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1 Un « fait frappant »… « The most striking fact about the relationship between evolutionary game theory and economic game theory is that, at the most basic level, a theory built of hyperrational actors and a theory built of possibly non- rational actors are in fundamental agreement. This fact has been widely noticed, and its importance can hardly be overestimated » (Skyrms 2000, p. 273) « The most striking fact about the relationship between evolutionary game theory and economic game theory is that, at the most basic level, a theory built of hyperrational actors and a theory built of possibly non- rational actors are in fundamental agreement. This fact has been widely noticed, and its importance can hardly be overestimated » (Skyrms 2000, p. 273)

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2 Rationality & Evolution 1 Two Optimizing Processes 2 Isomorphism 2.1 Sex and Fairness 2.1.1 Rationality as (economic) game theory 2.2 Evolution as evolutionary game theory 2.2.1 Biological evolutionary game theory 2.2.2 Economic evolutionary game theory 2.3 Evolutionary Generalism 2.4 Why isomorphism is important 3 Differences 3.1 Symmetry 3.2 Dominated Strategies 3.3 Actual Fitness and Intended Outcomes 4 Simulations and multi-level models 4.1 Axelrod 4.2 A methodology: Multi-level modeling 4.3 Computational Differences 5 Normativity 5.1 Normative Rationality vs. Descriptive Evolution 5.2 What are the prospects for convergence? 1 Two Optimizing Processes 2 Isomorphism 2.1 Sex and Fairness 2.1.1 Rationality as (economic) game theory 2.2 Evolution as evolutionary game theory 2.2.1 Biological evolutionary game theory 2.2.2 Economic evolutionary game theory 2.3 Evolutionary Generalism 2.4 Why isomorphism is important 3 Differences 3.1 Symmetry 3.2 Dominated Strategies 3.3 Actual Fitness and Intended Outcomes 4 Simulations and multi-level models 4.1 Axelrod 4.2 A methodology: Multi-level modeling 4.3 Computational Differences 5 Normativity 5.1 Normative Rationality vs. Descriptive Evolution 5.2 What are the prospects for convergence?

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3 Rationality & Evolution 1 Two Optimizing Processes 2 Isomorphism 2.1 Sex and Fairness 2.1.1 Rationality as (economic) game theory 2.2 Evolution as evolutionary game theory 2.2.1 Biological evolutionary game theory 2.2.2 Economic evolutionary game theory 2.3 Evolutionary Generalism 2.4 Why isomorphism is important 3 Differences 3.1 Symmetry 3.2 Dominated Strategies 3.3 Actual Fitness and Intended Outcomes 4 Simulations and multi-level models 4.1 Axelrod 4.2 A methodology: Multi-level modeling 4.3 Computational Differences 5 Normativity 5.1 Normative Rationality vs. Descriptive Evolution 5.2 What are the prospects for convergence? 1 Two Optimizing Processes 2 Isomorphism 2.1 Sex and Fairness 2.1.1 Rationality as (economic) game theory 2.2 Evolution as evolutionary game theory 2.2.1 Biological evolutionary game theory 2.2.2 Economic evolutionary game theory 2.3 Evolutionary Generalism 2.4 Why isomorphism is important 3 Differences 3.1 Symmetry 3.2 Dominated Strategies 3.3 Actual Fitness and Intended Outcomes 4 Simulations and multi-level models 4.1 Axelrod 4.2 A methodology: Multi-level modeling 4.3 Computational Differences 5 Normativity 5.1 Normative Rationality vs. Descriptive Evolution 5.2 What are the prospects for convergence?

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4 « All that the evolution-hypothesis tells us is that certain kinds of conduct are more evolved than others; […]. Yet [Mr. Spencer] tells us that one of the things he has proved is that conduct gains ethical sanction in proportion as it displays certain characteristics. What he has tried to prove is only that in proportion as it displays those characteristics, it is more evolved, it is plain, then, that Mr. Spencer identifies the gaining of ethical sanction with the being more evolved. » Moore, Principia Ethica, pp. 48-4. « All that the evolution-hypothesis tells us is that certain kinds of conduct are more evolved than others; […]. Yet [Mr. Spencer] tells us that one of the things he has proved is that conduct gains ethical sanction in proportion as it displays certain characteristics. What he has tried to prove is only that in proportion as it displays those characteristics, it is more evolved, it is plain, then, that Mr. Spencer identifies the gaining of ethical sanction with the being more evolved. » Moore, Principia Ethica, pp. 48-4. Le « sophisme naturaliste »

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5 Lheuristique de la personnalisation permet déchapper au sophisme naturaliste… « If natural selection controls which of traits T, A1, A2,…, An, evolves in a given population, then T will evolve, rather than the alternatives listed, if and only if a rational agent who wanted to maximize fitness would choose T over A1, A2,…, An » (Sober 1998, pp. 408f.) « Rational choice only gets value out by optimizing the value input captured by the agents preferences. Conversely, what evolution optimizes is only a value if reproductive fitness is valued. » (p. 3) « If natural selection controls which of traits T, A1, A2,…, An, evolves in a given population, then T will evolve, rather than the alternatives listed, if and only if a rational agent who wanted to maximize fitness would choose T over A1, A2,…, An » (Sober 1998, pp. 408f.) « Rational choice only gets value out by optimizing the value input captured by the agents preferences. Conversely, what evolution optimizes is only a value if reproductive fitness is valued. » (p. 3)

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6 Fitness individuelle vs. fitness collective « And as natural selection works solely by and for the good of each being, all corporeal and mental endowments will tend to progress towards perfection » (Darwin 1859,p. 489) « The economists of Darwins time tended to think that since a society is nothing but a collection of individuals, the society will maximize its well-being if each individual endeavors to maximize his welfare. … » (Sober 1984) « And as natural selection works solely by and for the good of each being, all corporeal and mental endowments will tend to progress towards perfection » (Darwin 1859,p. 489) « The economists of Darwins time tended to think that since a society is nothing but a collection of individuals, the society will maximize its well-being if each individual endeavors to maximize his welfare. … » (Sober 1984)

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7 Dépendance envers la fréquence: la tragédie du pré communal « [T]he rational herdsman concludes that the only sensible course for him to pursue is to add another animal to his herd. And another.... But this is the conclusion reached by each and every rational herdsman sharing a commons. Therein is the tragedy. Each man is locked into a system that compels him to increase his herd without limit -- in a world that is limited. Ruin is the destination toward which all men rush, each pursuing his own best interest in a society that believes in the freedom of the commons. Freedom in a commons brings ruin to all. » Garrett Hardin, Science, 162(1968):1243-1248. « [T]he rational herdsman concludes that the only sensible course for him to pursue is to add another animal to his herd. And another.... But this is the conclusion reached by each and every rational herdsman sharing a commons. Therein is the tragedy. Each man is locked into a system that compels him to increase his herd without limit -- in a world that is limited. Ruin is the destination toward which all men rush, each pursuing his own best interest in a society that believes in the freedom of the commons. Freedom in a commons brings ruin to all. » Garrett Hardin, Science, 162(1968):1243-1248.

