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5. Alternative Approaches

5. Alternative Approaches. 1. Introduction 2. Individual Decision Making 3. Basic Topics in Game Theory 4. The Theories and the Real World 5. Alternative Approaches 5.1 Psychology 5.2 Evolution 5.3 Artificial Intelligence. 5.1 Psychology Remember the main assumptions in Game Theory.

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5. Alternative Approaches

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  1. 5. Alternative Approaches

  2. Strategic Bahavior in Business and Econ 1. Introduction 2. Individual Decision Making 3. Basic Topics in Game Theory 4. The Theories and the Real World 5. Alternative Approaches 5.1 Psychology 5.2 Evolution 5.3 Artificial Intelligence

  3. Strategic Bahavior in Business and Econ 5.1 Psychology Remember the main assumptions in Game Theory • Rationality • Players aim to maximize their payoffs • They are selfish, they only care about their payoffs • Players are perfect calculators • Common Knowledge • Each player knows the environment and the rules of the game • Each player knows that each player knows the environment and the rules • Each player knows that each player knows that each player knows the environment and the rules • Etc. Etc. Etc.

  4. Strategic Bahavior in Business and Econ 5.1 Psychology Many are criticized since experimental evidence is in contradiction • Rationality • Players aim to maximize their payoffs • They are selfish, they only care about their payoffs • Players are perfect calculators • Common Knowledge • Each player knows the environment and the rules of the game • Each player knows that each player knows the environment and the rules • Each player knows that each player knows that each player knows the environment and the rules • Etc. Etc. Etc.

  5. Strategic Bahavior in Business and Econ 5.1 Psychology In general, experiments show that • People do not have (or do not use) all the information • People have limited memory • People have limited computational abilities Therefore, people's observed behavior often does not match the predictions of Rational Theories

  6. Strategic Bahavior in Business and Econ 5.1 Psychology In general, experiments show that • People do not have (or do not use) all the information • People have limited memory • People have limited computational abilities Therefore, people's observed behavior often does not match the predictions of Rational Theories This does not mean that people is not rational !

  7. Strategic Bahavior in Business and Econ • 5.1 Psychology • In general, experiments show that • People do not have (or do not use) all the information • People have limited memory • People have limited computational abilities Therefore, people's observed behavior often does not match the predictions of Rational Theories This does not mean that people is not rational ! People is “boundedly” rational

  8. Strategic Bahavior in Business and Econ Bounded Rationality The term is thought to have been coined by Herbert Simon. In Models of My Life, Herbert Simon points out that most people are only partly rational, and are in fact emotional/irrational in the remaining part of their actions. In another work, he states "boundedly rational agents experience limits in formulating and solving complex problems and in processing (receiving, storing, retrieving, transmitting) information"

  9. Strategic Bahavior in Business and Econ Bounded Rationality The term is thought to have been coined by Herbert Simon. In Models of My Life, Herbert Simon points out that most people are only partly rational, and are in fact emotional/irrational in the remaining part of their actions. In another work, he states "boundedly rational agents experience limits in formulating and solving complex problems and in processing (receiving, storing, retrieving, transmitting) information" Experiments suggest that individual's behavior depends on previous experiences, a process of “learning”, some intuition, innovation, experimentation, . . .

  10. Strategic Bahavior in Business and Econ Alternative Approaches • Among others, the following incorporate some of the • criticisms to rationality • Evolution: Nature takes “good” decisions without any rationality at all, without any computation • Artificial Intelligence: Allows for “full control” of the degree of rationality, computational power, memory restrictions, etc

  11. Strategic Bahavior in Business and Econ 1. Introduction 2. Individual Decision Making 3. Basic Topics in Game Theory 4. The Theories and the Real World 5. Alternative Approaches 5.1 Psychology 5.2 Evolution 5.3 Artificial Intelligence

  12. Strategic Bahavior in Business and Econ 5.2 Evolutionary Game Theory Darwinian evolution is based on three fundamental principles: • reproduction, • mutation and • selection

