This dissertation is a compilation of essays highlighting the usefulness of game theory in understanding socio-economic phenomena. The second chapter tries to provide a reason for the strict codes of conduct that have been imposed on unmarried girls in almost every society at some point of time in its history using tools from classical game theory. If men prefer to marry submissive women, then parents of girls will have an incentive to signal the submissiveness of their daughters in various ways in order to attract better matches. At the same time, parents will find it costlier to signal the submissiveness of girls who are not really submissive. This line of reasoning thus helps us interpret phenomena such as veiling, footbinding, and sequestration of women in general as signals of submissiveness. The third chapter attempts to rationalize some of the ad hoc rules proposed for dividing a bankrupt estate using tools from evolutionary game theory. The ad hoc rules differ from each other because of the axioms that are imposed in addition to efficiency and claims boundedness. Efficiency requires that the estate be completely divided between the claimants, and claims boundedness requires that no claimant be awarded more than her initial contribution. This dissertation tries to show that an ad hoc rule can be rationalized as the unique self-enforcing long run outcome of Young's [46] evolutionary bargaining model by using certain intuitive rules for the Nash demand game. In the fourth chapter I present a simple model of conflict over inputs in an economy with ill-defined property rights. Agents produce output from the land they hold, which in turn can be allocated to consumption or the production of guns. There is no agency to enforce rights over the initial land holdings, and the future holdings of land are determined using a contest success function that depends on the guns produced by both agents. I characterize the equilibria in which only one, both, and none of the agents produce guns, as a function of the total land and the inequality of initial land holdings for general forms of utility, production, cost, and contest success functions.

Many evolutionary game theory papers have obtained their results when the bounded rationality which creates change vanishes. In our first chapter we consider whether such results are actually a good reflection of a population whose bounded rationality is small yet persistent. Our model consists of a two type population with three stable equilibria. Firstly we find that results from the standard vanishing noise approach can be very different from those obtained when noise is small but constant. Secondly when the results differ the small and persistent noise approach selects an equilibrium with a co-existence of conventions. Our second chapter generalises the model of our first chapter to a population of many player types and several stable equilibria. Firstly we produce the characteristics of the long run equilibria under vanishing noise analysis. Secondly we find that the introduction of a small neutral group into a divided society can produce a welfare improving switch in the long run equilibrium towards social co-ordination. Our third chapter combines the model of the second chapter with the message of the first. We show numerically that the long run location of a heterogenous population with extremely low levels of bounded rationality can be completely different to the equilibria selected through vanishing noise analysis. We also show that such an event is not a rare occurrence and find that over a third of populations are misrepresented by stochastic stability. Our final chapter conducts a review of the literature on social threshold models. We give a thorough description of each paper and discuss the main assumptions that drive the key results.

This dissertation consists of three essays related to revision games. The first essay proposes and analyzes a new model that we call “revision games,” which captures a situation where players in advance prepare their actions in a game. After the initial preparation, they have some opportunities to revise their actions, which arrive stochastically. Prepared actions are assumed to be mutually observable. We show that players can achieve a certain level of cooperation. The optimal behavior of players can be described by a simple differential equation. The second essay studies a version of revision games in which revision opportunities are asynchronous across players. In 2-player “common interest” games where there exists a best action profile for all players, this best action profile is the only equilibrium outcome of the revision game. In “opposing interest” games which are 2 x 2 games with Pareto-unranked strict Nash equilibria, the equilibrium outcome of the revision game is generically unique and corresponds to one of the stage-game Nash equilibria. Which equilibrium prevails depends on the payoff structure and on the relative frequency of the arrivals of revision opportunities for each of the players. The third essay studies a multi-agent search problem with a deadline: for instance, the situation that arises when a husband and a wife need to find an apartment by September 1. We provide an understanding of the factors that determine the positive search duration in reality. Specifically, we show that the expected search duration does not shrink to zero even in the limit as the search friction vanishes. Additionally, we find that the limit duration increases as more agents are involved, for two reasons: the ascending acceptability effect and the preference heterogeneity effect. The convergence speed is high, suggesting that the mere existence of some search friction is the main driving force of the positive duration in reality. Welfare implications and a number of discussions are provided. Results and proof techniques developed in the first two essays are useful in proving and understanding the results in the third essay. / Economics

We consider the class of two-player symmetric n x n games with the total bandwagon property (TBP) introduced by Kandori and Rob (1998). We show that a game has TBP if and only if the game has 2^n - 1 symmetric Nash equilibria. We extend this result to bimatrix games by introducing the generalized TBP. This sheds light on the (wrong) conjecture of Quint and Shubik (1997) that any n x n bimatrix game has at most 2^n - 1 Nash equilibria. As for an equilibrium selection criterion, I show the existence of a ½-dominant equilibrium for two subclasses of games with TBP: (i) supermodular games; (ii) potential games. As an application, we consider the minimum-effort game, which does not satisfy TBP, but is a limit case of TBP. (author's abstract) / Series: Department of Economics Working Paper Series

[pt] Este trabalho desenvolve e estabelece a existência de equilíbrio para um modelo sequencial com dois estágios, mercados financeiros incompletos, risco de crédito e colateral endógeno. No primeiro estágio, ao escolherem o colateral, de acordo com uma regra exogenamente determinada, os agentes emitem ativos personalizados que serão transacionados no segundo estágio, em uma economia Walrasiana com dois períodos. A nossa estrutura permite o surgimento de modelos nos quais os próprios agentes escolhem suas garantias, de forma similar aos modelos já existentes de colateral endógeno. Tais modelos exibem o que podemos chamar de A Maldição do Vencedor, situação na qual o agente escolhe, racionalmente, oferecer colateral nulo, inviabilizando, em equilíbrio, a transação de ativos. Com isso, a economia é jogada para um equilíbrio Pareto inferior no qual não existem mercados financeiros. Ao introduzir uma sequencialidade nas escolhas, conseguimos resolver esse problema, pois os agentes antecipam o efeito da escolha de colateral sobre os payoffs de equilíbrio, escolhendo, racionalmente, colaterais positivos. Assim, conseguimos não somente solucionar uma limitação dos modelos existentes, como ainda, permitir o surgimento de inúmeros sub-modelos através das diversas possibilidades para a regra de escolha na determinação do colateral. / [en] This paper develops and establishes the existence of equilibrium for a sequential model with two stages, incomplete financial markets, credit risk and endogenous collateral. In the first stage, by choosing the collateral, according to a predetermined and exogenously given rule, the agents issue personalized securities that will be traded in the second stage in aWalrasian economy with two periods. Our structure allows for models in which the agents choose their own collateral, similar to the existing endogenous collateral models. Those models exhibit what we might call, The Winner s Curse, a situation in which the agent choose, rationally, to offer no collateral, making asset trading impossible, in equilibrium. The economy is then thrown in a Paretoinferior equilibria in which there are no financial markets. By introducing the agent s choice in a sequential fashion, we avoid such a problem, because the agents anticipate the effects of their collateral choice over the equilibrium payoffs, therefore choosing rationally, positive collateral. That way, we are able, not only to solve a shortcoming of the existing models, but also to allow for a variety of sub-models through the several possible choices for the collateral determining rule.