scholarly journals Erratum to: A nonstandard characterization of sequential equilibrium, perfect equilibrium, and proper equilibrium

2016 ◽  
Vol 46 (2) ◽  
pp. 591-594
Author(s):  
Joseph Y. Halpern
Keyword(s):  
Sequential Equilibrium ◽  
Perfect Equilibrium ◽  
Proper Equilibrium

scholarly journals ON GAMES OF PERFECT INFORMATION: EQUILIBRIA, ε–EQUILIBRIA AND APPROXIMATION BY SIMPLE GAMES

2005 ◽  
Vol 07 (04) ◽  
pp. 491-499 ◽  
Author(s):  
GUILHERME CARMONA
Keyword(s):  
Payoff Function ◽  
Perfect Information ◽  
Perfect Equilibrium ◽  
Simple Games ◽  
Original Game ◽  
Approximation Sequence ◽  
Perfect Equilibria

We show that every bounded, continuous at infinity game of perfect information has an ε–perfect equilibrium. Our method consists of approximating the payoff function of each player by a sequence of simple functions, and to consider the corresponding sequence of games, each differing from the original game only on the payoff function. In addition, this approach yields a new characterization of perfect equilibria: A strategy f is a perfect equilibrium in such a game G if and only if it is an 1/n–perfect equilibrium in Gn for all n, where {Gn} stands for our approximation sequence.

PRIORITY OPTION: THE VALUE OF BEING A LEADER

2013 ◽  
Vol 16 (01) ◽  
pp. 1350004 ◽  
Author(s):  
M. R. GRASSELLI ◽  
V. LECLÈRE ◽  
M. LUDKOVSKI
Keyword(s):  
Market Power ◽  
Incomplete Markets ◽  
Continuous Time ◽  
Strategic Interaction ◽  
Perfect Equilibrium ◽  
Complete Markets ◽  
Utility Indifference ◽  
Uncertain Future ◽  
The Right

We consider the strategic interaction between two firms competing for the opportunity to invest in a project with uncertain future values. Starting in complete markets, we provide a rigorous characterization of the strategies followed by each firm in continuous time in the context of a timing/coordination game. In particular, the roles of leader and follower emerge from the resulting symmetric, Markov, sub-game perfect equilibrium. Comparing the expected value obtained by each firm in this case with that obtained when the roles of leader and follower are predetermined, we are able to calculate the amount of money that a firm would be willing to spend in advance (either by paying a license or acquiring market power) to have the right to be the leader in a subsequent game — what we call the priority option. We extend these results to incomplete markets by using utility-indifference arguments.

scholarly journals On Perfect Nash Equilibria of Polymatrix Games

Game Theory ◽  
2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Slim Belhaiza
Keyword(s):  
Nash Equilibria ◽  
Convex Polytopes ◽  
Finite Union ◽  
Perfect Equilibrium ◽  
Small Game ◽  
Dominated Strategies ◽  
Polymatrix Games ◽  
Linear Programming Formulation ◽  
Perfect Equilibria

When confronted with multiple Nash equilibria, decision makers have to refine their choices. Among all known Nash equilibrium refinements, the perfectness concept is probably the most famous one. It is known that weakly dominated strategies of two-player games cannot be part of a perfect equilibrium. In general, this undominance property however does not extend to n-player games (E. E. C. van Damme, 1983). In this paper we show that polymatrix games, which form a particular class of n-player games, verify the undominance property. Consequently, we prove that every perfect equilibrium of a polymatrix game is undominated and that every undominated equilibrium of a polymatrix game is perfect. This result is used to set a new characterization of perfect Nash equilibria for polymatrix games. We also prove that the set of perfect Nash equilibria of a polymatrix game is a finite union of convex polytopes. In addition, we introduce a linear programming formulation to identify perfect equilibria for polymatrix games. These results are illustrated on two small game applications. Computational experiments on randomly generated polymatrix games with different size and density are provided.

scholarly journals A Procedural Characterization of Solution Concepts in Games

2014 ◽  
Vol 49 ◽  
pp. 143-170 ◽  
Author(s):  
J. Y. Halpern ◽  
Y. Moses
Keyword(s):  
Nash Equilibrium ◽  
Correlated Equilibrium ◽  
Sequential Equilibrium ◽  
Solution Concepts ◽  
Knowledge Based ◽  
Precise Sense ◽  
Uniform Definition ◽  
Game Theoretic ◽  
Theoretic Solution

We show how game-theoretic solution concepts such as Nash equilibrium, correlated equilibrium, rationalizability, and sequential equilibrium can be given a uniform definition in terms of a knowledge-based program with counterfactual semantics. In a precise sense, this program can be viewed as providing a procedural characterization of rationality.

Morphological Characterization of Mycobacteriophage R1

1974 ◽  
Vol 32 ◽  
pp. 254-255
Author(s):  
B. L. Soloff ◽  
T. A. Rado
Keyword(s):  
Carbon Source ◽  
Stationary Phase ◽  
Growth Phase ◽  
Minimal Medium ◽  
Morphological Characterization ◽  
Logarithmic Growth Phase ◽  
Complete Lysis ◽  
Lysogenic Culture ◽  
Logarithmic Growth

Mycobacteriophage R1 was originally isolated from a lysogenic culture of M. butyricum. The virus was propagated on a leucine-requiring derivative of M. smegmatis, 607 leu−, isolated by nitrosoguanidine mutagenesis of typestrain ATCC 607. Growth was accomplished in a minimal medium containing glycerol and glucose as carbon source and enriched by the addition of 80 μg/ ml L-leucine. Bacteria in early logarithmic growth phase were infected with virus at a multiplicity of 5, and incubated with aeration for 8 hours. The partially lysed suspension was diluted 1:10 in growth medium and incubated for a further 8 hours. This permitted stationary phase cells to re-enter logarithmic growth and resulted in complete lysis of the culture.

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