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Un « fait frappant »…

Un « fait frappant »….

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Un « fait frappant »…

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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)

  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?

  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?

  4. Le « sophisme naturaliste » « 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.

  5. L’heuristique de la personnalisation permet d’échapper 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 agent’s preferences. Conversely, what evolution optimizes is only a value if reproductive fitness is valued. » (p. 3)

  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 Darwin’s 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)

  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.

  8. By the way, c’est exactement ce qui est arrivé à nos morues…

  9. L’évolution 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)

  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)

  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?

  12. Le problème de l’égalité (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)

  13. 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 other’s 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)

  14. Problème: il y a une infinité d’équilibres de Nash 1 Demande A 0 1 0 Demande B

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

  16. Payoffs par stratégie, en termes de reproductive fitness

  17. Fitness attendues, avec distribution égale des stratégies

  18. Fitness attendues, une fois que les cupides sont disparus SES

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

  20. Dynamique de l’égalité Demande 1/2 Demande 1/3 Demande 2/3

  21. C’est la même chose pour le sex ratio (Fisher 1930, p. 142)

  22. 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?

  23. 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.

  24. 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?

  25. La théorie des jeux s’applique mieux à la biologie qu’à l’économie… « 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).

  26. 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?

  27. Qu’est-ce qu’une 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, • u(x,x) ≥ u(y,x) • If u(x,x) = u(y,x) then u(x,y) > u(y,y) » (p. 10)

  28. 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?

  29. 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)

  30. 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?

  31. Un pas de plus: généralisme évolutionniste « [Fair division’s] 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)

  32. 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?

  33. 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)

  34. 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?

  35. 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)

  36. 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?

  37. 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)

  38. 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)

  39. 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)

  40. Le jeu de l’ultimatum

  41. Le jeu de l’ultimatum:répartition égale des stratégies

  42. Le jeu de l’ultimatum:les Mad Dogs (faiblement dominés) survivent!

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

  44. Le jeu de l’ultimatum:haute proportion initiale de fairmen

  45. Le jeu de l’ultimatum:les fairmen (faiblement dominés) survivent

  46. Dynamique de l’ultimatum

  47. 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?

  48. « Rational choice is concerned with the intendedoutcomes 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)

  49. 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?

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