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8 By the way, cest exactement ce qui est arrivé à nos morues…

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9 Lévolution optimise quand même la rationnalité… « While grazers and fishers welfare will not be maximized by evolution in a commons, their rationality should be. Rationality, after all, is the perfection of just those abilities useful for exploiting any situation, including social dilemmas. » (p. 4) « While grazers and fishers welfare will not be maximized by evolution in a commons, their rationality should be. Rationality, after all, is the perfection of just those abilities useful for exploiting any situation, including social dilemmas. » (p. 4)

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10 Le « rationalisme évolutionniste » « Creatures inveterately wrong in their inductions have a pathetic but praise-worthy tendency to die before reproducing their kind. » (Quine 1969) « Natural selection guarantees that most of an organism's beliefs will be true, most of its strategies rational » (Dennett 1987) « Creatures inveterately wrong in their inductions have a pathetic but praise-worthy tendency to die before reproducing their kind. » (Quine 1969) « Natural selection guarantees that most of an organism's beliefs will be true, most of its strategies rational » (Dennett 1987)

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11 Rationality & Evolution 1 Two Optimizing Processes 2 Isomorphism 2.1 Sex and Fairness 2.1.1 Rationality as (economic) game theory 2.2 Evolution as evolutionary game theory 2.2.1 Biological evolutionary game theory 2.2.2 Economic evolutionary game theory 2.3 Evolutionary Generalism 2.4 Why isomorphism is important 3 Differences 3.1 Symmetry 3.2 Dominated Strategies 3.3 Actual Fitness and Intended Outcomes 4 Simulations and multi-level models 4.1 Axelrod 4.2 A methodology: Multi-level modeling 4.3 Computational Differences 5 Normativity 5.1 Normative Rationality vs. Descriptive Evolution 5.2 What are the prospects for convergence? 1 Two Optimizing Processes 2 Isomorphism 2.1 Sex and Fairness 2.1.1 Rationality as (economic) game theory 2.2 Evolution as evolutionary game theory 2.2.1 Biological evolutionary game theory 2.2.2 Economic evolutionary game theory 2.3 Evolutionary Generalism 2.4 Why isomorphism is important 3 Differences 3.1 Symmetry 3.2 Dominated Strategies 3.3 Actual Fitness and Intended Outcomes 4 Simulations and multi-level models 4.1 Axelrod 4.2 A methodology: Multi-level modeling 4.3 Computational Differences 5 Normativity 5.1 Normative Rationality vs. Descriptive Evolution 5.2 What are the prospects for convergence?

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12 Le problème de légalité (numérique) des sexes « [G]enerally females are the scarcity constraint on reproduction, so we should expect fewer males in an optimum sex mix. » (p. 5) « I formerly thought that when a tendency to produce the two sexes in equal numbers was advantageous to the species, it would follow from natural selection, but I now see that the whole problem is so intricate that it is safer to leave its solution for the future » (Darwin 1871) « [G]enerally females are the scarcity constraint on reproduction, so we should expect fewer males in an optimum sex mix. » (p. 5) « I formerly thought that when a tendency to produce the two sexes in equal numbers was advantageous to the species, it would follow from natural selection, but I now see that the whole problem is so intricate that it is safer to leave its solution for the future » (Darwin 1871)

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14 Problème parallèle : séparer le gâteau On sait que, pour être juste, il faut séparer le gâteau 50-50, mais la théorie des jeux ne nous dit pas pourquoi. Équilibre de Nash: « We have an equilibrium in informed rational self-interest if each of our claims are optimal given the others claim. In other words, given my claim you could not do better by changing yours and given your claim I could do no better by changing mine. » (Skyrm 1996, p. 5) On sait que, pour être juste, il faut séparer le gâteau 50-50, mais la théorie des jeux ne nous dit pas pourquoi. Équilibre de Nash: « We have an equilibrium in informed rational self-interest if each of our claims are optimal given the others claim. In other words, given my claim you could not do better by changing yours and given your claim I could do no better by changing mine. » (Skyrm 1996, p. 5)

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15 Problème: il y a une infinité déquilibres de Nash 0 0 0 1 1 1 1 Demande A Demande B

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16 Est-ce que cest moi qui ne comprend pas? « Skyrms argues that rational choice cannot answer this basic question about fairness » (p. 6) « Skyrms argues that rational choice cannot answer this basic question about fairness » (p. 6) Stratégie (demande x) Utilité attendue

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17 Payoffs par stratégie, en termes de reproductive fitness Demande 1/3 Demande 1/2 Demande 2/3 Modeste Demande 1/3 1/3 Impartial Demande 1/2 1/2 0 Cupide Demande 2/3 2/300

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18 Fitness attendues, avec distribution égale des stratégies Demande 1/3 Demande 1/2 Demande 2/3 Fitness attendue Modeste Demande 1/3 1/3 Impartial Demande 1/2 1/2 01/3 Cupide Demande 2/3 2/3002/9

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19 Fitness attendues, une fois que les cupides sont disparus Demande 1/3 Demande 1/2 Demande 2/3 Fitness attendue Modeste Demande 1/3 1/3 Impartial Demande 1/2 1/2 Cupide Demande 2/3 SES

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20 Une version en automate cellulaire http://www.ags.uci.edu/~jalex/lattice-models/

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21 Dynamique de légalité Demande 1/3 Demande 2/3 Demande 1/2

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22 Cest la même chose pour le sex ratio (Fisher 1930, p. 142)

