Arquivo da tag: Teoria dos jogos

Game theory and economics show how to steer evolution in a better direction (Science Daily)

Date: November 16, 2021

Source: PLOS

Summary: Human behavior drives the evolution of biological organisms in ways that can profoundly adversely impact human welfare. Understanding people’s incentives when they do so is essential to identify policies and other strategies to improve evolutionary outcomes. In a new study, researchers bring the tools of economics and game theory to evolution management.

Human behavior drives the evolution of biological organisms in ways that can profoundly adversely impact human welfare. Understanding people’s incentives when they do so is essential to identify policies and other strategies to improve evolutionary outcomes. In a new study publishing November 16thin the open access journal, PLOS Biology, researchers led by Troy Day at Queens University and David McAdams at Duke University bring the tools of economics and game theory to evolution management.

From antibiotic-resistant bacteria that endanger our health to control-resistant crop pests that threaten to undermine global food production, we are now facing the harmful consequences of our failure to efficiently manage the evolution of the biological world. As Day explains, “By modelling the joint economic and evolutionary consequences of people’s actions we can determine how best to incentivize behavior that is evolutionarily desirable.”

The centerpiece of the new analysis is a simple mathematical formula that determines when physicians, farmers, and other “evolution managers” will have sufficient incentive to steward the biological resources that are under their control, trading off the short-term costs of stewardship against the long-term benefits of delaying adverse evolution.

For instance, when a patient arrives in an urgent-care facility, screening them to determine if they are colonized by a dangerous superbug is costly, but protects future patients by allowing superbug carriers to be isolated from others. Whether the facility itself gains from screening patients depends on how it weighs these costs and benefits.

The researchers take the mathematical model further by implementing game theory, which analyzes how individuals’ decisions are interconnected and can impact each other — such as physicians in the same facility whose patients can infect each other or corn farmers with neighboring fields. Their game-theoretic analysis identifies conditions under which outcomes can be improved through policies that change incentives or facilitate coordination.

“In the example of antibiotic-resistant bacteria, hospitals could go above and beyond to control the spread of superbugs through methods like community contact tracing,” McAdams says. “This would entail additional costs and, alone, a hospital would likely not have an incentive to do so. But if every hospital took this additional step, they might all collectively benefit from slowing the spread of these bacteria. Game theory gives you a systematic way to think through those possibilities and maximize overall welfare.”

“Evolutionary change in response to human interventions, such as the evolution of resistance in response to drug treatment or evolutionary change in response to harvesting, can have significant economic repercussions,” Day adds. “We determine the conditions under which it is economically beneficial to employ costly strategies that limit evolution and thereby preserve the value of biological resources for longer.”

Journal Reference:

  1. Troy Day, David A. Kennedy, Andrew F. Read, David McAdams. The economics of managing evolution. PLOS Biology, 2021; 19 (11): e3001409 DOI: 10.1371/journal.pbio.3001409

‘Targeted punishments’ against countries could tackle climate change (Science Daily)

August 25, 2015
University of Warwick
Targeted punishments could provide a path to international climate change cooperation, new research in game theory has found.

This is a diagram of two possible strategies of targeted punishment studied in the paper. Credit: Royal Society Open Science

Targeted punishments could provide a path to international climate change cooperation, new research in game theory has found.

Conducted at the University of Warwick, the research suggests that in situations such as climate change, where everyone would be better off if everyone cooperated but it may not be individually advantageous to do so, the use of a strategy called ‘targeted punishment’ could help shift society towards global cooperation.

Despite the name, the ‘targeted punishment’ mechanism can apply to positive or negative incentives. The research argues that the key factor is that these incentives are not necessarily applied to everyone who may seem to deserve them. Rather, rules should be devised according to which only a small number of players are considered responsible at any one time.

The study’s author Dr Samuel Johnson, from the University of Warwick’s Mathematics Institute, explains: “It is well known that some form of punishment, or positive incentives, can help maintain cooperation in situations where almost everyone is already cooperating, such as in a country with very little crime. But when there are only a few people cooperating and many more not doing so punishment can be too dilute to have any effect. In this regard, the international community is a bit like a failed state.”

The paper, published in Royal Society Open Science, shows that in situations of entrenched defection (non-cooperation), there exist strategies of ‘targeted punishment’ available to would-be punishers which can allow them to move a community towards global cooperation.

“The idea,” said Dr Johnson, “is not to punish everyone who is defecting, but rather to devise a rule whereby only a small number of defectors are considered at fault at any one time. For example, if you want to get a group of people to cooperate on something, you might arrange them on an imaginary line and declare that a person is liable to be punished if and only if the person to their left is cooperating while they are not. This way, those people considered at fault will find themselves under a lot more pressure than if responsibility were distributed, and cooperation can build up gradually as each person decides to fall in line when the spotlight reaches them.”

