pittman\u27s experience representing Governor Bill Allain against allegations of homosexuality
Mary Louise Nash
No full textPublication of information about Mary Nash, a co-founder of the Sherman Female Institute in Sherman, Texas.Includes extract from memorial paper written by Mrs. Mattie Hardwick Jones. Mary Nash College was founded in Sherman in 1877 as Sherman Female Institute by Jesse G. and Mary Louise Nash. The school closed in 1901 and the property was sold to Kidd-Key College. Library's copy part of the Holloway family papers, A1989.1613
Computing nash equilibria gets harder : new results show hardness even for parameterized complexity
No full textIn this paper we show that some decision problems regarding the computation of Nash equilibria are to be considered particularly hard. Most decision problems regarding Nash equilibria have been shown to be NP-complete. While some NP-complete problems can find an alternative to tractability with the tools of Parameterized Complexity Theory, it is also the case that some classes of problems do not seem to have fixed-parameter tractable algorithms. We show that k-Uniform Nash and k-Minimal Nash support are W[2]-hard. Given a game G=(A,B) and a nonnegative integer k, the k-Uniform Nash problem asks whether G has a uniform Nash equilibrium of size k. The k-Minimal Nash support asks whether has Nash equilibrium such that the support of eacGh player’s Nash strategy has size equal to or less than k. First, we show that k-Uniform Nash (with k as the parameter) is W[2]-hard even when we have 2 players, or fewer than 4 different integer values in the matrices. Second, we illustrate that even in zerosum games k-Minimal Nash support is W[2]-hard (a sample Nash equilibrium in a zero-sum 2-player game can be found in polynomial time (von Stengel 2002)). Thus, it must be the case that other more general decision problems are also W[2]-hard. Therefore, the possible parameters for fixed parameter tractability in those decision problems regarding Nash equilibria seem elusive
Choice-Nash Equilibria
No full textWe provide existence results for equilibria of games where players employ abstract (non binary) choice rules. Such results are shown to encompass as a relevant instance that of games where players have (non-transitive) SSB (Skew-Symmetric Bilinear) preferences, as will as other well-known transitive (e. g. Nash´s) and non-transitive (e. g. Shafer and Sonnenschein´s) models in the literature. Further, our general model contains games where players display procedural rationality.
Partially-honest Nash implementation: Characterization results
No full textThis paper studies implementation problems in the wake of a recent trend of implementation of non-consequentialist nature, which draws on the evidence taken from experimental and behavioral economics. Specifically, following the seminal works by Matsushima (2008) and Dutta and Sen (2009), the paper considers implementation problems with partially-honest agents, which presume that there is at least one individual in society who concerns herself with not only outcomes but also honest behavior at least in a limited manner. Given this setting, the paper provides a general characterization of Nash implementation with partially-honest individuals. It also provides the necessary and sufficient condition for Nash implementation with partially-honest individuals by mechanisms with some types of strategy-space reductions. As a consequence, it shows that in contrast to the case of the standard framework, the equivalence between Nash implementation and Nash implementation with strategy space reduction no longer holds.Nash implementation, canonical-mechanisms, s-mechanisms, self-relevant mechanisms, partial-honesty, permissive results
Two-agent Nash implementation: A new result
No full text[Moore and Repullo, \emph{Econometrica} \textbf{58} (1990) 1083-1099] and [Dutta and Sen, \emph{Rev. Econom. Stud.} \textbf{58} (1991) 121-128] are two fundamental papers on two-agent Nash implementation. Both of them are based on Maskin's classic paper [Maskin, \emph{Rev. Econom. Stud.} \textbf{66} (1999) 23-38]. A recent work [Wu, http://arxiv.org/abs/1002.4294, \emph{Inter. J. Quantum Information}, 2010 (accepted)] shows that when an additional condition is satisfied, the Maskin's theorem will no longer hold by using a quantum mechanism. Furthermore, this result holds in the macro world by using an algorithmic mechanism. In this paper, we will investigate two-agent Nash implementation by virtue of the algorithmic mechanism. The main result is: The sufficient and necessary conditions for Nash implementation with two agents shall be amended, not only in the quantum world, but also in the macro world.Quantum game theory; Mechanism design; Nash implementation.
Uniform payoff security and Nash equilibrium in metric games
No full textWe introduce a condition, uniform payoff security, for games with separable metric strategy spaces and payoffs bounded and measurable in players' strategies. We show that if any such metric game G is uniformly payoff secure, then its mixed extension G is payoff secure. We also establish that if a uniformly payoff secure metric game G has compact strategy spaces, and if its mixed extension G has reciprocally upper semicontinuous payoffs, then G has a Nash equilibrium in mixed strategies. We provide several economic examples of metric games satisfying uniform payoff security.Uniform payoff security, Nash equilibrium, discontinuous games, mixed extension.
Nash Equilibrium Strategies in Discrete-Time Finite-Horizon Dynamic Games with Risk-and Effort-Averse Players
No full textThe objective of this paper is to re-examine the risk-and effort attitude in the context of strategic dynamic interactions stated as a discrete-time finite-horizon Nash game. The analysis is based on the assumption that players are endogenously risk-and effort-averse. Each player is characterized by distinct risk-and effort-aversion types that are unknown to his opponent. The goal of the game is the optimal risk-and effort-sharing between the players. It generally depends on the individual strategies adopted and, implicitly, on the the players' types or characteristics.Dynamic Nash game, optimal path, closed-loop control, endogenous risk-and effort-aversion, adaptive risk-and effort management, optimal risk-and effort-sharing.
Fairness, Efficiency, and the Nash Bargaining Solution
No full textA bargaining solution balances fairness and efficiency if each player's payoff lies between the minimum and maximum of the payoffs assigned to him by the egalitarian and utilitarian solutions. In the 2-person bargaining problem, the Nash solution is the unique scale-invariant solution satisfying this property. Additionally, a similar result, relating the weighted egalitarian and utilitarian solutions to a weighted Nash solution, is obtained. These results are related to a theorem of Shapley, which I generalize. For n>=3, there does not exist any n-person scale-invariant bargaining solution that balances fairness and efficiency.Bargaining; fairness; efficiency; Nash solution
Nash bargained consumption decisions: a revealed preference analysis.
No full textWe present a revealed preference analysis of the testable implications of the Nash bargaining solution. Our specific focus is on a two-player game involving consumption decisions. We consider a setting in which the empirical analyst has information on both the threat points bundles and the bargaining outcomes. We first establish a revealed preference characterization of the Nash bargaining solution. This characterization implies conditions that are both necessary and sufficient for consistency of observed consumption behavior with the Nash bargaining model. However, these conditions turn out to be nonlinear in unknowns and therefore difficult to verify. Given this, we subsequently present necessary conditions and sufficient conditions that are linear (and thus easily testable). We illustrate the practical usefulness of these conditions by means of an application to experimental data. Such an experimental setting implies a most powerful analysis of the empirical goodness of the Nash bargaining model for describing consumption decisions. To our knowledge, this provides a first empirical test of the Nash bargaining model on consumption data. Finally, we consider the possibility that threat point bundles are not observed. This obtains testable conditions for the Nash bargaining model that can be used in non-experimental (e.g. household consumption) settings, which often do not contain information on individual consumption bundles in threat points.
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