Causal assessment in finite extensive-form games

Two finite extensive-form games are empirically equivalent when theempirical distribution on action profiles generated by every behaviorstrategy in one can also be generated by an appropriately chosen behaviorstrategy in the other. This paper provides a characterization ofempirical equivalence. The central idea is to relate a game's informationstructure to the conditional independencies in the empirical distributionsit generates. We present a new analytical device, the influence opportunitydiagram of a game, describe how such a diagram is constructed for a givenextensive-form game, and demonstrate that it provides a complete summaryof the information needed to test empirical equivalence between two games.

Game theory and reciprocity in some extensive form experimental games

We examine decision making in two-person extensive form game trees using nine treatments that vary matching protocol, payoffs, and payoff information. Our objective is to establish replicable principles of cooperative versus noncooperative behavior that involve the use of signaling, reciprocity, and backward induction strategies, depending on the availability of dominated direct punishing strategies and the probability of repeated interaction with the same partner. Contrary to the predictions of game theory, we find substantial support for cooperation under complete information even in various single-play treatments.

Generalized correlated equilibrium for two-person games in extensive form with perfect information

A correlation scheme (leading to a special equilibrium called “soft” correlated equilibrium) is applied for two-person finite games in extensive form with perfect information. Randomization by an umpire takes place over the leaves of the game tree. At every decision point players have the choice either to follow the recommendation of the umpire blindly or freely choose any other action except the one suggested. This scheme can lead to Pareto-improved outcomes of other correlated equilibria. Computational issues of maximizing a linear function over the set of soft correlated equilibria are considered and a linear-time algorithm in terms of the number of edges in the game tree is given for a special procedure called “subgame perfect optimization”.

On some geometry and equivalence classes of normal form games

Equivalence classes of normal form games are defined using the geometryof correspondences of standard equilibiurm concepts like correlated, Nash,and robust equilibrium or risk dominance and rationalizability. Resultingequivalence classes are fully characterized and compared across differentequilibrium concepts for 2 x 2 games. It is argued that the procedure canlead to broad and game-theoretically meaningful distinctions of games aswell as to alternative ways of viewing and testing equilibrium concepts.Larger games are also briefly considered.

Stochastic evolution of rules for playing normal form games

The evolution of boundedly rational rules for playing normal form games is studied within stationary environments ofstochastically changing games. Rules are viewed as algorithms prescribing strategies for the different normal formgames that arise. It is shown that many of the folk results of evolutionary game theory typically obtained witha fixed game and fixed strategies carry over to the present case. The results are also related to recent experimentson rules and games.

A notion of subgame perfect Nash equilibrium under knightian uncertainty

We define a subgame perfect Nash equilibrium under Knightian uncertainty for two players, by means of a recursive backward induction procedure. We prove an extension of the Zermelo-von Neumann-Kuhn Theorem for games of perfect information, i. e., that the recursive procedure generates a Nash equilibrium under uncertainty (Dow and Werlang(1994)) of the whole game. We apply the notion for two well known games: the chain store and the centipede. On the one hand, we show that subgame perfection under Knightian uncertainty explains the chain store paradox in a one shot version. On the other hand, we show that subgame perfection under uncertainty does not account for the leaving behavior observed in the centipede game. This is in contrast to Dow, Orioli and Werlang(1996) where we explain by means of Nash equilibria under uncertainty (but not subgame perfect) the experiments of McKelvey and Palfrey(1992). Finally, we show that there may be nontrivial subgame perfect equilibria under uncertainty in more complex extensive form games, as in the case of the finitely repeated prisoner's dilemma, which accounts for cooperation in early stages of the game.