  13. Strategic Bahavior in Business and Econ Species tend to perpetuate by reproducing themselves, but only those that better fit in a changing environment will survive. Inheritance causes reproduction. Mutation is the source of change and, in turn, the way of adapting to the changes. Natural selection is the paradigm, the way nature uses to decide which species will survive and which will not. Such a simple explanation of such a complex phenomenon is the main virtue of that theory. It is not surprising, one might think, that other scientific disciplines involving some sort of dynamics or evolution (like economics or history among many others) try to approach their unsolved problems in a similar way. Nevertheless, the fact is that Darwin's is not the only way to study evolution, not even the first evolutionary theory to appear. As Hallpike (1985) points out, the theories of social evolution do not come after Darwin's. Indeed, economists like Malthus, Marx or Smith, to name only a few, all developed theories of social or economical evolution independently of any contribution from biology. As a matter of fact, it was when Darwin happened to read “for amusement” Malthus's Essay on Population that he got the idea of natural selection (Barlow,1958).

  14. Strategic Bahavior in Business and Econ 5.2 Evolutionary Game Theory Was initiated by John Maynard-Smith and George Price in 1973 and continued by Maynard-Smith in 1981 Originally, it was an application of Game Theory to Evolutionary Theory Very soon, it became an application of Evolutionary Theory to Game Theory

  15. Strategic Bahavior in Business and Econ 5.2 Evolutionary Game Theory Evolutionary Game Theory considers a population of “organisms” that interact with each other. The “genotype” of each organism is identified with an strategy in Game Theory. When (two) organisms interact, they use the strategies that correspond to their genotypes and collect some “payoff”. Organisms that “do well” (get high payoffs) pass the test of “natural selection” and reproduce themselves. Organisms that “do poorly” (get low payoffs) will be invaded and displaced by new “mutant”organisms that do better

  16. Strategic Bahavior in Business and Econ 5.2 Evolutionary Game Theory The core ingredient of Evolutionary Game Theory is the so called Evolutionary Stable Strategy(ESS) “A strategy such that if all members of the population adopt it, then no mutant can invade the population under the influence of selection”

  17. Strategic Bahavior in Business and Econ 5.2 Evolutionary Game Theory The core ingredient of Evolutionary Game Theory is the so called Evolutionary Stable Strategy(ESS) A genotype s is an Evolutionary Stable Strategy if: (1) U(s,s) ≥ U(s',s) for any other genotype s' (2) If U(s,s) = U(s',s) for some other s', then U(s,s') > U(s',s') Organism genotype Population genotype

  18. Strategic Bahavior in Business and Econ A strategy s is an Evolutionary Stable Strategy if: (1) U(s,s) ≥ U(s',s) for any other strategy s' (2) If U(s,s) = U(s',s) for some other s', then U(s,s') > U(s',s') Condition (1) says that the strategy of the population (s) is a Best Reply to itself (Equilibrium) Condition (2) says first that if another organism (a mutant s' ) can do as well as the population then it might invade the population ! The second part of this condition says that it that occurs then being the “original organism”s (not the mutant s' ) has a higher payoff (it's better for natural selection) (Stability)

  19. Strategic Bahavior in Business and Econ Example Think of a population of lions that have the following instructions embedded in their genotypes (strategy) • In the presence of another lion, act friendly unless it is behaves aggressively. In such case you should act aggressively as well • In the presence of a zebra, chase it and share the meal with the other lions and cabs This appears to be a “reasonable” strategy for lions.

  20. Strategic Bahavior in Business and Econ Example • In the same population of lions consider the • following “mutant” with this information • In the presence of another lion, chase it and share the meal with the other lions and cabs • In the presence of a zebra, act friendly unless it is behaves aggressively. In such case you should act aggressively as well Most likely, this sort of “mutation” will not be successful at all ! It will not satisfy condition (1)

  21. Strategic Bahavior in Business and Econ Example • In the same population of lions consider a • different “mutant” with this information • In the presence of another lion, act friendly unless it is behaves aggressively. In such case you should act aggressively as well • In the presence of a zebra, act friendly unless it is behaves aggressively. In such case you should act aggressively as well Most likely, this will satisfy condition (1)

  22. Strategic Bahavior in Business and Econ Example • In the same population of lions consider a • different “mutant” with this information • In the presence of another lion, act friendly unless it is behaves aggressively. In such case you should act aggressively as well • In the presence of a zebra, act friendly unless it is behaves aggressively. In such case you should act aggressively as well But will NOT satisfy condition (2). If all the lions were as this mutant, the whole population will die of starvation !! In such case, it's better to behave as the “original” lions

  23. Strategic Bahavior in Business and Econ Example: What does this have to do with business or economics ? Think of a population of firms that have the following instructions embedded in their strategies (genotypes) • In the presence of a partner, act friendly unless it is behaves aggressively. In such case you should act aggressively as well • In the presence of a competitor, be aggressive and share the meal with the other partners This appears to be a “reasonable” strategy for firms.

