Nowak, M. A., & May, R. M. (1992). Evolutionary games and spatial chaos. Nature, 359, 826-- 829.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....described by the model analysed here. The model is inspired by the possible effects of spatial heterogeneity, although true spatial structured interactions are not explored here. True spatial effects in a version of the Prisoner s Dilemma game have been thoroughly investigated by Nowak and May [14,15], who showed that spatial models with local effects, compared with panmictic models, can generate qualitatively different results in terms of coexistence or extinction of strategies. In a therapeutic context, the model suggests the intriguing possibility that gene therapy directed against ....

Nowak MA, May RM. Evolutionary games and spatial chaos. Nature 1992, 359, 82(829.

....Riolo Program for Study of Complex Systems The University of Michigan Ann Arbor, MI 48109 USA rlriolo umich.edu November, 1996 Abstract A simple model of tag mediated partner selection for agents playing the IPD is described. The agents strategies are represented as (i,q,q) triples as in [Nowak and May, 1992]. The tags are represented as arbitrary real numbers in [0, 1] and tag selection is biased toward agents with similar tags. Each agent plays a small sample of other agents each generation. The accumulated payoff from those plays is used as a fitness measure by an evolutionary algorithm which ....

.... individuals ( Stanley et al., 1994] Crowley et al. 1996] Individuals can be located in some spatial topology with a bias to inter act with nearby individuals, e.g. one dimensional grids ( Oliphant, 1994] Hoffmann and Waring, 1996] or two dimensional grids (pp.158 168 of [Axelrod, 1984] [Nowak and May, 1992], Grim, 1996] Individuals can use preferences for arbitrary tags (labels, surface markings) to bias selection of partners. Note that tag based selection of part ners in effect induces a kind of abstract topology in which the individuals are located near (prefer to interact) or far ....

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Nowak, Martin and May, R.M. "Evolutionary games and spatial chaos." Nature, 359, pp826-929.

....created randomly. A genetic algorithm[10] is then used to breed newer, more successful strategies (again, cumulative score in the IPD is taken as a measure of fitness) Different approaches have been taken to represent the strategies including: ffl (i; p; q) framework described in Nowak and May[12] and in Cohen and Axelrod [6] Three values are maintained: i, the probability of cooperating on the first move, p, the probability of cooperating following an opponent s cooperation and q, the probability of defecting following a defection by an opponent. For example, i = p = 1; q = 0 would ....

M.A. Nowak and R.M. May. Evolutionary games and spatial chaos. Nature, 335(827), 1992.

.... steady states and numerical computations in the framework of an ODE reaction model [1] For a cellular automata model it was shown numerically that a spiral wave structure may be stable against parasites [3] The chaotic dynamics for this type of model has been investigated numerically in [17] [28]. There are a number of recent results on the special case N = 1; n = 1 of our model, which is then also called Gray Scott system [13] 14] We would like to recall them here. In [10] by using Mel nikov method, Doelman, Kaper and Zegeling constructed single and multiple pulse solutions for (1.1) ....

M. A. Nowak and R. M. May, Evolutionary games and spatial chaos, Nature 359 (1993), 826-829.

....not permanent memory. This strategy would demonstrate behavioral gradualness and possess the potential for stability in front of changing worlds. In what follows, we are studying the issue of stability of the adaptive tit for tat strategy in spatial games of the sort introduced by Nowak and May ([12]) 2 The Adaptive Tit for Tat Strategy An adaptive tit for tat strategy should be essentially tit for tat in the sense of being good, retaliating and forgiving. Moreover, it should demonstrate some behavioral gradualness that would show as fewer oscillations between C and D. To this end, it ....

....intact. The same thing applies to the values of the observation window and the threshold, although they must be constrained so that the window will be sufficiently large and the threshold sufficiently small compared to the window. 3 Spatial Games I : Basic Model We have run spatial games ([12][9] in two dimensional grids consisting of diverse agents, i.e. agents having different IPD strategies. In these games, all agents run a finite IPD game against their neighbors at each cycle. After all games are finished, the agent at each place assumes the winner strategy among itself and its ....

Nowak, M.A., and May, R.M.: Evolutionary games and spatial chaos, Nature 359 (1992) 826-29

.... X N 1 Cooperate C 0 C 1 C x CN 1 Defect D 0 D 1 D x DN 1 There are a number of issues in the NIPD game which can in uence the evolution of gameplaying strategies and the nal evolved strategies, such as the payo function [6] noise [7] population structure [8], localization [9] the history length [10, 7, 3] the number of players [3] and so on. Most of the work did not use the evolutionary approach. The strategies used by players were largely xed. Yao and Darwen studied the NIPD game with N being up to 16 [3, 4, 5] Using the payo matrix given by ....

....opponents. However, the NIPD game with localization is a more realistic model of many real world systems. It is interesting to nd out the di erence between NIPD games with and without localization. Related work on the NIPD game with localization includes Nowak and May s work on spatial evolution [8]. In their model, a population of players are distributed on squares of a torus who are only capable of always defection (AD) and always cooperation (AC) Each player interacts only with his eight neighbors and imitates the strategy of any better performing one. Cooperative behavior can be ....

