João P. Hespanha
- Published in print:
- 2017
- Published Online:
- May 2018
- ISBN:
- 9780691175218
- eISBN:
- 9781400885442
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691175218.003.0004
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy
This chapter explores the concept of mixed policies and how the notions for pure policies can be adapted to this more general type of policies. A pure policy consists of choices of particular actions ...
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This chapter explores the concept of mixed policies and how the notions for pure policies can be adapted to this more general type of policies. A pure policy consists of choices of particular actions (perhaps based on some observation), whereas a mixed policy involves choosing a probability distribution to select actions (perhaps as a function of observations). The idea behind mixed policies is that the players select their actions randomly according to a previously selected probability distribution. The chapter first considers the rock-paper-scissors game as an example of mixed policy before discussing mixed action spaces, mixed security policy and saddle-point equilibrium, mixed saddle-point equilibrium vs. average security levels, and general zero-sum games. It concludes with practice exercises with corresponding solutions and an additional exercise.Less
This chapter explores the concept of mixed policies and how the notions for pure policies can be adapted to this more general type of policies. A pure policy consists of choices of particular actions (perhaps based on some observation), whereas a mixed policy involves choosing a probability distribution to select actions (perhaps as a function of observations). The idea behind mixed policies is that the players select their actions randomly according to a previously selected probability distribution. The chapter first considers the rock-paper-scissors game as an example of mixed policy before discussing mixed action spaces, mixed security policy and saddle-point equilibrium, mixed saddle-point equilibrium vs. average security levels, and general zero-sum games. It concludes with practice exercises with corresponding solutions and an additional exercise.
Daniel Friedman and Barry Sinervo
- Published in print:
- 2016
- Published Online:
- August 2016
- ISBN:
- 9780199981151
- eISBN:
- 9780190466657
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199981151.001.0001
- Subject:
- Economics and Finance, Behavioural Economics
This book’s goal is to introduce evolutionary game theory to applied researchers in a manner accessible to graduate students and advanced undergraduates in biology, economics, engineering, and allied ...
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This book’s goal is to introduce evolutionary game theory to applied researchers in a manner accessible to graduate students and advanced undergraduates in biology, economics, engineering, and allied disciplines. Chapters 1 through 6 present the basic ideas and techniques of this field, including fitness, replicator dynamics, memes and genes, single- and multiple-population games, Nash equilibrium and evolutionarily stable states, noisy best response and other adaptive processes, the Price equation, cellular automata, and estimating payoff and choice parameters from the data. Chapters 7 through 14 collect exemplary applications from many fields, providing templates for applied work everywhere. These include a new co-evolutionary predator-prey learning model extending the rock-paper-scissors game; using human subject laboratory data to estimate models of learning in games; new approaches to plastic strategies and life cycle strategies, including estimates for male elephant seals; a comparison of machine-learning techniques for preserving diversity to those seen in the natural world; analyses of congestion in traffic networks (either Internet or highways)Less
This book’s goal is to introduce evolutionary game theory to applied researchers in a manner accessible to graduate students and advanced undergraduates in biology, economics, engineering, and allied disciplines. Chapters 1 through 6 present the basic ideas and techniques of this field, including fitness, replicator dynamics, memes and genes, single- and multiple-population games, Nash equilibrium and evolutionarily stable states, noisy best response and other adaptive processes, the Price equation, cellular automata, and estimating payoff and choice parameters from the data. Chapters 7 through 14 collect exemplary applications from many fields, providing templates for applied work everywhere. These include a new co-evolutionary predator-prey learning model extending the rock-paper-scissors game; using human subject laboratory data to estimate models of learning in games; new approaches to plastic strategies and life cycle strategies, including estimates for male elephant seals; a comparison of machine-learning techniques for preserving diversity to those seen in the natural world; analyses of congestion in traffic networks (either Internet or highways)
Daniel Friedman, Barry Sinervo, Daniel Friedman, and Barry Sinervo
- Published in print:
- 2016
- Published Online:
- August 2016
- ISBN:
- 9780199981151
- eISBN:
- 9780190466657
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199981151.003.0002
- Subject:
- Economics and Finance, Behavioural Economics
This chapter takes a first look at strategic interdependence, known to biologists as frequency dependent selection. It distinguishes positive interaction effects (increasing returns or synergy) from ...
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This chapter takes a first look at strategic interdependence, known to biologists as frequency dependent selection. It distinguishes positive interaction effects (increasing returns or synergy) from negative effects (e.g., congestion). The chapter introduces Maynard Smith’s famous Hawk‐Dove game, and goes on to show that there are only two other generic types of 2 × 2 games: dominant strategy (DS), illustrated with biological data on RNA viruses and economic examples drawn from eBay; and coordination (CO) games. Conditions for the prisoner’s dilemma are defined. The remaining sections show how these games represent edges of the state space in games with three alternative strategies. This includes data on male side‐blotched lizards that shows they play the true rock‐paper‐scissors: each edge game has a different dominant strategy, forming an intransitive loop around the 2‐dimensional simplex.Less
This chapter takes a first look at strategic interdependence, known to biologists as frequency dependent selection. It distinguishes positive interaction effects (increasing returns or synergy) from negative effects (e.g., congestion). The chapter introduces Maynard Smith’s famous Hawk‐Dove game, and goes on to show that there are only two other generic types of 2 × 2 games: dominant strategy (DS), illustrated with biological data on RNA viruses and economic examples drawn from eBay; and coordination (CO) games. Conditions for the prisoner’s dilemma are defined. The remaining sections show how these games represent edges of the state space in games with three alternative strategies. This includes data on male side‐blotched lizards that shows they play the true rock‐paper‐scissors: each edge game has a different dominant strategy, forming an intransitive loop around the 2‐dimensional simplex.