  24. Strategic Bahavior in Business and Econ Example: What does this have to do with business or economics ? Darwinian evolution is based on three fundamental principles: • reproduction, • mutation and • selection

  25. Strategic Bahavior in Business and Econ Example: What does this have to do with business or economics ? Darwinian Social evolution is based on three fundamental principles: • reproduction, imitation • mutation and innovation (R&D) • selection competition

  26. Strategic Behavior in Business and Econ Example: The Hawk-Dove Game This is version of a Game of Chicken that is very useful in evolutionary biology The name "Hawk-Dove" refers to a situation in which two animals compete for a shared resource and the contestants can choose either conciliation or conflict. V is the value of the contested resource, and C is the cost of an escalated fight. It is (almost always) assumed that the value of the resource is less than the cost of a fight is, i.e., C > V > 0 If the two animals behave in the same way, the split the resource. Otherwise, the animal playing Hawk gets the whole resource

  27. Strategic Behavior in Business and Econ The environment of the game • Players: Animal 1 and Animal 2 • Strategies: Dove (show you intention) or Hawk (attack) • Payoffs: (see the table) The Rules of the Game • Timing of moves Simultaneous • Nature of conflict and interaction Conflict (anti-coordination) • Information conditions Symmetric

  28. Strategic Behavior in Business and Econ Animal 2 Dove Hawk 0 , V Dove V/2 , V/2 Animal 1 V , 0 (V-C)/2 , (V-C)/2 Hawk

  29. Strategic Behavior in Business and Econ The are 2 Nash Equilibria in pure strategies Animal 2 Dove Hawk 0 , V Dove V/2 , V/2 Animal 1 V , 0 (V-C)/2 , (V-C)/2 Hawk

  30. Strategic Behavior in Business and Econ • In real like, some animals behave as doves while others Are Hawks (mixed strategy !) • This example set the basis for a extremely fruitful application of Game Theory to Evolutionary Biology (John Maynard-Smith) • And vice versa, Evolutionary Theory can be applied to Game Theory !

  31. Strategic Behavior in Business and Econ Computation of the Evolutionary Stable Strategy Suppose that V=2 and C=6 Animal 2 Dove Hawk 0 , V Dove V/2 , V/2 Animal 1 V , 0 (V-C)/2 , (V-C)/2 Hawk

  32. Strategic Behavior in Business and Econ Computation of the Evolutionary Stable Strategy Suppose that V=2 and C=6 Animal 2 Dove Hawk 0 , 2 Dove 1 , 1 Animal 1 2 , 0 -2 , -2 Hawk

  33. Strategic Behavior in Business and Econ Computation of the Evolutionary Stable Strategy Animal 2 Dove Hawk 0 , 2 Dove 1 , 1 Animal 1 2 , 0 -2 , -2 Hawk If all the population behaves like a Dove, it's better to be a Hawk If all the population behaves like a Hawk, it's better to be a Dove

  34. Strategic Behavior in Business and Econ Computation of the Evolutionary Stable Strategy Animal 2 Dove Hawk 0 , 2 Dove 1 , 1 Animal 1 2 , 0 -2 , -2 Hawk No strategy (genotype) satisfies condition (1) !! ??