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23 Rationality & Evolution 1 Two Optimizing Processes 2 Isomorphism 2.1 Sex and Fairness 2.1.1 Rationality as (economic) game theory 2.2 Evolution as evolutionary game theory 2.2.1 Biological evolutionary game theory 2.2.2 Economic evolutionary game theory 2.3 Evolutionary Generalism 2.4 Why isomorphism is important 3 Differences 3.1 Symmetry 3.2 Dominated Strategies 3.3 Actual Fitness and Intended Outcomes 4 Simulations and multi-level models 4.1 Axelrod 4.2 A methodology: Multi-level modeling 4.3 Computational Differences 5 Normativity 5.1 Normative Rationality vs. Descriptive Evolution 5.2 What are the prospects for convergence? 1 Two Optimizing Processes 2 Isomorphism 2.1 Sex and Fairness 2.1.1 Rationality as (economic) game theory 2.2 Evolution as evolutionary game theory 2.2.1 Biological evolutionary game theory 2.2.2 Economic evolutionary game theory 2.3 Evolutionary Generalism 2.4 Why isomorphism is important 3 Differences 3.1 Symmetry 3.2 Dominated Strategies 3.3 Actual Fitness and Intended Outcomes 4 Simulations and multi-level models 4.1 Axelrod 4.2 A methodology: Multi-level modeling 4.3 Computational Differences 5 Normativity 5.1 Normative Rationality vs. Descriptive Evolution 5.2 What are the prospects for convergence?

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24 Rationality as (economic) game theory « Evolution is only isomorphic to rationality if we restrict the range of both concepts. » (p. 8) Danielson choisi de se limiter à la rationalité dans les interactions, qui est le problème le plus complexe de la rationalité. « Evolution is only isomorphic to rationality if we restrict the range of both concepts. » (p. 8) Danielson choisi de se limiter à la rationalité dans les interactions, qui est le problème le plus complexe de la rationalité.

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25 Rationality & Evolution 1 Two Optimizing Processes 2 Isomorphism 2.1 Sex and Fairness 2.1.1 Rationality as (economic) game theory 2.2 Evolution as evolutionary game theory 2.2.1 Biological evolutionary game theory 2.2.2 Economic evolutionary game theory 2.3 Evolutionary Generalism 2.4 Why isomorphism is important 3 Differences 3.1 Symmetry 3.2 Dominated Strategies 3.3 Actual Fitness and Intended Outcomes 4 Simulations and multi-level models 4.1 Axelrod 4.2 A methodology: Multi-level modeling 4.3 Computational Differences 5 Normativity 5.1 Normative Rationality vs. Descriptive Evolution 5.2 What are the prospects for convergence? 1 Two Optimizing Processes 2 Isomorphism 2.1 Sex and Fairness 2.1.1 Rationality as (economic) game theory 2.2 Evolution as evolutionary game theory 2.2.1 Biological evolutionary game theory 2.2.2 Economic evolutionary game theory 2.3 Evolutionary Generalism 2.4 Why isomorphism is important 3 Differences 3.1 Symmetry 3.2 Dominated Strategies 3.3 Actual Fitness and Intended Outcomes 4 Simulations and multi-level models 4.1 Axelrod 4.2 A methodology: Multi-level modeling 4.3 Computational Differences 5 Normativity 5.1 Normative Rationality vs. Descriptive Evolution 5.2 What are the prospects for convergence?

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26 La théorie des jeux sapplique mieux à la biologie quà léconomie… « There are two reasons for this. –First, the theory requires that the values of different outcomes […] be measured on a single scale. In human application, this measure is provided by utility – a somewhat artificial and uncomfortable concept: in biology, Darwinian fitness provides a natural and genuinely one- dimensional scale […]. –Secondly, and more importantly, in seeking the solution of a game, the concept of human rationality is replaced by that of evolutionarily stability. The advantage here is that there are good theoretical reasons to expect populations to evolve to stable states, whereas there are grounds for doubting whether human beings always behave rationally. » (Maynard Smith 1982, p. vii). « There are two reasons for this. –First, the theory requires that the values of different outcomes […] be measured on a single scale. In human application, this measure is provided by utility – a somewhat artificial and uncomfortable concept: in biology, Darwinian fitness provides a natural and genuinely one- dimensional scale […]. –Secondly, and more importantly, in seeking the solution of a game, the concept of human rationality is replaced by that of evolutionarily stability. The advantage here is that there are good theoretical reasons to expect populations to evolve to stable states, whereas there are grounds for doubting whether human beings always behave rationally. » (Maynard Smith 1982, p. vii).

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27 Rationality & Evolution 1 Two Optimizing Processes 2 Isomorphism 2.1 Sex and Fairness 2.1.1 Rationality as (economic) game theory 2.2 Evolution as evolutionary game theory 2.2.1 Biological evolutionary game theory 2.2.2 Economic evolutionary game theory 2.3 Evolutionary Generalism 2.4 Why isomorphism is important 3 Differences 3.1 Symmetry 3.2 Dominated Strategies 3.3 Actual Fitness and Intended Outcomes 4 Simulations and multi-level models 4.1 Axelrod 4.2 A methodology: Multi-level modeling 4.3 Computational Differences 5 Normativity 5.1 Normative Rationality vs. Descriptive Evolution 5.2 What are the prospects for convergence? 1 Two Optimizing Processes 2 Isomorphism 2.1 Sex and Fairness 2.1.1 Rationality as (economic) game theory 2.2 Evolution as evolutionary game theory 2.2.1 Biological evolutionary game theory 2.2.2 Economic evolutionary game theory 2.3 Evolutionary Generalism 2.4 Why isomorphism is important 3 Differences 3.1 Symmetry 3.2 Dominated Strategies 3.3 Actual Fitness and Intended Outcomes 4 Simulations and multi-level models 4.1 Axelrod 4.2 A methodology: Multi-level modeling 4.3 Computational Differences 5 Normativity 5.1 Normative Rationality vs. Descriptive Evolution 5.2 What are the prospects for convergence?