For the case of climate change, the paper suggests that countries should be divided into groups, and these groups placed in some order — ideally, according roughly to their natural tendencies to cooperate. Governments would make commitments (to reduce emissions or leave fossil fuels in the ground, for instance) conditional on the performance of the group before them. This way, any combination of sanctions and positive incentives that other countries might be willing to impose would have a much greater effect.

“In the mathematical model,” said Dr Johnson, “the mechanism works best if the players are somewhat irrational. It seems a reasonable assumption that this might apply to the international community.”

Journal Reference:

  1. Samuel Johnson. Escaping the Tragedy of the Commons through Targeted PunishmentRoyal Society Open Science, 2015 [link]

Uma mente brilhante e inquieta aos 86 anos (Fapesp)

John Nash, que ganhou o Nobel de Economia e teve sua vida contada em filme, fala sobre Teoria dos Jogos e sobre suas novas pesquisas (foto:Agência FAPESP)

Por Diego Freire

Agência FAPESP – A mente brilhante, que ganhou o prêmio Nobel de Economia em 1994 por revolucionar o campo da Matemática conhecido como Teoria dos Jogos, continua contribuindo para novas revoluções na ciência e na vida em sociedade. O matemático norte-americano John Nash, 86 anos, esteve em São Paulo no fim de julho e falou sobre suas pesquisas atuais na Princeton University.

Nash veio ao Brasil para ministrar palestra no International Workshop on Game Theory and Economic Applications of the Game Theory Society (IWGTS), realizado na Faculdade de Economia, Administração e Contabilidade da Universidade de São Paulo (FEA-USP) no âmbito da Escola São Paulo de Ciência Avançada (ESPCA), modalidade de apoio da FAPESP.

Também participaram do evento, entre 25 e 31 de julho, outros três laureados com o Nobel em Ciências Econômicas: o matemático Robert Aumann (2005), da Hebrew University of Jerusalem, em Israel, e os economistas Eric Maskin (2007), da Harvard University, e Alvin Roth (2012), da Stanford University.

Muito antes de se tornar conhecido do público geral por ter sua história contada no filme Uma Mente Brilhante, de 2001, John Forbes Nash Jr. ganhou notoriedade no mundo acadêmico por suas contribuições à Teoria dos Jogos, área sistematizada em 1944 pelo matemático John von Neumann (1903-1957) e pelo economista Oskar Morgenstern (1902-1977).

Originalmente, os trabalhos na área utilizavam jogos em que os participantes precisavam fazer escolhas com base nas decisões dos seus oponentes, e os pesquisadores estudavam funções matemáticas que explicariam a competição ou a cooperação entre os jogadores. A pesquisa de Nash determinou o ponto de equilíbrio dessa relação, que passou a ser conhecido como Equilíbrio de Nash.

“Antes, entendia-se que, a partir de uma importância estabelecida, o que quer que uma pessoa ganhasse, a outra perdia. Por conta disso, jogar era visto apenas como uma formalidade. Com o tempo, o fato de haver ganho ou perda e a importância daquilo que estava em jogo se tornaram interesse de estudos”, disse em entrevista à Agência FAPESP.

Uma das mais famosas aplicações do Equilíbrio de Nash é a usada no jogo conhecido como Dilema do Prisioneiro, em que dois homens são presos suspeitos de terem praticado o mesmo crime. Não há provas contra eles, que são interrogados separadamente e encorajados pela polícia a delatar um ao outro, ganhando em troca a liberdade.

Haveria, então, duas opções: calar-se ou acusar o companheiro. Se os dois se acusam mutuamente, são igualmente condenados; se calam, são soltos. Mas a desconfiança de um acusado sobre a decisão que o outro poderia tomar aumenta a probabilidade de os dois se acusarem, o que levaria ao pior resultado: a prisão de ambos.

A melhor solução para os dois jogadores é a menos provável, pois requer cooperação cega, dado que eles não conversam a respeito. Dessa forma, o mais provável é que eles se acusem, pois ambos têm mais a ganhar delatando o outro.

O Equilíbrio de Nash é a solução em que nenhum jogador pode melhorar seu resultado com uma ação unilateral. Nesse caso, se um acusado que tende a delatar o outro muda unilateralmente sua estratégia e decide colaborar com a polícia, ele “perde” no jogo e é preso.

O conceito proposto pelo matemático é considerado fundamental na Teoria dos Jogos e é um dos métodos mais usados nas Ciências Sociais para estimar o resultado de uma interação estratégica.

A partir desse entendimento, seu trabalho contribuiu para a aplicação de conceitos puramente matemáticos a diversas áreas do conhecimento que tenham situações análogas a jogos, entre as quais a Economia, a Antropologia, as Ciências Políticas e a Biologia.

