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1

The Long-Term Benefits of Following Fairness Norms under Dynamics of Learning and Evolution

Lorini E., Mühlenbernd R.

Fundamenta Informaticae

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2018

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Vol. 158, nr 1/3

121--148

EN

In this study we present a game-theoretic model of guilt in relation to sensitivity to norms of fairness. We focus on a specific kind of fairness norm à la Rawls according to which a fair society should be organized so as to admit economic inequalities to the extent that they are beneficial to the less advantaged agents. In a first step, we analyze the impact of the sensitivity to this fairness norm on the behavior of agents who play a repeated Prisoner’s Dilemma and learn via fictitious play. In a second step we transform the base game into a meta-game that represents a static description of a repeated game updated via fictitious play. We analyze such a meta-game under population dynamics by means of evolutionary game theory. Our results reveal two things: first of all, a great sensitivity to the fairness norm is beneficial in the long term when agents have the time to converge to mutual cooperation. Secondly, cooperativeness and fairness norm sensitivity can coevolve in a population of initially solely defectors.

2

Evolutionary stable strategies in networked games: the influence of topology

Kasthurirathna D., Piraveenan M., Uddin S.

Journal of Artificial Intelligence and Soft Computing Research

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2015

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Vol. 5, No. 2

83--95

EN

Evolutionary game theory is used to model the evolution of competing strategies in a population of players. Evolutionary stability of a strategy is a dynamic equilibrium, in which any competing mutated strategy would be wiped out from a population. If a strategy is weak evolutionarily stable, the competing strategy may manage to survive within the network. Understanding the network-related factors that affect the evolutionary stability of a strategy would be critical in making accurate predictions about the behaviour of a strategy in a real-world strategic decision making environment. In this work, we evaluate the effect of network topology on the evolutionary stability of a strategy. We focus on two well-known strategies known as the Zero-determinant strategy and the Pavlov strategy. Zero-determinant strategies have been shown to be evolutionarily unstable in a well-mixed population of players. We identify that the Zero-determinant strategy may survive, and may even dominate in a population of players connected through a non-homogeneous network. We introduce the concept of ‘topological stability’ to denote this phenomenon. We argue that not only the network topology, but also the evolutionary process applied and the initial distribution of strategies are critical in determining the evolutionary stability of strategies. Further, we observe that topological stability could affect other well-known strategies as well, such as the general cooperator strategy and the cooperator strategy. Our observations suggest that the variation of evolutionary stability due to topological stability of strategies may be more prevalent in the social context of strategic evolution, in comparison to the biological context.

3

Large population evolutionary games played within a life history framework

Ramsey D.

Badania Operacyjne i Decyzje

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2009

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nr 2

51-74

EN

In many evolutionary games, such as parental care games, the length of time spent playing a realisation of the game is dependent on the strategy of an individual. Also, the payoff of a deserting male cannot be defined in isolation from the strategies used in the population as a whole. Such games should be defined as games against the field (large population games) rather than two-player games. Several examples are presented to illustrate the theory of such games against the field.

PL

W dziedzinie gier ewolucyjnych zwykle zakłada się, że każda jednostka gra wiele razy w dany rodzaj gry dwuosobowej, z tym że za każdym razem jej przeciwnik zmienia się. W przypadku gier ewolucyjnych, takich jak „wojna na wyczerpanie” czy „opieka rodzicielska”, czas wykorzystany na realizację gry zależy od strategii wybranej przez jednostkę. W takich przypadkach należy brać pod uwagę nie tylko średnią wypłatę z każdej realizacji gry, ale też średni czas potrzebny na jej realizację. W tej sytuacji model standardowej gry dwuosobowej powinien być zastąpiony grą wieloosobową. Dodatkowo, w grach typu „opieka rodzicielska” wypłata samca, który nie opiekuje się swoimi dziećmi, zależy od możliwości uzyskania dodatkowych partnerek, co z kolei zależy od strategii używanych w całej populacji. W pracy rozważono kilka przykładów gier wieloosobowych, które są wygenerowane przez grę dwuosobową.