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28 Quest-ce quune SES? « It is a strategy such that, if most of the members of a population adopt it, there is no mutant strategy that would give higher reproductive fitness » (Maynard Smith & Price 1973, p. 15) « For distinct strategies x and y and utility function u, 1)u(x,x) u(y,x) 2)If u(x,x) = u(y,x) then u(x,y) > u(y,y) » (p. 10) « It is a strategy such that, if most of the members of a population adopt it, there is no mutant strategy that would give higher reproductive fitness » (Maynard Smith & Price 1973, p. 15) « For distinct strategies x and y and utility function u, 1)u(x,x) u(y,x) 2)If u(x,x) = u(y,x) then u(x,y) > u(y,y) » (p. 10)

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29 Rationality & Evolution 1 Two Optimizing Processes 2 Isomorphism 2.1 Sex and Fairness 2.1.1 Rationality as (economic) game theory 2.2 Evolution as evolutionary game theory 2.2.1 Biological evolutionary game theory 2.2.2 Economic evolutionary game theory 2.3 Evolutionary Generalism 2.4 Why isomorphism is important 3 Differences 3.1 Symmetry 3.2 Dominated Strategies 3.3 Actual Fitness and Intended Outcomes 4 Simulations and multi-level models 4.1 Axelrod 4.2 A methodology: Multi-level modeling 4.3 Computational Differences 5 Normativity 5.1 Normative Rationality vs. Descriptive Evolution 5.2 What are the prospects for convergence? 1 Two Optimizing Processes 2 Isomorphism 2.1 Sex and Fairness 2.1.1 Rationality as (economic) game theory 2.2 Evolution as evolutionary game theory 2.2.1 Biological evolutionary game theory 2.2.2 Economic evolutionary game theory 2.3 Evolutionary Generalism 2.4 Why isomorphism is important 3 Differences 3.1 Symmetry 3.2 Dominated Strategies 3.3 Actual Fitness and Intended Outcomes 4 Simulations and multi-level models 4.1 Axelrod 4.2 A methodology: Multi-level modeling 4.3 Computational Differences 5 Normativity 5.1 Normative Rationality vs. Descriptive Evolution 5.2 What are the prospects for convergence?

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30 Economic evolutionary game theory « Where biological evolutionary game theory is intentionally broad in the scope of its agents, economic evolutionary game theory focuses more narrowly on explaining human action. [E]conomic evolutionary game theory modeling is based on a human learning dynamic. » (p. 11-12) « Where biological evolutionary game theory is intentionally broad in the scope of its agents, economic evolutionary game theory focuses more narrowly on explaining human action. [E]conomic evolutionary game theory modeling is based on a human learning dynamic. » (p. 11-12)

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31 Rationality & Evolution 1 Two Optimizing Processes 2 Isomorphism 2.1 Sex and Fairness 2.1.1 Rationality as (economic) game theory 2.2 Evolution as evolutionary game theory 2.2.1 Biological evolutionary game theory 2.2.2 Economic evolutionary game theory 2.3 Evolutionary Generalism 2.4 Why isomorphism is important 3 Differences 3.1 Symmetry 3.2 Dominated Strategies 3.3 Actual Fitness and Intended Outcomes 4 Simulations and multi-level models 4.1 Axelrod 4.2 A methodology: Multi-level modeling 4.3 Computational Differences 5 Normativity 5.1 Normative Rationality vs. Descriptive Evolution 5.2 What are the prospects for convergence? 1 Two Optimizing Processes 2 Isomorphism 2.1 Sex and Fairness 2.1.1 Rationality as (economic) game theory 2.2 Evolution as evolutionary game theory 2.2.1 Biological evolutionary game theory 2.2.2 Economic evolutionary game theory 2.3 Evolutionary Generalism 2.4 Why isomorphism is important 3 Differences 3.1 Symmetry 3.2 Dominated Strategies 3.3 Actual Fitness and Intended Outcomes 4 Simulations and multi-level models 4.1 Axelrod 4.2 A methodology: Multi-level modeling 4.3 Computational Differences 5 Normativity 5.1 Normative Rationality vs. Descriptive Evolution 5.2 What are the prospects for convergence?

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32 Un pas de plus: généralisme évolutionniste « [Fair divisions] strong stability properties guarantee that is an attracting equilibrium in the replicator dynamics, but also make the details of the dynamics unimportant. Fair division will be stable in any dynamics with a tendency to increase the proportion (or probability) of strategies with greater payoffs … For this reason, the Darwinian story can be transposed into the context of cultural evolution, in which imitation and learning may play an important role in the dynamics » (Skyrms 1996, p. 11) « [Fair divisions] strong stability properties guarantee that is an attracting equilibrium in the replicator dynamics, but also make the details of the dynamics unimportant. Fair division will be stable in any dynamics with a tendency to increase the proportion (or probability) of strategies with greater payoffs … For this reason, the Darwinian story can be transposed into the context of cultural evolution, in which imitation and learning may play an important role in the dynamics » (Skyrms 1996, p. 11)

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33 Rationality & Evolution 1 Two Optimizing Processes 2 Isomorphism 2.1 Sex and Fairness 2.1.1 Rationality as (economic) game theory 2.2 Evolution as evolutionary game theory 2.2.1 Biological evolutionary game theory 2.2.2 Economic evolutionary game theory 2.3 Evolutionary Generalism 2.4 Why isomorphism is important 3 Differences 3.1 Symmetry 3.2 Dominated Strategies 3.3 Actual Fitness and Intended Outcomes 4 Simulations and multi-level models 4.1 Axelrod 4.2 A methodology: Multi-level modeling 4.3 Computational Differences 5 Normativity 5.1 Normative Rationality vs. Descriptive Evolution 5.2 What are the prospects for convergence? 1 Two Optimizing Processes 2 Isomorphism 2.1 Sex and Fairness 2.1.1 Rationality as (economic) game theory 2.2 Evolution as evolutionary game theory 2.2.1 Biological evolutionary game theory 2.2.2 Economic evolutionary game theory 2.3 Evolutionary Generalism 2.4 Why isomorphism is important 3 Differences 3.1 Symmetry 3.2 Dominated Strategies 3.3 Actual Fitness and Intended Outcomes 4 Simulations and multi-level models 4.1 Axelrod 4.2 A methodology: Multi-level modeling 4.3 Computational Differences 5 Normativity 5.1 Normative Rationality vs. Descriptive Evolution 5.2 What are the prospects for convergence?