A notion of subgame perfect nash equilibrium under knightian uncertainty

We define a subgame perfect Nash equilibrium under Knightian uncertainty for two players, by means of a recursive backward induction procedure. We prove an extension of the Zermelo-von Neumann-Kuhn Theorem for games of perfect information, i. e., that the recursive procedure generates a Nash equilibrium under uncertainty (Dow and Werlang(1994)) of the whole game. We apply the notion for two well known games: the chain store and the centipede. On the one hand, we show that subgame perfection under Knightian uncertainty explains the chain store paradox in a one shot version. On the other hand, we show that subgame perfection under uncertainty does not account for the leaving behavior observed in the centipede game. This is in contrast to Dow, Orioli and Werlang(1996) where we explain by means of Nash equilibria under uncertainty (but not subgame perfect) the experiments of McKelvey and Palfrey(1992). Finally, we show that there may be nontrivial subgame perfect equilibria under uncertainty in more complex extensive form games, as in the case of the finitely repeated prisoner's dilemma, which accounts for cooperation in early stages of the game .

Exact Solution of Bayes and Minimax Change-Detection Problems

The challenge of detecting a change in the distribution of data is a sequential decision problem that is relevant to many engineering solutions, including quality control and machine and process monitoring. This dissertation develops techniques for exact solution of change-detection problems with discrete time and discrete observations. Change-detection problems are classified as Bayes or minimax based on the availability of information on the change-time distribution. A Bayes optimal solution uses prior information about the distribution of the change time to minimize the expected cost, whereas a minimax optimal solution minimizes the cost under the worst-case change-time distribution. Both types of problems are addressed. The most important result of the dissertation is the development of a polynomial-time algorithm for the solution of important classes of Markov Bayes change-detection problems. Existing techniques for epsilon-exact solution of partially observable Markov decision processes have complexity exponential in the number of observation symbols. A new algorithm, called constellation induction, exploits the concavity and Lipschitz continuity of the value function, and has complexity polynomial in the number of observation symbols. It is shown that change-detection problems with a geometric change-time distribution and identically- and independently-distributed observations before and after the change are solvable in polynomial time. Also, change-detection problems on hidden Markov models with a fixed number of recurrent states are solvable in polynomial time. A detailed implementation and analysis of the constellation-induction algorithm are provided. Exact solution methods are also established for several types of minimax change-detection problems. Finite-horizon problems with arbitrary observation distributions are modeled as extensive-form games and solved using linear programs. Infinite-horizon problems with linear penalty for detection delay and identically- and independently-distributed observations can be solved in polynomial time via epsilon-optimal parameterization of a cumulative-sum procedure. Finally, the properties of policies for change-detection problems are described and analyzed. Simple classes of formal languages are shown to be sufficient for epsilon-exact solution of change-detection problems, and methods for finding minimally sized policy representations are described.

An existence result for discontinuous games

We introduce a notion of upper semicontinuity, weak upper semicontinuity, and show that it, together with a weak form of payoff security, is enough to guarantee the existence of Nash equilibria in compact, quasiconcave normal form games. We show that our result generalizes the pure strategy existence theorem of Dasgupta and Maskin (1986) and that it is neither implied nor does it imply the existence theorems of Baye, Tian, and Zhou (1993) and Reny (1999). Furthermore, we show that an equilibrium may fail to exist when, while maintaining weak payoff security, weak upper semicontinuity is weakened to reciprocal upper semicontinuity.