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M. A. Nowak and R. M. May, \Evolutionary games and spatial chaos," Nature, vol. 359, pp. 826-829, 29 October 1992.

.... be a very reliable estimate, it does appear that for most social networks quite a short chain is needed to connect even the most distant of the network s members [1] an observation which has important consequences for, amongst other things, the spread of disease [2,3] and evolutionary game theory [4], as well as related topics concerning genetic regulatory networks [5] and networks of synchronized oscillators [6,7] At rst sight this does not seem too surprising a result; random networks have average vertex vertex distances which increase as the logarithm of the number of vertices and which ....

M. A. Nowak and R. M. May, \Evolutionary games and spatial chaos", Nature 359, 826-829 (1992).

....suggests that in our real society with fundamentally imperfect information the action of referring to others behaviour causes such hindrance in the case of not only special goods but also ordinary goods and service. It is shown that the relationship between 5 In the model of Nowak and May [13], players adopts much simpler strategy. They always cooperate or always defect. In this case, the externally observable actions seem to coincide with the internal strategies. This coincident can, however, also be recognized only by external observers. Players cannot know whether strategy of others ....

Nowak, M. and May, R. (1992) Evolutionary Games and Spatial Chaos, Nature, vol. 359: 826-829.

....by marked rhythms. In order to do this, we will provide a simple way of de ning and measuring pseudo periodic behaviour, and use this measure to guide an evolutionary algorithm in the search for cases exhibiting this pseudo periodicity. Asynchrony as the default modelling choice The work by Nowak and May (1992) on spatial patterns in a population of players of the Prisoner s Dilemma is by now almost a classic in the growing literature on the role of artefacts in simulation models. The complex spatial patterns obtained in their model, which suggest interesting implications regarding the polymorphic ....

Nowak, M. A., & May, R. M. (1992). Evolutionary games and spatial chaos. Nature, 359, 836-829.

....between the actions of agents, are largely absent from simulation based models. Further characteristics of natural phenomena which prove difficult to incorporate within equational models include the representation of spatially distributed phenotypes, and repeated interactions between individuals (Nowak May, 1992; Lindgren Nordahl, 1994) The difficulty in constructing equational models of many verbal arguments is highlighted by Miller (1995) and Di Paolo (1996) Both suggest that simulation models of such arguments might prove easier to construct. However, some authors go further, claiming that ....

Nowak, M. A., & May, R. M. (1992). Evolutionary games and spatial chaos. Nature, 359, 826--829.

....obvious that it is rare that only two players play against each other. Further, it is also rare that all agents play all other agents. Typically, there is a network of connections between agents. One approach to studying such networks is to model them as spatial behavior on a d dimensional lattice [4, 2, 8, 21, 1]. Axelrod [4] already reports on experiments similar to ours on a lattice, but in his work agents play their neighbors separately. Almost all studies of evolutionary processes assume random or uniform matching rules in pairing players or strategies. This assumption corresponds to ergodicity ....

....i and i 1. In order to keep this scheme consistent, it is performed in going through the lattice sequentially, thus introducing some kind of anisotropy. It should be noted that after the initialization the whole game still is totally deterministic. The idea of a take over is the same as in [21]. But in contrast to the two strategies which were allowed in their model, we allow 2 16 different strategies (in the 2d case) We therefore restricted ourselves to only one payoff scheme. An increasing r leads to a higher number of dying agents. r is therefore reminiscent to the biological ....

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Nowak, M. A., and R. M. May, "Evolutionary games and spatial chaos." Nature 359 (1992):826.

....line of enquiry involves the application of simple learning rules within game theoretic environments (Liebrand Messick 1996) This approach assumes that agents are individual satisficing learners. Another approach applies selective mimicry from a spatial neighbourhood based on maximum payoff (Nowak May 1992). Although elegant, and able to produce cooperation, neither can produce sustained altruism where individual needs are driven by the needs of a group to the individuals detriment. Here, a fresh perspective on cooperation is applied which is a synthesis of these two approaches yet moves beyond ....

Nowak, M. & May R. (1992), "Evolutionary Games and Spatial Chaos." Nature, 359, pp826-929.

....of multiple satisfactions, or else governed by multiple hedonistic motivations, will unavoidably seek compromises between those motivations. Returning to the prisoner s dilemma and games theory that have benefited from a recent resurrection within the sciences of complexity and artificial life (Nowak May 1992), Sigmund 1992) Angeline 1994) Batali Kitcher 1994) the above presented quantitative tit for tat model may certainly be instantiated in such contexts by simply adding a special play maker agent who will set the rules of the interaction and will manipulate the rest of the agents by ....