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34 Retour sur la citation de départ « The most striking fact about the relationship between evolutionary game theory and economic game theory is that, at the most basic level, a theory built of hyper-rational actors and a theory built of possibly non- rational actors are in fundamental agreement. This fact has been widely noticed, and its importance can hardly be overestimated. Criticism of game theory based on the failure of rationality assumptions must be reconsidered from the viewpoint of adaptive processes. There are many roads to the Nash equilibrium concept, only one of which is based on highly idealized rationality assumptions » (Skyrms 2000, p. 273) « The most striking fact about the relationship between evolutionary game theory and economic game theory is that, at the most basic level, a theory built of hyper-rational actors and a theory built of possibly non- rational actors are in fundamental agreement. This fact has been widely noticed, and its importance can hardly be overestimated. Criticism of game theory based on the failure of rationality assumptions must be reconsidered from the viewpoint of adaptive processes. There are many roads to the Nash equilibrium concept, only one of which is based on highly idealized rationality assumptions » (Skyrms 2000, p. 273)

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35 Rationality & Evolution 1 Two Optimizing Processes 2 Isomorphism 2.1 Sex and Fairness 2.1.1 Rationality as (economic) game theory 2.2 Evolution as evolutionary game theory 2.2.1 Biological evolutionary game theory 2.2.2 Economic evolutionary game theory 2.3 Evolutionary Generalism 2.4 Why isomorphism is important 3 Differences 3.1 Symmetry 3.2 Dominated Strategies 3.3 Actual Fitness and Intended Outcomes 4 Simulations and multi-level models 4.1 Axelrod 4.2 A methodology: Multi-level modeling 4.3 Computational Differences 5 Normativity 5.1 Normative Rationality vs. Descriptive Evolution 5.2 What are the prospects for convergence? 1 Two Optimizing Processes 2 Isomorphism 2.1 Sex and Fairness 2.1.1 Rationality as (economic) game theory 2.2 Evolution as evolutionary game theory 2.2.1 Biological evolutionary game theory 2.2.2 Economic evolutionary game theory 2.3 Evolutionary Generalism 2.4 Why isomorphism is important 3 Differences 3.1 Symmetry 3.2 Dominated Strategies 3.3 Actual Fitness and Intended Outcomes 4 Simulations and multi-level models 4.1 Axelrod 4.2 A methodology: Multi-level modeling 4.3 Computational Differences 5 Normativity 5.1 Normative Rationality vs. Descriptive Evolution 5.2 What are the prospects for convergence?

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36 Symétrie « A single population evolutionary setting imposes a symmetry requirement which selects Nash equilibria which appear implausible in other settings » (Skyrms 2000, p. 273) « [Evolution] often (but not always) leads to selection of fair division in a simple bargaining game. » (Skyrms 1996, ch. 1) « A single population evolutionary setting imposes a symmetry requirement which selects Nash equilibria which appear implausible in other settings » (Skyrms 2000, p. 273) « [Evolution] often (but not always) leads to selection of fair division in a simple bargaining game. » (Skyrms 1996, ch. 1)

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37 Rationality & Evolution 1 Two Optimizing Processes 2 Isomorphism 2.1 Sex and Fairness 2.1.1 Rationality as (economic) game theory 2.2 Evolution as evolutionary game theory 2.2.1 Biological evolutionary game theory 2.2.2 Economic evolutionary game theory 2.3 Evolutionary Generalism 2.4 Why isomorphism is important 3 Differences 3.1 Symmetry 3.2 Dominated Strategies 3.3 Actual Fitness and Intended Outcomes 4 Simulations and multi-level models 4.1 Axelrod 4.2 A methodology: Multi-level modeling 4.3 Computational Differences 5 Normativity 5.1 Normative Rationality vs. Descriptive Evolution 5.2 What are the prospects for convergence? 1 Two Optimizing Processes 2 Isomorphism 2.1 Sex and Fairness 2.1.1 Rationality as (economic) game theory 2.2 Evolution as evolutionary game theory 2.2.1 Biological evolutionary game theory 2.2.2 Economic evolutionary game theory 2.3 Evolutionary Generalism 2.4 Why isomorphism is important 3 Differences 3.1 Symmetry 3.2 Dominated Strategies 3.3 Actual Fitness and Intended Outcomes 4 Simulations and multi-level models 4.1 Axelrod 4.2 A methodology: Multi-level modeling 4.3 Computational Differences 5 Normativity 5.1 Normative Rationality vs. Descriptive Evolution 5.2 What are the prospects for convergence?

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38 Deux différences: stratégies faiblement dominées et rationalité modulaire [R]efinements of the Nash equilibrium are handled differently. –Standard evolutionary dynamics […] does not guarantee elimination of weakly dominated strategies. –[E]volutionary dynamics need not eliminate strategies which fail the test of sequential rationality » (Skyrms 2000, p. 273) [R]efinements of the Nash equilibrium are handled differently. –Standard evolutionary dynamics […] does not guarantee elimination of weakly dominated strategies. –[E]volutionary dynamics need not eliminate strategies which fail the test of sequential rationality » (Skyrms 2000, p. 273)

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39 Concept de dominance When a player tries to choose the "best" strategy among a multitude of options, that player may compare two strategies A and B to see which one is better. –B dominates A: choosing B always gives at least as good an outcome as choosing A. There are 2 possibilities: B strictly dominates A: choosing B always gives a better outcome than choosing A, no matter what the other player(s) do. B weakly dominates A: There is at least one set of opponents' action for which B is superior, and all other sets of opponents' actions give A and B the same payoff. This notion can be generalized beyond the comparison of two strategies. –Strategy B is strictly dominant if strategy B strictly dominates every other possible strategy. –Strategy B is weakly dominant if strategy B dominates all other strategies, but some are only weakly dominated. http://en.wikipedia.org/wiki/Dominance_(game_theory) When a player tries to choose the "best" strategy among a multitude of options, that player may compare two strategies A and B to see which one is better. –B dominates A: choosing B always gives at least as good an outcome as choosing A. There are 2 possibilities: B strictly dominates A: choosing B always gives a better outcome than choosing A, no matter what the other player(s) do. B weakly dominates A: There is at least one set of opponents' action for which B is superior, and all other sets of opponents' actions give A and B the same payoff. This notion can be generalized beyond the comparison of two strategies. –Strategy B is strictly dominant if strategy B strictly dominates every other possible strategy. –Strategy B is weakly dominant if strategy B dominates all other strategies, but some are only weakly dominated. http://en.wikipedia.org/wiki/Dominance_(game_theory)

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40 Rationalité modulaire « In a credible contingency plan for a situation in which an agent faces a sequence of choices, her plan should specify a rational choice at each choice point, relative to her situation at that choice point » (Skyrm 1996, p. 24) « In a credible contingency plan for a situation in which an agent faces a sequence of choices, her plan should specify a rational choice at each choice point, relative to her situation at that choice point » (Skyrm 1996, p. 24)

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41 Le jeu de lultimatum Si joueur 1Si joueur 2 GamesmanS1Offre 1Accepte tout S2Offre 1Rejette tout S3Offre 1Accepte 5, rejette 1 Mad DogS4Offre 1Rejette 5, accepte 1 Easy RiderS5Offre 5Accepte tout S6Offre 5Rejette tout FairmanS7Offre 5Accepte 5, rejette 1 S8Offre 5Rejette 5, accepte 1

