Undominated (and) perfect equilibria in Poisson games

In 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

Three essays on game theory

The 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

Maximum Sustainable Government Debt in the Overlapping Generations Model.

The theoretical determinants of maximum sustainable government debt are investigated using Diamond's overlapping-generations model. A level of debt is defined to be 'sustainable' f a steady state with non-degenerate values of economic variables exists. We show that a maximum sustainable level of debt almost always exists. Most interestingly, it normally occurs at a 'catastrophe' ather than a 'degeneracy' , i.e. where variables such as capital and consumption are in the interiors, rather than at the limits, of their economically meaningful ranges. This means that if debt is increased step by step, the economy may suddenly collapse without obvious warning.GOVERNMENT DEBT ; OVERLAPPING GENERATIONS

Sincere Scoring Rules

Approval Voting is shown to be the unique scoring rule that leads strategic voters to sincere behavior of three candidates elections in Poisson Games. However, Approval Voting can lead to insincere behavior in elections with more than three candidates.Sincerity, Approval Voting, Scoring rules, Poisson Games

When are plurality rule voting games dominance-solvable?

This paper studies the dominance-solvability (by iterated deletion of weakly dominated strategies) of plurality rule voting games. For K > 3 alternatives and n > 3 voters, we find sufficient conditions for the game to be dominance-solvable (DS) and not to be DS. These conditions can be stated in terms of only one statistic of the game, the largest proportion of voters who agree on which alternative is worst in a sequence of subsets of the original set of alternatives. When n is large, “almost all” games can be classified as either DS or not DS. If the game is DS, a Condorcet Winner always exists when n > 4, and the outcome is always the Condorcet Winner when the electorate is sufficiently replicate

Preference Intensity Representation : Strategic Overstating in Large Elections

International audienceIf voters vote strategically, is it useful to offer them the possibility of expressing nuanced opinions, or would they always overstate the intensity of their preferences? For additive voting rules, say that a ballot is extremal if it is neither abstention-like nor can be expressed as a mixture of the available ballots. We give a sufficient condition for strategic equivalence: if two rules share the same set of extremal ballots (up to an homothetic transformation), they are strategically equivalent in large elections. This condition is also necessary for the strategic equivalence of positional rules. These results do not hold for small electorates

Collective Sampling: An Ex Ante Perspective

I study collective dynamic information acquisition. Players determine when to end sequential sampling via a collective choice rule. My analysis focuses on the case of two players, but extends to many players. With two players, collective stopping is determined either unilaterally or unanimously. I develop a methodology to characterize equilibrium outcomes using an ex ante perspective on posterior distributions. Under unilateral stopping, each player chooses a mean-preserving contraction of the other's posterior distribution; under unanimous stopping, they choose meanpreserving spreads. Equilibrium outcomes can be determined via concavification. Players learn Pareto inefficiently: too little under unilateral stopping, while too much under unanimous stopping; these learning inefficiencies are amplified when players' preferences become less aligned. I demonstrate the value of my methodological approach in three applications: committee search, dynamic persuasion, and competition in persuasion

Spectrum Leasing as an Incentive towards Uplink Macrocell and Femtocell Cooperation

The concept of femtocell access points underlaying existing communication infrastructure has recently emerged as a key technology that can significantly improve the coverage and performance of next-generation wireless networks. In this paper, we propose a framework for macrocell-femtocell cooperation under a closed access policy, in which a femtocell user may act as a relay for macrocell users. In return, each cooperative macrocell user grants the femtocell user a fraction of its superframe. We formulate a coalitional game with macrocell and femtocell users being the players, which can take individual and distributed decisions on whether to cooperate or not, while maximizing a utility function that captures the cooperative gains, in terms of throughput and delay.We show that the network can selforganize into a partition composed of disjoint coalitions which constitutes the recursive core of the game representing a key solution concept for coalition formation games in partition form. Simulation results show that the proposed coalition formation algorithm yields significant gains in terms of average rate per macrocell user, reaching up to 239%, relative to the non-cooperative case. Moreover, the proposed approach shows an improvement in terms of femtocell users' rate of up to 21% when compared to the traditional closed access policy.Comment: 29 pages, 11 figures, accepted at the IEEE JSAC on Femtocell Network