arXiv subjects

Anders Eriksson

Publications and source records attributed to Anders Eriksson.

41 records · Page 3Linked to original sources

arXiv2006

The effect of finite population size on the evolutionary dynamics in multi-person Prisoner's Dilemma

We study the influence of stochastic effects due to finite population size in the evolutionary dynamics of populations interacting in the multi-person Prisoner's Dilemma game. This paper is an extension of the investigation presented in a recent paper [Eriksson and Lindgren (2005), J. Theor. Biol. 232(3), 399]. One of the main results of the previous study is that there are modes of dynamic behaviour, such as limit cycles and fixed points, that are maintained due to a non-zero mutation level, resulting in a significantly higher level of cooperation than was reported in earlier studies. In the present study, we investigate two mechanisms in the evolutionary dynamics for finite populations: (i) a stochastic model of the mutation process, and (ii) a stochastic model of the selection process. The most evident effect comes from the second extension, where we find that a previously stable limit cycle is replaced by a trajectory that to a large extent is close to a fixed point that is stable in the deterministic model. The effect is strong even when population size is as large as 10,000. The effect of the first mechanism is less pronounced, and an argument for this difference is given.

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arXiv2006

A simple model of cognitive processing in repeated games

In repeated interactions between individuals, we do not expect that exactly the same situation will occur from one time to another. Contrary to what is common in models of repeated games in the literature, most real situations may differ a lot and they are seldom completely symmetric. The purpose of this paper is to discuss a simple model of cognitive processing in the context of a repeated interaction with varying payoffs. The interaction between players is modelled by a repeated game with random observable payoffs. Cooperation is not simply associated with a certain action but needs to be understood as a phenomenon of the behaviour in the repeated game. The players are thus faced with a more complex situation, compared to the Prisoner's Dilemma that has been widely used for investigating the conditions for cooperation in evolving populations. Still, there are robust cooperating strategies that usually evolve in a population of players. In the cooperative mode, these strategies select an action that allows for maximizing the sum of the payoff of the two players in each round, regardless of the own payoff. Two such players maximise the expected total long-term payoff. If the opponent deviates from this scheme, the strategy invokes a punishment action, which aims at lowering the opponent's score for the rest of the (possibly infinitely) repeated game. The introduction of mistakes to the game actually pushes evolution towards more cooperative strategies even though the game becomes more difficult.

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arXiv2005

Quasi-Species and Aggregate Dynamics

At an early stage in pre-biotic evolution, groups of replicating molecules must coordinate their reproduction to form aggregated units of selection. Mechanisms that enable this to occur are currently not well understood. In this paper we introduce a deterministic model of primitive replicating aggregates, proto-organisms, that host populations of replicating information carrying molecules. Some of the molecules promote the reproduction of the proto-organism at the cost of their individual replication rate. A situation resembling that of group selection arises. We derive and analytically solve a partial differential equation that describes the system. We find that the relative prevalence of fast and slow replicators is determined by the relative strength of selection at the aggregate level to the selection strength at the molecular level. The analysis is concluded by a preliminary treatment of finite population size effects.

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arXiv2004

Cooperation driven by mutations in multi-person Prisoner's Dilemma

The n-person Prisoner's Dilemma is a widely used model for populations where individuals interact in groups. The evolutionary stability of populations has been analysed in the literature for the case where mutations in the population may be considered as isolated events. For this case, and assuming simple trigger strategies and many iterations per game, we analyse the rate of convergence to the evolutionarily stable populations. We find that for some values of the payoff parameters of the Prisoner's Dilemma this rate is so low that the assumption, that mutations in the population are infrequent on that timescale, is unreasonable. Furthermore, the problem is compounded as the group size is increased. In order to address this issue, we derive a deterministic approximation of the evolutionary dynamics with explicit, stochastic mutation processes, valid when the population size is large. We then analyse how the evolutionary dynamics depends on the following factors: mutation rate, group size, the value of the payoff parameters, and the structure of the initial population. In order to carry out the simulations for groups of more than just a few individuals, we derive an efficient way of calculating the fitness values. We find that when the mutation rate per individual and generation is very low, the dynamics is characterised by populations which are evolutionarily stable. As the mutation rate is increased, other fixed points with a higher degree of cooperation become stable. For some values of the payoff parameters, the system is characterised by (apparently) stable limit cycles dominated by cooperative behaviour. The parameter regions corresponding to high degree of cooperation grow in size with the mutation rate, and in number with the group size.

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arXiv2004

War of attrition with implicit time cost

In the game-theoretic model war of attrition, players are subject to an explicit cost proportional to the duration of contests. We construct a model where the time cost is not explicitly given, but instead depends implicitly on the strategies of the whole population. We identify and analyse the underlying mechanisms responsible for the implicit time cost. Each player participates in a series of games, where those prepared to wait longer win with higher certainty but play less frequently. The model is characterised by the ratio of the winner's score to the loser's score, in a single game. The fitness of a player is determined by the accumulated score from the games played during a generation. We derive the stationary distribution of strategies under the replicator dynamics. When the score ratio is high, we find that the stationary distribution is unstable, with respect to both evolutionary and dynamical stability, and the dynamics converge to a limit cycle. When the ratio is low, the dynamics converge to the stationary distribution. For an intermediate interval of the ratio, the distribution is dynamically but not evolutionarily stable. Finally, the implications of our results for previous models based on the war of attrition are discussed.

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