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42 Le jeu de lultimatum: répartition égale des stratégies Si joueur 1Si joueur 2% init. GamesmanS1Offre 1Accepte tout12.5 S2Offre 1Rejette tout12.5 S3Offre 1Accepte 5, rejette 112.5 Mad DogS4Offre 1Rejette 5, accepte 112.5 Easy RiderS5Offre 5Accepte tout12.5 S6Offre 5Rejette tout12.5 FairmanS7Offre 5Accepte 5, rejette 112.5 S8Offre 5Rejette 5, accepte 112.5

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43 Le jeu de lultimatum: les Mad Dogs (faiblement dominés) survivent! Si joueur 1Si joueur 2% init.% final GamesmanS1Offre 1Accepte tout12.587 S2Offre 1Rejette tout12.50 S3Offre 1Accepte 5, rejette 112.50 Mad DogS4Offre 1Rejette 5, accepte 112.513 Easy RiderS5Offre 5Accepte tout12.50 S6Offre 5Rejette tout12.50 FairmanS7Offre 5Accepte 5, rejette 112.50 S8Offre 5Rejette 5, accepte 112.50

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44 En version automate cellulaire http://www.ags.uci.edu/~jalex/lattice-models/

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45 Le jeu de lultimatum: haute proportion initiale de fairmen Si joueur 1Si joueur 2% init. GamesmanS1Offre 1Accepte tout32 S2Offre 1Rejette tout2 S3Offre 1Accepte 5, rejette 110 Mad DogS4Offre 1Rejette 5, accepte 12 Easy RiderS5Offre 5Accepte tout10 S6Offre 5Rejette tout2 FairmanS7Offre 5Accepte 5, rejette 140 S8Offre 5Rejette 5, accepte 12

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46 Le jeu de lultimatum: les fairmen (faiblement dominés) survivent Si joueur 1Si joueur 2% init.% final GamesmanS1Offre 1Accepte tout320 S2Offre 1Rejette tout20 S3Offre 1Accepte 5, rejette 1100 Mad DogS4Offre 1Rejette 5, accepte 120 Easy RiderS5Offre 5Accepte tout1043.5 S6Offre 5Rejette tout20 FairmanS7Offre 5Accepte 5, rejette 14056.5 S8Offre 5Rejette 5, accepte 120

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47 Dynamique de lultimatum

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48 Rationality & Evolution 1 Two Optimizing Processes 2 Isomorphism 2.1 Sex and Fairness 2.1.1 Rationality as (economic) game theory 2.2 Evolution as evolutionary game theory 2.2.1 Biological evolutionary game theory 2.2.2 Economic evolutionary game theory 2.3 Evolutionary Generalism 2.4 Why isomorphism is important 3 Differences 3.1 Symmetry 3.2 Dominated Strategies 3.3 Actual Fitness and Intended Outcomes 4 Simulations and multi-level models 4.1 Axelrod 4.2 A methodology: Multi-level modeling 4.3 Computational Differences 5 Normativity 5.1 Normative Rationality vs. Descriptive Evolution 5.2 What are the prospects for convergence? 1 Two Optimizing Processes 2 Isomorphism 2.1 Sex and Fairness 2.1.1 Rationality as (economic) game theory 2.2 Evolution as evolutionary game theory 2.2.1 Biological evolutionary game theory 2.2.2 Economic evolutionary game theory 2.3 Evolutionary Generalism 2.4 Why isomorphism is important 3 Differences 3.1 Symmetry 3.2 Dominated Strategies 3.3 Actual Fitness and Intended Outcomes 4 Simulations and multi-level models 4.1 Axelrod 4.2 A methodology: Multi-level modeling 4.3 Computational Differences 5 Normativity 5.1 Normative Rationality vs. Descriptive Evolution 5.2 What are the prospects for convergence?

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49 « Rational choice is concerned with the intended outcomes of action. Selection mechanisms operate through actual outcomes. In explanations of animal behavior, where intentions have at best a minimal place, actual outcomes must bear most of the explanatory burden. It is more controversial which mechanism is the most important in the study of human action » (Elster 1989, p. 71) « Rational choice is concerned with the intended outcomes of action. Selection mechanisms operate through actual outcomes. In explanations of animal behavior, where intentions have at best a minimal place, actual outcomes must bear most of the explanatory burden. It is more controversial which mechanism is the most important in the study of human action » (Elster 1989, p. 71)

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50 Rationality & Evolution 1 Two Optimizing Processes 2 Isomorphism 2.1 Sex and Fairness 2.1.1 Rationality as (economic) game theory 2.2 Evolution as evolutionary game theory 2.2.1 Biological evolutionary game theory 2.2.2 Economic evolutionary game theory 2.3 Evolutionary Generalism 2.4 Why isomorphism is important 3 Differences 3.1 Symmetry 3.2 Dominated Strategies 3.3 Actual Fitness and Intended Outcomes 4 Simulations and multi-level models 4.1 Axelrod 4.2 A methodology: Multi-level modeling 4.3 Computational Differences 5 Normativity 5.1 Normative Rationality vs. Descriptive Evolution 5.2 What are the prospects for convergence? 1 Two Optimizing Processes 2 Isomorphism 2.1 Sex and Fairness 2.1.1 Rationality as (economic) game theory 2.2 Evolution as evolutionary game theory 2.2.1 Biological evolutionary game theory 2.2.2 Economic evolutionary game theory 2.3 Evolutionary Generalism 2.4 Why isomorphism is important 3 Differences 3.1 Symmetry 3.2 Dominated Strategies 3.3 Actual Fitness and Intended Outcomes 4 Simulations and multi-level models 4.1 Axelrod 4.2 A methodology: Multi-level modeling 4.3 Computational Differences 5 Normativity 5.1 Normative Rationality vs. Descriptive Evolution 5.2 What are the prospects for convergence?