Interactive Epistemology and Reasoning: On the Foundations of Game Theory

Game theory describes and analyzes strategic interaction. It is usually distinguished between static games, which are strategic situations in which the players choose only once as well as simultaneously, and dynamic games, which are strategic situations involving sequential choices. In addition, dynamic games can be further classified according to perfect and imperfect information. Indeed, a dynamic game is said to exhibit perfect information, whenever at any point of the game every player has full informational access to all choices that have been conducted so far. However, in the case of imperfect information some players are not fully informed about some choices. Game-theoretic analysis proceeds in two steps. Firstly, games are modelled by so-called form structures which extract and formalize the significant parts of the underlying strategic interaction. The basic and most commonly used models of games are the normal form, which rather sparsely describes a game merely in terms of the players' strategy sets and utilities, and the extensive form, which models a game in a more detailed way as a tree. In fact, it is standard to formalize static games with the normal form and dynamic games with the extensive form. Secondly, solution concepts are developed to solve models of games in the sense of identifying the choices that should be taken by rational players. Indeed, the ultimate objective of the classical approach to game theory, which is of normative character, is the development of a solution concept that is capable of identifying a unique choice for every player in an arbitrary game. However, given the large variety of games, it is not at all certain whether it is possible to device a solution concept with such universal capability. Alternatively, interactive epistemology provides an epistemic approach to game theory of descriptive character. This rather recent discipline analyzes the relation between knowledge, belief and choice of game-playing agents in an epistemic framework. The description of the players' choices in a given game relative to various epistemic assumptions constitutes the fundamental problem addressed by an epistemic approach to game theory. In a general sense, the objective of interactive epistemology consists in characterizing existing game-theoretic solution concepts in terms of epistemic assumptions as well as in proposing novel solution concepts by studying the game-theoretic implications of refined or new epistemic hypotheses. Intuitively, an epistemic model of a game can be interpreted as representing the reasoning of the players. Indeed, before making a decision in a game, the players reason about the game and their respective opponents, given their knowledge and beliefs. Precisely these epistemic mental states on which players base their decisions are explicitly expressible in an epistemic framework. In this PhD thesis, we consider an epistemic approach to game theory from a foundational point of view. In Chapter 1, basic game-theoretic notions as well as Aumann's epistemic framework for games are expounded and illustrated. Also, Aumann's sufficient conditions for backward induction are presented and his conceptual views discussed. In Chapter 2, Aumann's interactive epistemology is conceptually analyzed. In Chapter 3, which is based on joint work with Conrad Heilmann, a three-stage account for dynamic games is introduced and a type-based epistemic model is extended with a notion of agent connectedness. Then, sufficient conditions for backward induction are derived. In Chapter 4, which is based on joint work with Jérémie Cabessa, a topological approach to interactive epistemology is initiated. In particular, the epistemic-topological operator limit knowledge is defined and some implications for games considered. In Chapter 5, which is based on joint work with Jérémie Cabessa and Andrés Perea, Aumann's impossibility theorem on agreeing to disagree is revisited and weakened in the sense that possible contexts are provided in which agents can indeed agree to disagree.

Cutaneous Collagenous Vasculopathy: A Rare Form of Microangiopathy Successfully Treated with a Combination of Multiplex Laser and Optimized Pulsed Light with a Review of the Literature.

Cutaneous collagenous vasculopathy (CCV) is a rare idiopathic microangiopathy of the cutaneous vasculature characterized histologically by the presence of dilated small blood vessels with flat endothelial cells and thickened walls containing hyaline material in the upper dermis. We report an elderly patient presenting with an extensive form of CCV involving the trunk, upper and lower limbs. She was treated with Multiplex PDL 595-nm/Nd:YAG 1,064-nm laser and optimized pulsed light. This approach, which has never been reported for CCV so far, resulted in a striking and almost complete clearance of the widespread lesions. We here review our knowledge about CCV and therapeutic options available with a survey of the literature.