Transferências de poder

Na palestra ministrada na ESPCA, Nash descreveu um de seus experimentos recentes. “Em um jogo experimental, os vários jogadores participantes não foram orientados sobre como deveriam reagir ao comportamento daqueles com quem estavam interagindo. A interação foi sendo repetida mais e mais ao longo do jogo até que, naturalmente, os participantes passaram a incentivar o cooperativismo entre si, formando coalizões”, disse.

Durante o processo, Nash observou o comportamento dos jogadores quanto às transferências de poder realizadas na formação das coalizões, a aceitação por parte de alguns deles e a distribuição de recompensas por parte dos favorecidos.

“A aceitação dependia das gratificações. E jogadores com forças diferentes poderiam aceitar uma transferência de poder para outro participante, caso fossem recompensados por isso”, afirmou.

O experimento permitiu a Nash colocar o processo real de formação de coalizões e seus métodos de aceitação em um modelo matemático, demonstrado pelo cientista no evento.

O trabalho com jogos repetitivos, a formação de coalizões e os métodos de aceitação revelou ainda um aparente paradoxo observado pelo matemático: a evolução natural do comportamento cooperativo mesmo entre organismos ou espécies que interagem apenas por motivações egoístas, fenômeno que tem estudado nos últimos anos.

A exemplo do que ocorreu na concepção do Equilíbrio de Nash, a motivação para as novas pesquisas veio da observação inquieta do mundo.

“A ideia dos métodos de aceitações ocorreu quando eu estava contribuindo com um acampamento científico para jovens, ministrando uma palestra sobre a evolução e como ela naturalmente ocorre em modelos de cooperação entre duas ou mais espécies”, contou.

O episódio evidencia o interesse do matemático por novidades, demonstrado também durante o evento. Nash não esteve no local apenas para sua palestra. Ele participou como ouvinte de diversas outras apresentações e acompanhou atentamente a exposição de pôsteres, demonstrando interesse pelo trabalho desenvolvido no Brasil com a Teoria dos Jogos.

“Atualmente, em meus estudos, também tento dar continuidade a uma área mais complexa, que trata de jogos que podem ser parcialmente competitivos e parcialmente colaborativos”, disse. “Não estou certo sobre como vão se referir a essa área de pesquisa no futuro, se vão incluí-la na Teoria dos Jogos, se vão dizer que é estatística ou se é econometria. O certo é que há muito a se fazer.”

When Leaving Your Wealth to Your Sister’s Sons Makes Sense (Science Daily)

ScienceDaily (Oct. 16, 2012) — To whom a man’s possessions go when he dies is both a matter of cultural norm and evolutionary advantage.

In most human societies, men pass on their worldly goods to their wife’s children. But in about 10 percent of societies, men inexplicably transfer their wealth to their sister’s sons — what’s called “mother’s brother-sister’s son” inheritance. A new study on this unusual form of matrilineal inheritance by Santa Fe Institute reseacher Laura Fortunato has produced insights into this practice.

Her findings appear October 17 in the online edition of Proceedings of the Royal Society B.

“Matrilineal inheritance is puzzling for anthropologists because it causes tension for a man caught between his sisters and wife,” explains Fortunato, who has used game theory to study mother’s brother-sister’s son inheritance. “From an evolutionary perspective it’s also puzzling because you expect an individual to invest in his closest relatives — usually the individual’s own children.”

For decades research on the practice of matrilineal inheritance focused on the probabilities of a man being the biological father of his wife’s children — probabilities that lie on a sliding scale depending on the rate of promiscuity or whether polyandrous marriage (when a woman takes two or more husbands) is practiced.

Of special interest has been the probability value below which man is more closely related to his sister’s children than to his wife’s children. Below this “paternity threshold” a man is better off investing in his sister’s offspring, who are sure to be blood relatives, than his own wife’s children.

In her work modeling the evolutionary payoffs of marriage and inheritance strategies, Fortunato looked beyond the paternity threshold to see, among other things, what payoffs there were for men and women in different marital situations — including polygamy.

“What emerges is quite interesting,” says Fortunato. “Where inheritance is matrilineal, a man with multiple wives ‘wins’ over a man with a single wife.” That’s because wives have brothers, and those brothers will pass on their wealth to the husband’s sons. So more wives means more brothers-in-laws to invest in your sons.

The model also shows an effect for women with multiple husbands. The husband of a woman with multiple husbands is unsure of his paternity, so he may be better off investing in his sister’s offspring.

“A woman does not benefit from multiple husbands where inheritance is matrilineal, however,” Fortunato explains, “because her husbands will invest in their sisters’ kids.” Family structure determines how societies handle relatedness and reproduction issues, Fortunato says. Understanding these practices and their evolutionary implications is a prerequisite for a theory of human behavior.

Journal Reference:

  1. Dr Laura Fortunato. The evolution of matrilineal kinship organizationProceedings of the Royal Society B, October 17, 2012 DOI: 10.1098/rspb.2012.1926