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51 Méthodes: simulations vs. modèles « Roughly, the contrast between rationality and evolution projects onto methods, with evolution characterized more by simulations and rationality by more formal models. » (p. 16) « Roughly, the contrast between rationality and evolution projects onto methods, with evolution characterized more by simulations and rationality by more formal models. » (p. 16)

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52 Rationality & Evolution 1 Two Optimizing Processes 2 Isomorphism 2.1 Sex and Fairness 2.1.1 Rationality as (economic) game theory 2.2 Evolution as evolutionary game theory 2.2.1 Biological evolutionary game theory 2.2.2 Economic evolutionary game theory 2.3 Evolutionary Generalism 2.4 Why isomorphism is important 3 Differences 3.1 Symmetry 3.2 Dominated Strategies 3.3 Actual Fitness and Intended Outcomes 4 Simulations and multi-level models 4.1 Axelrod 4.2 A methodology: Multi-level modeling 4.3 Computational Differences 5 Normativity 5.1 Normative Rationality vs. Descriptive Evolution 5.2 What are the prospects for convergence? 1 Two Optimizing Processes 2 Isomorphism 2.1 Sex and Fairness 2.1.1 Rationality as (economic) game theory 2.2 Evolution as evolutionary game theory 2.2.1 Biological evolutionary game theory 2.2.2 Economic evolutionary game theory 2.3 Evolutionary Generalism 2.4 Why isomorphism is important 3 Differences 3.1 Symmetry 3.2 Dominated Strategies 3.3 Actual Fitness and Intended Outcomes 4 Simulations and multi-level models 4.1 Axelrod 4.2 A methodology: Multi-level modeling 4.3 Computational Differences 5 Normativity 5.1 Normative Rationality vs. Descriptive Evolution 5.2 What are the prospects for convergence?

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53 Axelrod Axelrod 1984: The Evolution of Cooperation –Évolution des stratégies dans le dilemme du prisonnier itéré; –Stratégie gagnante: TIT-FOR-TAT Critiques: –On connaissait déjà le folk theorem… –Trop demphase sur TIT-FOR-TAT; Binmore 1998: « The folk theorem of game theory proved by several authors simultaneously in the early fifties … describes in precise detail all of the outcomes of a repeated game that can be sustained as equilibria. [Axelrod] did us the service of focusing our attention on the importance of evolution in selecting an equilibrium from the infinitude of possibilities whose existence is demonstrated by the folk theorem. » Axelrod 1984: The Evolution of Cooperation –Évolution des stratégies dans le dilemme du prisonnier itéré; –Stratégie gagnante: TIT-FOR-TAT Critiques: –On connaissait déjà le folk theorem… –Trop demphase sur TIT-FOR-TAT; Binmore 1998: « The folk theorem of game theory proved by several authors simultaneously in the early fifties … describes in precise detail all of the outcomes of a repeated game that can be sustained as equilibria. [Axelrod] did us the service of focusing our attention on the importance of evolution in selecting an equilibrium from the infinitude of possibilities whose existence is demonstrated by the folk theorem. »

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54 Rationality & Evolution 1 Two Optimizing Processes 2 Isomorphism 2.1 Sex and Fairness 2.1.1 Rationality as (economic) game theory 2.2 Evolution as evolutionary game theory 2.2.1 Biological evolutionary game theory 2.2.2 Economic evolutionary game theory 2.3 Evolutionary Generalism 2.4 Why isomorphism is important 3 Differences 3.1 Symmetry 3.2 Dominated Strategies 3.3 Actual Fitness and Intended Outcomes 4 Simulations and multi-level models 4.1 Axelrod 4.2 A methodology: Multi-level modeling 4.3 Computational Differences 5 Normativity 5.1 Normative Rationality vs. Descriptive Evolution 5.2 What are the prospects for convergence? 1 Two Optimizing Processes 2 Isomorphism 2.1 Sex and Fairness 2.1.1 Rationality as (economic) game theory 2.2 Evolution as evolutionary game theory 2.2.1 Biological evolutionary game theory 2.2.2 Economic evolutionary game theory 2.3 Evolutionary Generalism 2.4 Why isomorphism is important 3 Differences 3.1 Symmetry 3.2 Dominated Strategies 3.3 Actual Fitness and Intended Outcomes 4 Simulations and multi-level models 4.1 Axelrod 4.2 A methodology: Multi-level modeling 4.3 Computational Differences 5 Normativity 5.1 Normative Rationality vs. Descriptive Evolution 5.2 What are the prospects for convergence?

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55 Évolution et rationalité « Stepping back, it is obvious that the complete picture must include both; evolution has historically produced some rational agents. So the question arises, how might one model the interaction between evolution and rationality? Given the difference in time scales of the two processes, a natural way to approach the relation of rationality and evolution is by a two level model.» (p. 18) « Stepping back, it is obvious that the complete picture must include both; evolution has historically produced some rational agents. So the question arises, how might one model the interaction between evolution and rationality? Given the difference in time scales of the two processes, a natural way to approach the relation of rationality and evolution is by a two level model.» (p. 18)

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56 Exemple de modélisation multi- niveau

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57 Rationality & Evolution 1 Two Optimizing Processes 2 Isomorphism 2.1 Sex and Fairness 2.1.1 Rationality as (economic) game theory 2.2 Evolution as evolutionary game theory 2.2.1 Biological evolutionary game theory 2.2.2 Economic evolutionary game theory 2.3 Evolutionary Generalism 2.4 Why isomorphism is important 3 Differences 3.1 Symmetry 3.2 Dominated Strategies 3.3 Actual Fitness and Intended Outcomes 4 Simulations and multi-level models 4.1 Axelrod 4.2 A methodology: Multi-level modeling 4.3 Computational Differences 5 Normativity 5.1 Normative Rationality vs. Descriptive Evolution 5.2 What are the prospects for convergence? 1 Two Optimizing Processes 2 Isomorphism 2.1 Sex and Fairness 2.1.1 Rationality as (economic) game theory 2.2 Evolution as evolutionary game theory 2.2.1 Biological evolutionary game theory 2.2.2 Economic evolutionary game theory 2.3 Evolutionary Generalism 2.4 Why isomorphism is important 3 Differences 3.1 Symmetry 3.2 Dominated Strategies 3.3 Actual Fitness and Intended Outcomes 4 Simulations and multi-level models 4.1 Axelrod 4.2 A methodology: Multi-level modeling 4.3 Computational Differences 5 Normativity 5.1 Normative Rationality vs. Descriptive Evolution 5.2 What are the prospects for convergence?

