5. Alternative Approaches. Strategic Bahavior in Business and Econ 1. Introduction 2. Individual...

5. Alternative Approaches

Strategic Bahavior in Business and Econ

1. Introduction2. Individual Decision Making3. Basic Topics in Game Theory4. The Theories and the Real World5. Alternative Approaches

5.1 Psychology5.2 Evolution5.3 Artificial Intelligence


5.1 Psychology

Remember the main assumptions in Game Theory

RationalityPlayers aim to maximize their payoffs

They are selfish, they only care about their payoffs

Players are perfect calculators

Common KnowledgeEach 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.


5.1 Psychology

Many are criticized since experimental evidence is in contradiction

RationalityPlayers aim to maximize their payoffs

They are selfish, they only care about their payoffs

Players are perfect calculators

Common KnowledgeEach 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.


5.1 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 matchthe predictions of Rational Theories


5.1 Psychology






This does not mean that people is not rational !


5.1 Psychology






This does not mean that people is not rational !

People is “boundedly” rational


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"


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, . . .


Alternative Approaches

Among others, the following incorporate some of thecriticisms to rationality

Evolution: Nature takes “good” decisions withoutany rationality at all, without any computation

Artificial Intelligence: Allows for “full control” of thedegree of rationality, computational power, memory restrictions, etc


1. Introduction2. Individual Decision Making3. Basic Topics in Game Theory4. The Theories and the Real World5. Alternative Approaches

5.1 Psychology5.2 Evolution5.3 Artificial Intelligence


Darwinian evolution is based on three fundamental principles:

reproduction, mutation and selection

5.2 Evolutionary Game Theory


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).


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



Evolutionary Game Theory considers a populationof “organisms” that interact with each other.The “genotype” of each organism is identified withan strategy in Game Theory. When (two) organismsinteract, they use the strategies that correspond to their genotypes and collect some “payoff”.Organisms that “do well” (get high payoffs) pass thetest of “natural selection” and reproduce themselves.Organisms that “do poorly” (get low payoffs) will beinvaded and displaced by new “mutant” organisms that do better



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”



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')


Population genotypeOrganism genotype


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 mightinvade the population ! The second part of this condition saysthat it that occurs then being the “original organism” s (notthe mutant s' ) has a higher payoff (it's better for naturalselection) (Stability)


Example

Think of a population of lions that have the followinginstructions embedded in their genotypes (strategy)

In the presence of another lion, act friendly unlessit is behaves aggressively. In such case you shouldact aggressively as well

In the presence of a zebra, chase it and share themeal with the other lions and cabs

This appears to be a “reasonable” strategy for lions.


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 unlessit is behaves aggressively. In such case you shouldact aggressively as well

Most likely, this sort of “mutation” will not besuccessful at all !It will not satisfy condition (1)


Example

In the same population of lions consider adifferent “mutant” with this information



Most likely, this will satisfy condition (1)


Example

In the same population of lions consider adifferent “mutant” with this information



But will NOT satisfy condition (2). If all the lionswere as this mutant, the whole population willdie of starvation !! In such case, it's better to behaveas the “original” lions


Example: What does this have to do withbusiness or economics ?

Think of a population of firms that have the followinginstructions embedded in their strategies (genotypes)

In the presence of a partner, act friendly unlessit is behaves aggressively. In such case you shouldact 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.


Darwinian evolution is based on three fundamental principles:

reproduction, mutation and selection



Darwinian Social evolution is based on three fundamental principles:

reproduction, imitationmutation and innovation (R&D)selection competition


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


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


Dove Hawk

Dove 0 , V

V , 0 (V-C)/2 , (V-C)/2HawkAnimal 1

Animal 2

V/2 , V/2


Dove Hawk

Dove 0 , V


Animal 2

V/2 , V/2

The are 2 Nash Equilibria

in pure strategies


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 !


Computation of the Evolutionary Stable Strategy

Suppose that V=2 and C=6

Dove Hawk

Dove 0 , V


Animal 2

V/2 , V/2



Suppose that V=2 and C=6

Dove Hawk

Dove 0 , 2

2 , 0 -2 , -2HawkAnimal 1

Animal 2

1 , 1



Dove Hawk

Dove 0 , 2


Animal 2

1 , 1

If all the population behaves like a Dove, it's better to be a HawkIf all the population behaves like a Hawk, it's better to be a Dove



Dove Hawk

Dove 0 , 2


Animal 2

1 , 1

No strategy (genotype) satisfies condition (1) !! ??



Dove (2/3) Hawk (1/3)

Dove 0 , 2


Animal 2

1 , 1

Suppose that 2/3 of the population are Doves and 1/3are Hawks



Dove (2/3) Hawk (1/3)

Dove 0 , 2


Animal 2

1 , 1

If I behave like a Dove, my expected payoff will be:

E(Dove)= (2/3)·( 1 ) + (1/3)· ( 0 ) = 2/3



Dove (2/3) Hawk (1/3)

Dove 0 , 2


Animal 2

1 , 1

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



Dove (2/3) Hawk (1/3)

Dove 0 , 2


Animal 2

1 , 1

Thus, if 2/3 of the population are Doves and 1/3 are Hawks, beinga Dove or a Hawk pays the same !!!



Dove (2/3) Hawk (1/3)

Dove 0 , 2


Animal 2

1 , 1

This IS the ESS:

2/3 of the population are Doves and 1/3 are Hawks



Dove (2/3) Hawk (1/3)

Dove 0 , 2


Animal 2

1 , 1

Notice !!!

Any other “genotype” will satisfy condition (1) !!!



Dove (2/3) Hawk (1/3)

Dove 0 , 2


Animal 2

1 , 1

But if there are more that 2/3 of Doves, then it is betterto be a Hawk (will not satisfy condition (2))And if there are more that 1/3 of Hawks then it is betterto be a Dove (will not satisfy condition (2))


Evolutionary Stable Dynamics

How evolution takes place can be studied dynamicallyas well.

We might, for instance, say that the proportion oforganisms that play a given strategy evolves in the following way:

If the payoff of such strategy is above the averagepayoff of the population, then the proportion of organisms using that strategy will increaseIf the payoff of such strategy is below the averagepayoff of the population, then the proportion of organisms using that strategy will decrease




Payoff of spt+1(s) = pt(s)·

Average Payoff

This is known as the “Replicator Dynamics”




Payoff of spt+1(s) = pt(s)·

Average Payoff

Roughly speaking the solution of the “Replicator Dynamics” coincideswith the Evolutionary Stable Strategy


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


Behavior of the “Replicator Dynamics”


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 becamean application of Biological Evolution to Game Theory

Evolutionary Game Theory is useful to single out thoseequilibria that can be achieved without rationality

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