APLICAÇÃO DA TEORIA DOS JOGOS NA GESTÃO DE PESSOAS: UMA ANÁLISE DA VARIÁVEL SALÁRIO

Esta dissertação apresenta os principais aspectos da Teoria dos Jogos, mostrando sua aplicação como instrumento analítico na Gestão de Pessoas no que diz respeito à variável salário. Considera a organização e o trabalhador como conceitos gerais, sem identificar o setor de atuação, ramo de atividade, classificação jurídica em função do seu faturamento, total de empregados ou participação de mercado dessa organização. Da mesma forma o conceito trabalhador não recebe qualquer identificação em relação ao setor de atividade onde trabalha, função, salário ou formação profissional. A organização é toda estrutura que gera bens e serviços para a sociedade e o trabalhador é todo elemento que emprega sua força de trabalho na produção de bens e serviços. Os objetivos estabelecidos para este estudo são: identificar as possibilidades de aplicação da Teoria dos Jogos na Gestão de Pessoas considerando a variável salário como elemento de conflito entre a organização e o trabalhador; mostrar se a forma de representação extensiva é mais apropriada ou não para analisar o cenário de embate na decisão de contratar ou não o trabalhador ou pagar mais ou menos salário e a existência do Equilíbrio de Nash. A metodologia qualitativa com apoio bibliográfico e documental caracteriza esta pesquisa qualitativa quanto a metodologia de pesquisa. Os métodos qualitativos contribuem para interpretar fenômenos do cotidiano, podendo ser composto por dados simbólicos situados em determinado contexto. A pesquisa documental é uma contribuição importante ao estudo do tema proposto, já que a pesquisa qualitativa não é uma proposta rigidamente estruturada e isto permite que o pesquisador use a imaginação e criatividade para atingir o objetivo. Os resultados obtidos pela pesquisa dão conta de que é possível a aplicação da Teoria dos Jogos na Gestão de Pessoas considerando o embate entre os jogadores (o trabalhador e a organização) em torno do salário, discutido no capítulo 4 nas representações da matriz de payoff de um jogo estratégico e nas figuras 9,10,11,e 16. A representação na forma extensiva, outro objetivo, indicando os payoffs entre duas decisões centrais representadas por X = flexibilização com renúncia dos direitos pelos trabalhadores e Y = flexibilização/adaptação/negociação, conforme figura 16. O gestor de pessoas percebe as estratégias existentes para a organização e trabalhador para a tomada de decisão, ao mesmo tempo em que pode avaliar a situação que esteja vivendo e fazer simulações em busca de novas propostas. Por fim, o Equilíbrio de Nash para a aplicação na Gestão de Pessoas é discutido no item 4.1.3, sendo possível verificar que tanto o trabalhador como a organização podem chegar a uma decisão favorável para ambos e manter seus objetivos pretendidos inicialmente. Na figura 17, esse equilíbrio é apresentado depois da tomada de decisão do trabalhador pela proposta feita pela organização na sequência O2 e o trabalhador ficou com o ramo de sequência T2 com o valor de 20 moedas. A potencialidade da Teoria dos Jogos na Gestão de Pessoas está no fato de que quem atua em uma organização compartilha resultados bons ou ruins obtidos pelas escolhas alheias, individuais e construídas coletivamente.