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58 Mieux que rationnel? « One point is particularly important for economists to appreciate: it can be demonstrated that rational decision-making methods … are computationally very weak: incapable of solving the natural adaptive problems our ancestors had to solve reliably in order to reproduce… This poor performance on most natural problems is the primary reason why problem- solving specializations were favored by natural selection over general purpose problem-solvers. …. On evolutionarily recurrent computational tasks, such as object recognition, grammar acquisition, or speech comprehension the human mind greatly outperforms the best artificial problem-solving systems that decades of research have produced, and it solves large classes of problems that even now no human-engineered system can solve at all. » (Cosmides et Tooby 1994) « One point is particularly important for economists to appreciate: it can be demonstrated that rational decision-making methods … are computationally very weak: incapable of solving the natural adaptive problems our ancestors had to solve reliably in order to reproduce… This poor performance on most natural problems is the primary reason why problem- solving specializations were favored by natural selection over general purpose problem-solvers. …. On evolutionarily recurrent computational tasks, such as object recognition, grammar acquisition, or speech comprehension the human mind greatly outperforms the best artificial problem-solving systems that decades of research have produced, and it solves large classes of problems that even now no human-engineered system can solve at all. » (Cosmides et Tooby 1994)

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59 Rationality & Evolution 1 Two Optimizing Processes 2 Isomorphism 2.1 Sex and Fairness 2.1.1 Rationality as (economic) game theory 2.2 Evolution as evolutionary game theory 2.2.1 Biological evolutionary game theory 2.2.2 Economic evolutionary game theory 2.3 Evolutionary Generalism 2.4 Why isomorphism is important 3 Differences 3.1 Symmetry 3.2 Dominated Strategies 3.3 Actual Fitness and Intended Outcomes 4 Simulations and multi-level models 4.1 Axelrod 4.2 A methodology: Multi-level modeling 4.3 Computational Differences 5 Normativity 5.1 Normative Rationality vs. Descriptive Evolution 5.2 What are the prospects for convergence? 1 Two Optimizing Processes 2 Isomorphism 2.1 Sex and Fairness 2.1.1 Rationality as (economic) game theory 2.2 Evolution as evolutionary game theory 2.2.1 Biological evolutionary game theory 2.2.2 Economic evolutionary game theory 2.3 Evolutionary Generalism 2.4 Why isomorphism is important 3 Differences 3.1 Symmetry 3.2 Dominated Strategies 3.3 Actual Fitness and Intended Outcomes 4 Simulations and multi-level models 4.1 Axelrod 4.2 A methodology: Multi-level modeling 4.3 Computational Differences 5 Normativity 5.1 Normative Rationality vs. Descriptive Evolution 5.2 What are the prospects for convergence?

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60 Pourquoi la rationalité est normative, mais pas lévolution? Comparez: « Pourquoi devrais-je me préoccuper dêtre copié? » « Pourquoi devrais-je me préoccuper de mes propres préférences? » Comparez: « Pourquoi devrais-je me préoccuper dêtre copié? » « Pourquoi devrais-je me préoccuper de mes propres préférences? »

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61 Les paradoxes de la rationalité La rationalité est auto- référentielle: il est rationnel dêtre rationnel. –Notre concept de rationalité est fondé sur un « mélange dintuition, danalogies et didéologie » (Samuelson 1997) –Lévolution peut peut-être Modifier ces intuitions Nous éclairer sur leur source La rationalité est auto- référentielle: il est rationnel dêtre rationnel. –Notre concept de rationalité est fondé sur un « mélange dintuition, danalogies et didéologie » (Samuelson 1997) –Lévolution peut peut-être Modifier ces intuitions Nous éclairer sur leur source

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62 Linfluence du positif sur le normatif « If I have strong reasons, based on evolutionary equilibrium selection, to expect you to choose a particular strategy, normative rationality gives me a reason to coordinate with your choice. » (p. 22) « If possibility is construed generously we have utopian theory. Those who would deal with men as they are need to work with a more restrictive sense of possibility. » (Skyrms 1996, pp. 108-9) « If I have strong reasons, based on evolutionary equilibrium selection, to expect you to choose a particular strategy, normative rationality gives me a reason to coordinate with your choice. » (p. 22) « If possibility is construed generously we have utopian theory. Those who would deal with men as they are need to work with a more restrictive sense of possibility. » (Skyrms 1996, pp. 108-9)

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63 Rationality & Evolution 1 Two Optimizing Processes 2 Isomorphism 2.1 Sex and Fairness 2.1.1 Rationality as (economic) game theory 2.2 Evolution as evolutionary game theory 2.2.1 Biological evolutionary game theory 2.2.2 Economic evolutionary game theory 2.3 Evolutionary Generalism 2.4 Why isomorphism is important 3 Differences 3.1 Symmetry 3.2 Dominated Strategies 3.3 Actual Fitness and Intended Outcomes 4 Simulations and multi-level models 4.1 Axelrod 4.2 A methodology: Multi-level modeling 4.3 Computational Differences 5 Normativity 5.1 Normative Rationality vs. Descriptive Evolution 5.2 What are the prospects for convergence? 1 Two Optimizing Processes 2 Isomorphism 2.1 Sex and Fairness 2.1.1 Rationality as (economic) game theory 2.2 Evolution as evolutionary game theory 2.2.1 Biological evolutionary game theory 2.2.2 Economic evolutionary game theory 2.3 Evolutionary Generalism 2.4 Why isomorphism is important 3 Differences 3.1 Symmetry 3.2 Dominated Strategies 3.3 Actual Fitness and Intended Outcomes 4 Simulations and multi-level models 4.1 Axelrod 4.2 A methodology: Multi-level modeling 4.3 Computational Differences 5 Normativity 5.1 Normative Rationality vs. Descriptive Evolution 5.2 What are the prospects for convergence?

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64 Chacun tire la couverte… « [T]he combination of education and evolution drives society in the direction of [game] theory. …. A widely applicable theory of games would, of necessity, involve a strong element of self-prophecy in the sense that the existence of the theory itself would be partly responsible for bringing about stabilizing the event which it predicts » (Binmore 1990, p. 18f). « One might then reasonably expect to see [constrained choice in cooperative dilemmas] drive out more costly precommitment and enforcement methods, and this through nothing more than what economists like to describe as the ordinary competitive process. » (McLennen 1998) « [T]he combination of education and evolution drives society in the direction of [game] theory. …. A widely applicable theory of games would, of necessity, involve a strong element of self-prophecy in the sense that the existence of the theory itself would be partly responsible for bringing about stabilizing the event which it predicts » (Binmore 1990, p. 18f). « One might then reasonably expect to see [constrained choice in cooperative dilemmas] drive out more costly precommitment and enforcement methods, and this through nothing more than what economists like to describe as the ordinary competitive process. » (McLennen 1998)

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65 Fin.

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