## The evolution of language.
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The emergence of language was a defining moment in the evolution of modern humans. It was an innovation that changed radically the character of human society. Here, we provide an approach to language evolution based on evolutionary game theory. We explore the ways in which protolanguages can evolve in a nonlinguistic society and how specific signals can become associated with specific objects. We assume that early in the evolution of language, errors in signaling and perception would be common. We model the probability of misunderstanding a signal and show that this limits the number of objects that can be described by a protolanguage. This "error limit" is not overcome by employing more sounds but by combining a small set of more easily distinguishable sounds into words. The process of "word formation" enables a language to encode an essentially unlimited number of objects. Next, we analyze how words can be combined into sentences and specify the conditions for the evolution of very simple grammatical rules. We argue that grammar originated as a simplified rule system that evolved by natural selection to reduce mistakes in communication. Our theory provides a systematic approach for thinking about the origin and evolution of human language. (

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## Committee proposals and restrictive rules.
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I analyze a game-theoretic model of committee-legislature interaction in which a majority decision to adopt either an open or closed amendment rule occurs following the committee's proposal of a bill. I find that, in equilibrium, the closed rule is almost always chosen when the dimension of the policy space is >1. Furthermore, the difference between the equilibrium outcome and that which would have occurred under the open rule can be arbitrarily small. (

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## Stochastic game theory: for playing games, not just for doing theory.
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Recent theoretical advances have dramatically increased the relevance of game theory for predicting human behavior in interactive situations. By relaxing the classical assumptions of perfect rationality and perfect foresight, we obtain much improved explanations of initial decisions, dynamic patterns of learning and adjustment, and equilibrium steady-state distributions. (

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## Preplay contracting in the Prisoners' dilemma.
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We consider a modified Prisoners' Dilemma game in which each agent can offer to pay the other agent to cooperate. The subgame perfect equilibrium of this two-stage game is Pareto efficient. We examine experimentally whether subjects actually manage to achieve this efficient outcome. We find an encouraging level of support for the mechanism, but also find some evidence that subjects' tastes for cooperation and equity may have significant interactions with the incentives provided by the mechanism. (

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## Variable investment, the Continuous Prisoner's Dilemma, and the origin of cooperation.
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Cooperation is fundamental to many biological systems. A common metaphor for studying the evolution of cooperation is the Prisoner's Dilemma, a game with two strategies: cooperate or defect. However, cooperation is rare all or nothing, and its evolution probably involves the gradual extension of initially modest degrees of assistance. The inability of the Prisoner's Dilemma to capture this basic aspect limits its use for understanding the evolutionary origins of cooperation. Here we consider a framework for cooperation based on the concept of investment: an act which is costly, but which benefits other individuals, where the cost and benefit depend on the level of investment made. In the resulting Continuous Prisoner's Dilemma the essential problem of cooperation remains: in the absence of any additional structure non-zero levels of investment cannot evolve. However, if investments are considered in a spatially structured context, selfish individuals who make arbitrarily low investments can be invaded by higher-investing mutants. This results in the mean level of investment evolving to significant levels, where it is maintained indefinitely. This approach provides a natural solution to the fundamental problem of how cooperation gradually increases from a non-cooperative state. (

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## Fairness versus reason in the ultimatum game.
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In the Ultimatum Game, two players are offered a chance to win a certain sum of money. All they must do is divide it. The proposer suggests how to split the sum. The responder can accept or reject the deal. If the deal is rejected, neither player gets anything. The rational solution, suggested by game theory, is for the proposer to offer the smallest possible share and for the responder to accept it. If humans play the game, however, the most frequent outcome is a fair share. In this paper, we develop an evolutionary approach to the Ultimatum Game. We show that fairness will evolve if the proposer can obtain some information on what deals the responder has accepted in the past. Hence, the evolution of fairness, similarly to the evolution of cooperation, is linked to reputation. (

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## Special review: game theory to analyse management options in gastro-oesophageal reflux disease.
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This study aims to demonstrate the applicability of linear programming to threshold analysis, using, as an example, patients with new onset of gastro-oesophageal reflux disease (GERD). The choice amongst competing management options is modelled as a decision tree, using threshold analysis, as well as an m x n matrix on an Excel spreadsheet. The different options of medical management correspond to the m rows, whilst the different disease states correspond to the n columns of the matrix. Each number at the intersection of a row and a column represents the outcome associated with that particular combination of management and disease state. The threshold values are calculated by the built-in functions for linear programming of Excel using its Solver tool. Varying the cost estimates in the sensitivity analysis translates into solving a set of different matrices. Threshold analysis provides a formalism to phrase problems of medical decision analysis in a concise fashion. (

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## Fundamental clusters in spatial 2x2 games.
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The notion of fundamental clusters is introduced, serving as a rule of thumb to characterize the statistical properties of the complex behaviour of cellular automata such as spatial 2 x 2 games. They represent the smallest cluster size determining the fate of the entire system. Checking simple growth criteria allows us to decide whether the cluster-individuals, e.g. some mutant family, are capable of surviving and invading a resident population. In biology, spatial 2 x 2 games have a broad spectrum of applications ranging from the evolution of cooperation and intraspecies competition to disease spread. This methodological study allows simple classifications and long-term predictions in various biological and social models to be made. For minimal neighbourhood types, we show that the intuitive candidate, a 3 x 3 cluster, turns out to be fundamental with certain weak limitations for the Moore neighbourhood but not for the Von Neumann neighbourhood. However, in the latter case, 2 x 2 clusters generally serve as reliable indicators to whether a strategy survives. Stochasticity is added to investigate the effects of varying fractions of one strategy present at initialization time and to discuss the rich dynamic properties in greater detail. Finally, we derive Liapunov exponents for the system and show that chaos reigns in a small region where the two strategies coexist in dynamical equilibrium. (

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