APLICAÇÃO DA TEORIA DOS JOGOS NA GESTÃO DE PESSOAS: UMA ANÁLISE DA VARIÁVEL SALÁRIO

Esta dissertação apresenta os principais aspectos da Teoria dos Jogos, mostrando sua aplicação como instrumento analítico na Gestão de Pessoas no que diz respeito à variável salário. Considera a organização e o trabalhador como conceitos gerais, sem identificar o setor de atuação, ramo de atividade, classificação jurídica em função do seu faturamento, total de empregados ou participação de mercado dessa organização. Da mesma forma o conceito trabalhador não recebe qualquer identificação em relação ao setor de atividade onde trabalha, função, salário ou formação profissional. A organização é toda estrutura que gera bens e serviços para a sociedade e o trabalhador é todo elemento que emprega sua força de trabalho na produção de bens e serviços. Os objetivos estabelecidos para este estudo são: identificar as possibilidades de aplicação da Teoria dos Jogos na Gestão de Pessoas considerando a variável salário como elemento de conflito entre a organização e o trabalhador; mostrar se a forma de representação extensiva é mais apropriada ou não para analisar o cenário de embate na decisão de contratar ou não o trabalhador ou pagar mais ou menos salário e a existência do Equilíbrio de Nash. A metodologia qualitativa com apoio bibliográfico e documental caracteriza esta pesquisa qualitativa quanto a metodologia de pesquisa. Os métodos qualitativos contribuem para interpretar fenômenos do cotidiano, podendo ser composto por dados simbólicos situados em determinado contexto. A pesquisa documental é uma contribuição importante ao estudo do tema proposto, já que a pesquisa qualitativa não é uma proposta rigidamente estruturada e isto permite que o pesquisador use a imaginação e criatividade para atingir o objetivo. Os resultados obtidos pela pesquisa dão conta de que é possível a aplicação da Teoria dos Jogos na Gestão de Pessoas considerando o embate entre os jogadores (o trabalhador e a organização) em torno do salário, conforme pode ser visto no capítulo 4 nas representações da matriz de payoff de um jogo estratégico e nas figuras 9,10,11,e 16. A representação na forma extensiva, constitui outro objetivo, indicando os payoffs entre duas decisões centrais representadas por X = flexibilização com renúncia dos direitos pelos trabalhadores e Y = flexibilização/adaptação/negociação, conforme figura 16. Ao analisar a figura, o gestor de pessoas percebe as estratégias existentes para a organização e trabalhador para a tomada de decisão, ao mesmo tempo em que pode avaliar a situação que esteja vivendo e fazer simulações em busca de novas propostas. Por fim, o Equilíbrio de Nash para a aplicação na Gestão de Pessoas é discutido no item 4.1.3, sendo possível verificar que tanto o trabalhador como a organização podem chegar a uma decisão favorável para ambos e manter seus objetivos pretendidos inicialmente. Na figura 17, esse equilíbrio é apresentado depois da tomada de decisão do trabalhador pela proposta feita pela organização na sequência O2 e o trabalhador ficou com o ramo de sequência T2 com o valor de 20 moedas. A potencialidade da Teoria dos Jogos na Gestão de Pessoas surge do fato de que quem atua em uma organização compartilha resultados bons ou ruins obtidos pelas escolhas alheias, escolhas individuais e pelas escolhas construídas coletivamente. Quando o trabalhador resolve produzir menos, a empresa sofre com a perda do lucro gerado pelo ritmo mais lento de trabalho. Para mudar esse quadro, a empresa toma a decisão de aumentar o salário e o trabalhador por sua vez desenvolve a tarefa com maior velocidade e em maior quantidade e ela pode retomar o seu lucro. Nesses jogos há cobranças de desempenho, exigência para atingir metas, pressões, conflitos com clientes e lideranças. Logo, a Teoria dos Jogos pode ser aplicada como instrumento para o gestor de Pessoas avaliar a situação vivida para a tomada de decisão que resolva a situação de embate.

Ex post bargaining, labor coordination and wage formation at the firm level

We lay out a model of wage bargaining with two leading features:bargaining is ex post to relevant investments and there isindividual bargaining in firms without a Union. We compareindividual ex post bargaining to coordinated ex post bargainingand we analyze the effects on wage formation. As opposed to exante bargaining models, the costs of destroying the employmentrelationship play a crucial role in determining wages. Highfiring costs in particular yield a rent for employees. Ourtheory points to a employer size-wage effect that is independentof the production function and market power. We derive a simpleleast squares specification from the theoretical model thatallow us to estimate components of the wage premium fromcoordination. We reject the hypothesis that labor coordinationdoes not alter the extensive form of the bargaining game. Laborcoordination substantially increases bargaining power butdecreases labor's ability to pose costly threats to the firm.

On forward induction and evolutionary and strategic stability

We analyze which normal form solution concepts capture the notion offorward induction, as defined by van Damme (JET, 1989) in the classof generic two player normal form games preceded by an outsideoption. We find that none of the known strategic stability concepts(including Mertens stable sets and hyperstable sets) captures this form of forward induction. On the other hand, we show that the evolutionary concept of EES set (Swinkels, JET, 1992) is always consistent with forward induction.