Individual variation evades the Prisoner's Dilemma

Johnson, Dominic; Stopka, Pavel; Bell, Josh

doi:10.1186/1471-2148-2-15

Cited by 19 publications

(9 citation statements)

References 31 publications

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“…In general, these results support the idea proposed by Johnson et al (2002), that individual variation means that true PD scenarios occur relatively infrequently in nature. Johnson et al (2002) show that if there is variance in perception of twice the payoff interval in a linear PD game (a game in which the intervals between T , R , S , and P are the same) then only 15.8% remain valid PD games.…”

Section: Resultssupporting

confidence: 90%

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A game theoretic framework for incentive-based models of intrinsic motivation in artificial systems

Kasmarik

Shafi

2013

Front. Psychol.

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An emerging body of research is focusing on understanding and building artificial systems that can achieve open-ended development influenced by intrinsic motivations. In particular, research in robotics and machine learning is yielding systems and algorithms with increasing capacity for self-directed learning and autonomy. Traditional software architectures and algorithms are being augmented with intrinsic motivations to drive cumulative acquisition of knowledge and skills. Intrinsic motivations have recently been considered in reinforcement learning, active learning and supervised learning settings among others. This paper considers game theory as a novel setting for intrinsic motivation. A game theoretic framework for intrinsic motivation is formulated by introducing the concept of optimally motivating incentive as a lens through which players perceive a game. Transformations of four well-known mixed-motive games are presented to demonstrate the perceived games when players' optimally motivating incentive falls in three cases corresponding to strong power, affiliation and achievement motivation. We use agent-based simulations to demonstrate that players with different optimally motivating incentive act differently as a result of their altered perception of the game. We discuss the implications of these results both for modeling human behavior and for designing artificial agents or robots.

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Section: Resultssupporting

confidence: 90%

“…More recently, however, biologists have argued that individual variation in motivation and perception means that a majority of strategic interactions do not, in fact, conform to the PD model (Johnson et al, 2002). The models presented in our paper demonstrate one possible explanation for this latter view.…”

Section: Introductionmentioning

confidence: 99%

A game theoretic framework for incentive-based models of intrinsic motivation in artificial systems

Kasmarik

Shafi

2013

Front. Psychol.

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“…We assume that the payoffs are constant in time and identical for individuals of the same type. If individuals vary in their payoffs despite being of the same type, the results are altered by this additional source of randomness [34,35]. In a population with two types, we calculate a particular value θ ∗ , where the probability that the average fitness increases is equal to the probability it decreases.…”

Section: Discussionmentioning

confidence: 99%

The impact of random frequency-dependent mutations on the average population fitness

2012

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BackgroundIn addition to selection, the process of evolution is accompanied by stochastic effects, such as changing environmental conditions, genetic drift and mutations. Commonly it is believed that without genetic drift, advantageous mutations quickly fixate in a halpoid population due to strong selection and lead to a continuous increase of the average fitness. This conclusion is based on the assumption of constant fitness. However, for frequency dependent fitness, where the fitness of an individual depends on the interactions with other individuals in the population, this does not hold.ResultsWe propose a mathematical model that allows to understand the consequences of random frequency dependent mutations on the dynamics of an infinite large population. The frequencies of different types change according to the replicator equations and the fitness of a mutant is random and frequency dependent. To capture the interactions of different types, we employ a payoff matrix of variable size and thus are able to accommodate an arbitrary number of mutations. We assume that at most one mutant type arises at a time. The payoff entries to describe the mutant type are random variables obeying a probability distribution which is related to the fitness of the parent type.ConclusionsWe show that a random mutant can decrease the average fitness under frequency dependent selection, based on analytical results for two types and simulations for n types. Interestingly, in the case of at most two types the probabilities to increase or decrease the average fitness are independent of the concrete probability density function. Instead, they only depend on the probability that the payoff entries of the mutant are larger than the payoff entries of the parent type.

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“…A few previous studies have explicitly taken aging into account (Johnson et al, 2002; Szolnoki et al, 2009; Liu et al 2012) and the effect of dispersal and reproductive timing on the evolution of cooperation are well-established (Lehmann and Rousset, 2010). However, our focus on the reproductive schedule in a life history context uniquely emphasizes the potential interactions between biological aging and social evolution.…”

Section: Discussionmentioning

confidence: 99%

“…However, practically the study system was too complex to be solved analytically, requiring this simulation approach. Although the model could be refined in multiple ways, such as asymmetrical costs and benefits of cooperation (Johnson et al, 2002), it provides an important step in our understanding of the potential interactions between life history and social evolution.…”

Section: Discussionmentioning

confidence: 99%

A structured population model suggests that long life and post-reproductive lifespan promote the evolution of cooperation

Ross

Rychtář

Rueppell

2015

Journal of Theoretical Biology

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Social organization correlates with longevity across animal taxa. This correlation has been explained by selection for longevity by social evolution. The reverse causality is also conceivable but has not been sufficiently considered. We constructed a simple, spatially structured population model of asexually reproducing individuals to study the effect of temporal life history structuring on the evolution of cooperation. Individuals employed fixed strategies of cooperation or defection towards all neighbours in a basic Prisoner’s Dilemma paradigm. Individuals aged and transitioned through different life history stages asynchronously without migration. An individual’s death triggered a reproductive event by one immediate neighbour. The specific neighbour was chosen probabilistically according to the cumulative payoff from all local interactions. Varying the duration of pre-reproductive, reproductive, and post-reproductive life history stages, long-term simulations allowed a systematic evaluation of the influence of the duration of these specific life history stages. Our results revealed complex interactions among the effects of the three basic life history stages and the benefit to defect. Overall, a long post-reproductive stage promoted the evolution of cooperation, while a prolonged pre-reproductive stage has a negative effect. In general, the total length of life also increased the probability of the evolution of cooperation. Thus, our specific model suggests that the timing of life history transitions and total duration of life history stages may affect the evolution of cooperative behaviour. We conclude that the causation of the empirically observed association of life expectancy and sociality may be more complex than previously realized.

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Individual variation evades the Prisoner's Dilemma

Cited by 19 publications

References 31 publications

A game theoretic framework for incentive-based models of intrinsic motivation in artificial systems

A game theoretic framework for incentive-based models of intrinsic motivation in artificial systems

The impact of random frequency-dependent mutations on the average population fitness

A structured population model suggests that long life and post-reproductive lifespan promote the evolution of cooperation

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