  35. Strategic Behavior in Business and Econ Computation of the Evolutionary Stable Strategy Animal 2 Dove (2/3) Hawk (1/3) 0 , 2 Dove 1 , 1 Animal 1 2 , 0 -2 , -2 Hawk Suppose that 2/3 of the population are Doves and 1/3 are Hawks

  36. Strategic Behavior in Business and Econ Computation of the Evolutionary Stable Strategy Animal 2 Dove (2/3) Hawk (1/3) 0 , 2 Dove 1 , 1 Animal 1 2 , 0 -2 , -2 Hawk If I behave like a Dove, my expected payoff will be: E(Dove)= (2/3)·( 1 ) + (1/3)· ( 0 ) = 2/3

  37. Strategic Behavior in Business and Econ Computation of the Evolutionary Stable Strategy Animal 2 Dove (2/3) Hawk (1/3) 0 , 2 Dove 1 , 1 Animal 1 2 , 0 -2 , -2 Hawk If I behave like a Hawk, my expected payoff will be: E(Hawk)= (2/3)·( 2 ) + (1/3)· ( -2 ) = 4/3 – 2/3 = 2/3

  38. Strategic Behavior in Business and Econ Computation of the Evolutionary Stable Strategy Animal 2 Dove (2/3) Hawk (1/3) 0 , 2 Dove 1 , 1 Animal 1 2 , 0 -2 , -2 Hawk Thus, if 2/3 of the population are Doves and 1/3 are Hawks, being a Dove or a Hawk pays the same !!!

  39. Strategic Behavior in Business and Econ Computation of the Evolutionary Stable Strategy Animal 2 Dove (2/3) Hawk (1/3) 0 , 2 Dove 1 , 1 Animal 1 2 , 0 -2 , -2 Hawk This IS the ESS: 2/3 of the population are Doves and 1/3 are Hawks

  40. Strategic Behavior in Business and Econ Computation of the Evolutionary Stable Strategy Animal 2 Dove (2/3) Hawk (1/3) 0 , 2 Dove 1 , 1 Animal 1 2 , 0 -2 , -2 Hawk Notice !!! Any other “genotype” will satisfy condition (1) !!!

  41. Strategic Behavior in Business and Econ Computation of the Evolutionary Stable Strategy Animal 2 Dove (2/3) Hawk (1/3) 0 , 2 Dove 1 , 1 Animal 1 2 , 0 -2 , -2 Hawk But if there are more that 2/3 of Doves, then it is better to be a Hawk (will not satisfy condition (2)) And if there are more that 1/3 of Hawks then it is better to be a Dove (will not satisfy condition (2))

  42. Strategic Behavior in Business and Econ Evolutionary Stable Dynamics How evolution takes place can be studied dynamically as well. We might, for instance, say that the proportion of organisms that play a given strategy evolves in the following way: • If the payoff of such strategy is above the average payoff of the population, then the proportion of organisms using that strategy will increase • If the payoff of such strategy is below the average payoff of the population, then the proportion of organisms using that strategy will decrease

  43. Strategic Behavior in Business and Econ Evolutionary Stable Dynamics • If the payoff of such strategy is above the average payoff of the population, then the proportion of organisms using that strategy will increase • If the payoff of such strategy is below the average payoff of the population, then the proportion of organisms using that strategy will decrease Payoff of s pt+1(s) = pt(s)· Average Payoff This is known as the “Replicator Dynamics”

  44. Strategic Behavior in Business and Econ Evolutionary Stable Dynamics • If the payoff of such strategy is above the average payoff of the population, then the proportion of organisms using that strategy will increase • If the payoff of such strategy is below the average payoff of the population, then the proportion of organisms using that strategy will decrease Payoff of s pt+1(s) = pt(s)· Average Payoff Roughly speaking the solution of the “Replicator Dynamics”coincides with the Evolutionary Stable Strategy

  45. Strategic Behavior in Business and Econ Example: The Repeated Prisoners' Dilemma • Consider a population of organisms that play the Prisoners' • Dilemma repeatedly • For simplicity, suppose that there are only three types of • “genotypes” • (C) Always Cooperate • (D) Always Defect • (T) Tit-for-Tat

  46. Strategic Behavior in Business and Econ Behavior of the “Replicator Dynamics”

  47. Strategic Behavior in Business and Econ Summary • The main criticism form Psychologists and Experimentalist to the “rational theories” is that individuals are only “boundedly rational” • The ideas of Biological Evolution can be successfully adapted to Social Evolution • Evolutionary Game Theory was initiated as an application of Game Theory to Biological Evolution but soon became an application of Biological Evolution to Game Theory • Evolutionary Game Theory is useful to single out those equilibria that can be achieved without rationality

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