619 research outputs found
Three essays on game theory
No full textThe main text of this thesis is divided into three chapters. The three
papers are contributions to the literature on equilibrium refinements in noncooperative
game theory. Each chapter can be read independently of the
rest.
Chapter 2 characterizes the class of finite extensive forms for which the
sets of Subgame Perfect and Sequential equilibrium strategy profiles coincide
for any possible payoff function. In addition, it identifies the class of
finite extensive forms for which the outcomes induced by these two solution
concepts coincide, and study the implications of our results for perfect
Bayesian equilibrium.
Chapter 3 shows that in games with population uncertainty some perfect
equilibria are in dominated strategies. It is proved that every Poisson game
has at least one perfect equilibrium in undominated strategies.
Chapter 4 shows that the set of probability distributions over networks
induced by Nash equilibria of the network formation game proposed by
Myerson (1991) is finite for a generic assignment of payoffs to networks.
The same result can be extended to several variations of the game found in
the literature.
____________________________________________________________________________________________________El texto de esta tesis está dividido en tres capítulos. Cada uno de ellos es
una contribución a la literatura de los refinamientos de equilibrio en juegos
no cooperativos. Cada capítulo se puede leer de manera independiente.
El capítulo 2 caracteriza la clase de formas extensivas finitas para las
que los conjuntos de estrategias de equilibrio para el equilibrio perfecto
en subjuegos y el equilibrio secuencial coinciden para cualquier función
de pagos. Además, identifica la clase de formas extensivas finitas para las
que los conjuntos de resultados derivados de ambos conceptos de equilibrio
coinciden, y estudia las implicaciones que estos resultados tienen en cuanto
al equilibrio perfecto en subjuegos.
El capítulo 3 muestra que en juegos con incertidumbre acerca del número
de jugadores algunos equilibrios perfectos pueden estar dominados y
demostramos que todo juego de Poisson tiene al menos un equilibrio perfecto
en estrategias no dominadas.
El capítulo 4 se demuestra que el conjunto de distribuciones de probabilidad
sobre redes inducidas por equilibrios de Nash del juego de formación
de redes propuesto por Myerson (1991) es finito para toda asignación genérica
de pagos a redes. Este mismo resultado se puede extender a varias
versiones del juego que se pueden encontrar en la literatura
The structure of Nash equilibria in Poisson games
No full textWe show that many results on the structure and stability of equilibria in finite games extend to Poisson games. In particular, the set of Nash equilibria of a Poisson game consists of finitely many connected components and at least one of them contains a stable set (De Sinopoli et al., 2014). In a similar vein, we prove that the number of Nash equilibria in Poisson voting games under plurality, negative plurality, and (when there are at most three candidates) approval rule, as well as in Poisson coordination games, is generically finite. As in finite games, these results are obtained exploiting the geometric structure of the set of Nash equilibria which, in the case of Poisson games, is shown to be semi analytic
COSTLY NETWORK FORMATION AND REGULAR EQUILIBRIA
No full textWe prove that for generic network-formation games where players incur a strictly positive cost to propose links the number of Nash equilibria is finite. Furthermore all Nash equilibria are regular and, therefore, stable sets
Entre fronteras. Presente y pasado del narcotráfico en el corrido mexicano
No full textBook review of Juan Carlos Ramírez Pimienta, Una historia temprana del crimen organizado en los corridos de Ciudad Juárez, ISBN 978-607-536-072-0, México, Universidad Autónoma de Sinaloa / Universidad Autónoma de Chihuahua, 2021, 324 pp.Reseña bibliográfica de Juan Carlos Ramírez Pimienta, Una historia temprana del crimen organizado en los corridos de Ciudad Juárez, ISBN 978-607-536-072-0, México, Universidad Autónoma de Sinaloa / Universidad Autónoma de Chihuahua, 2021, 324 pp
Counterexamples on the Superiority of Approval vs Plurality
No full textWe present a simple voting environment with three candidates where the Condorcet winner exists. Under plurality rule, the derived game has a stable set where such a candidate is elected with probability one. However, no stable set of the approval game elects the Condorcet winner with positive probability. We also analyze the robustness of such an example to changes in the number of voters and their preferences. To conclude, we present a generic four-candidate voting environment with the same properties
Double Round-Robin Tournaments
No full textA tournament is a simultaneous n-player game that is built on a two-player game g. We generalize Arad and Rubinstein’s model assuming that every player meets each of his opponents twice to play a (possibly) asymmetric game g in alternating roles (using sports terminology, once "at home" and once "away"). The winner of the tournament is the player who attains the highest total score, which is given by the sum of the payoffs that he gets in all the matches he plays. We explore the relationship between the equilibria of the tournament and the equilibria of the game g. We prove that limit points of equilibria of tournaments as the number of players goes to infinity are equilibria of g. Such a refinement criterion is satisfied by strict equilibria. Being able to analyze arbitrary two-player games allows us to study meaningful economic applications that are not symmetric, such as the ultimatum game
Undominated (and) Perfect Equilibria in Poisson Games
No full textIn games with population uncertainty some perfect equilibria are in dominated strategies. We prove that every Poisson game has at least one perfect equilibrium in undominated strategies................................................................................................................................................................................................................................
On stable outcomes of approval, plurality, and negative plurality games
No full textWe prove two results on the generic determinacy of Nash equilibrium in voting games. The first one is for negative plurality games. The second one is for approval games under the condition that the number of candidates is equal to three. These results are combined with the analogous one obtained in De Sinopoli (Games Econ Behav 34:270–286, 2001) for plurality rule to show that, for generic utilities, three of the most well-known scoring rules, plurality, negative plurality and approval, induce finite sets of equilibrium outcomes in their corresponding derived games—at least when the number of candidates is equal to three. This is a necessary requirement for the development of a systematic comparison amongst these three voting rules and a useful aid to compute the stable sets of equilibria Mertens (Math Oper Res 14:575–625, 1989) of the induced voting games. To conclude, we provide some examples of voting environments with three candidates where we carry out this comparison
Scoring Rules: A Game-Theoretical Analysis
No full textWe prove two results on the generic determinacy of Nash equilibrium in voting games. The first one is for negative plurality games. The second one is for approval games under the condition that the number of candidates is equal to three. These results are combined with the analogous one obtained in De Sinopoli (2001) for plurality rule to show that, for generic utilities, three of the most well-known scoring rules, plurality, negative plurality and approval, induce finite sets of equilibrium outcomes in their corresponding derived games - at least when the number of candidates is equal to three. This is a necessary requirement for the development of a systematic comparison amongst these three voting rules and a useful aid to compute the stable sets of equilibria (Mertens, 1989) of the induced voting games. To conclude, we provide some examples of voting environments with three candidates where we carry out this comparison
Strategic Stability in Poisson Games
No full textIn Poisson games, an extension of perfect equilibrium based on
perturbations of the strategy space does not guarantee that players use admissible
actions. This observation suggests that such a class of perturbations
is not the correct one. We characterize the right space of perturbations to define
perfect equilibrium in Poisson games. Furthermore, we use such a space
to define the corresponding strategically stable sets of equilibria. We show
that they satisfy existence, admissibility, and iterated deletion of dominated
strategies and inferior replies
- …