Daniel Friedman, Barry Sinervo, Daniel Friedman, and Barry Sinervo
- Published in print:
- 2016
- Published Online:
- August 2016
- ISBN:
- 9780199981151
- eISBN:
- 9780190466657
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199981151.003.0003
- Subject:
- Economics and Finance, Behavioural Economics
This chapter analyzes more complex forms of interaction. Using the rock-paper-scissors game of the European common lizard as an example, it introduces helpful geometric techniques for analyzing 3 × 3 ...
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This chapter analyzes more complex forms of interaction. Using the rock-paper-scissors game of the European common lizard as an example, it introduces helpful geometric techniques for analyzing 3 × 3 and higher dimensional games and shows how to extend them to nonlinear games. The authors then consider two-population games, both the usual “asymmetric” analysis and own-population effects. The chapter also introduces more general dynamics than replicator, including several forms of monotone dynamics. Finally, it explains how to estimate the payoff matrix from time-series data on the side-blotched lizard using maximum likelihood techniques and state-of-the-art multinomial logit and Dirichlet models.Less
This chapter analyzes more complex forms of interaction. Using the rock-paper-scissors game of the European common lizard as an example, it introduces helpful geometric techniques for analyzing 3 × 3 and higher dimensional games and shows how to extend them to nonlinear games. The authors then consider two-population games, both the usual “asymmetric” analysis and own-population effects. The chapter also introduces more general dynamics than replicator, including several forms of monotone dynamics. Finally, it explains how to estimate the payoff matrix from time-series data on the side-blotched lizard using maximum likelihood techniques and state-of-the-art multinomial logit and Dirichlet models.
Daniel Friedman and Barry Sinervo
- Published in print:
- 2016
- Published Online:
- August 2016
- ISBN:
- 9780199981151
- eISBN:
- 9780190466657
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199981151.003.0006
- Subject:
- Economics and Finance, Behavioural Economics
This chapter formalizes spatial strategic interaction as games on grids. It develops cellular automata examples ranging from Conway’s classic Game of Life to complex cooperation, and revisits several ...
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This chapter formalizes spatial strategic interaction as games on grids. It develops cellular automata examples ranging from Conway’s classic Game of Life to complex cooperation, and revisits several earlier examples of assortative and disassortative interactions in an explicit spatial framework. The chapter features simulations of viscous game dynamics with emergent features such as cooperative groups in public goods games, including density and frequency dependent interactions. Two-population versions of the cellular automata are developed (e.g., for the buyer-seller game). Esherichia coli bacteria provide an example of a spatial rock-paper-scissors game: a colicin-producing/colicin-resistant type is beaten by a colicin-resistant type, which is beaten by an undefended type, which is beaten in turn by the first type.Less
This chapter formalizes spatial strategic interaction as games on grids. It develops cellular automata examples ranging from Conway’s classic Game of Life to complex cooperation, and revisits several earlier examples of assortative and disassortative interactions in an explicit spatial framework. The chapter features simulations of viscous game dynamics with emergent features such as cooperative groups in public goods games, including density and frequency dependent interactions. Two-population versions of the cellular automata are developed (e.g., for the buyer-seller game). Esherichia coli bacteria provide an example of a spatial rock-paper-scissors game: a colicin-producing/colicin-resistant type is beaten by a colicin-resistant type, which is beaten by an undefended type, which is beaten in turn by the first type.
Daniel Friedman, Barry Sinervo, Daniel Friedman, and Barry Sinervo
- Published in print:
- 2016
- Published Online:
- August 2016
- ISBN:
- 9780199981151
- eISBN:
- 9780190466657
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199981151.003.0007
- Subject:
- Economics and Finance, Behavioural Economics
This chapter documents general RPS interactions in mating systems for isopods, damselflies, fish, and birds. It applies Hadamard products to show how mate preferences can change one RPS game into ...
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This chapter documents general RPS interactions in mating systems for isopods, damselflies, fish, and birds. It applies Hadamard products to show how mate preferences can change one RPS game into another. Regular RPS cycles in one sex favor invasion of a rule of thumb in the other sex in which common mating types are avoided and rare types are preferred. From such interactions, the one-population true RPS game is converted into an apostatic RPS game. The RPS can also be broken if mates evolve preference for self-mating types, with implications for cooperation and speciation. A new co-evolutionary model describes predator/prey interactions with learning. The model is referred to as ABC-NR after the conspicuous and toxic aposematic model, harmless Batesian mimics, and cryptic types in prey, while predators are either naÏve or responsive to aposematic signals. Fisher’s conjecture of an advantage from prey clustering is required for an interior ESS.Less
This chapter documents general RPS interactions in mating systems for isopods, damselflies, fish, and birds. It applies Hadamard products to show how mate preferences can change one RPS game into another. Regular RPS cycles in one sex favor invasion of a rule of thumb in the other sex in which common mating types are avoided and rare types are preferred. From such interactions, the one-population true RPS game is converted into an apostatic RPS game. The RPS can also be broken if mates evolve preference for self-mating types, with implications for cooperation and speciation. A new co-evolutionary model describes predator/prey interactions with learning. The model is referred to as ABC-NR after the conspicuous and toxic aposematic model, harmless Batesian mimics, and cryptic types in prey, while predators are either naÏve or responsive to aposematic signals. Fisher’s conjecture of an advantage from prey clustering is required for an interior ESS.