....studies presented. 10 Humans are fortunately unlike animals in that they are able to scale this sociality, to learn different things and somehow choose to become social or the opposite. 11 The combined role of diversity and spatiality for the evolution of cooperation has been stressed in (Nowak May 1992), Nowak et al. 1995) 17 6 Lessons We have presented a model of social behavior based on reciprocity and participation (implicit kinship) The model is a generalization of the well known tit for tat model : generalization consists in having continuous satisfaction functions and cooperation ....

Nowak, M.A., R.M. May (1992). Evolutionary games and spatial chaos, Nature, 359:826-829, 1992.

....by Wedekind and Milinski (1997) support this distinction between strategies for the simultaneous and the alternating PD. If players do not interact at random, but only within a certain neighborhood structure, cooperation becomes much more readily established, even for the one shot PD (see Nowak and May, 1992 and 1993, Sigmund, 1992, Huberman and Glance, 1993, Nowak et al., 1994a,b, Lindgren and Nordahl, 1994, Killingback and Doebeli, 1996, and for a general introduction to cellular automata in this context, Durrett and Levin, 1994) Again, if players have the possibility of choice and refusal of ....

Nowak, M.A. and May, R.M. (1992) Evolutionary Games and Spatial Chaos, Nature 359, 826-29.

....cannot be maintained since there will always appear exploiting strategies that grows at the expense of the more cooperative ones. It is well known that the introduction of spatial dimensions may increase the possibility for cooperative behaviour, see e.g. Boerlijst and Hoegeweg 1991, 1992, Nowak and May 1992, 1993, Lindgren and Nordahl 1994a] In the CA model, the individuals are put on a 128x128 square lattice with periodic boundary conditions. Contrary to what we saw in the mean field case, cooperation is maintained for a large part of parameter space defining the PD game. This is made possible either by ....

Nowak, M. A., and May, R. M. (1993). "Evolutionary games and spatial chaos," Nature 359, 826-829.

....between individuals in a 2 dimensional grid produces separate groups with different cultures split along cultural barriers of non communication. An extension of this model into a resource sharing scenario shows that in group altruism and out group hostility readily emerge [13] Nowak and May [25] reduce the number of interaction partners to small overlapping spatially determined groups playing only pure strategies in single round PD. Agents are given the ability to determine (after each round) which agent within their spatial neighbourhood of interaction got the highest pay off and copy ....

Nowak, M. & May, R.: Evolutionary Games and Spatial Chaos. Nature, 359, (1992) 532554

.... be investigated more formally: when if ever do the agents find the optimal, i.e. stable, matching (in terms of Gale Shapley) and how, in general, does loyalty affect matching 6 This is possible because, in relation to Huberman and Glance s (1993) criticism regarding the synchronization in Nowak and May s (1992) prisoner s dilemma simulations, in each timestep, the order in which the different buyers are activated is randomized. 7 There are no switching costs in this case, since producing for a buyer who sells undifferentiated products requires no specific investments to be made. at the top are the ....

Nowak, Martin A. and Robert M. May (1992). Evolutionary games and spatial chaos. Nature 359, 826--829.

....simultaneously plays IPD against its neighbors. The cell s score is then compared to its neighbors and the highest scoring strategy is adopted by the cell at the next time step. In this case evolution was carried out with a fixed set of strategies, i.e. without application of genetic operators. In [Nowak and May, 1992] the dynamics of two interacting memoryless strategies were considered: cooperators and defectors (also known in the IPD literature as AllC and AllD) Spatiotemporal chaos was observed when interactions occured on a two dimensional grid. A spatial evolutionary model was also considered in ....

....are updated simultaneously at each time step. Recently, it has been observed that when asynchronous updating is used (i.e. one cell is updated at each time step) results may be different. For example, in [Huberman and Glance, 1993] it was shown that when asynchrony is introduced in the model of [Nowak and May, 1992] (see Section 4.3) a fixed state is arrived at rather than the chaotic spatiotemporal behavior induced by the synchronous model. Asynchrony has also been shown to freeze the game of life, i.e. convergence to a fixed point occurs, rather than complex, class IV phenomena of the synchronous model ....

M. A. Nowak and R. M. May. Evolutionary games and spatial chaos. Nature, 359:826--829, October 1992.

....in recent years of asynchronous updating [1, 13] and a recognition that the behaviour of synchronous and asynchronous versions can vary widely. In [7] it was pointed out by Huberman and Glance that CA simulations by Nowak and May of Prisoner s Dilemma interactions based on synchronous updating [10] lead to conclusions which cannot be justified when more realistic assumptions of asynchrony are tested out. This led to a response at the Third European Conference on Artificial Life by Nowak and May [9] There are, however, some situations where it may be more appropriate to work in continuous ....

M. A. Nowak and R. M. May. Evolutionary games and spatial chaos. Nature, 359:826--829, 1992.

....in a non spatial population. First, simulations involving the prisoner s dilemma will be presented, and then the framework will be applied to the problem of communication. Evidence from prisoner s dilemma simulations The earliest work done on spatializing the prisoner s dilemma was done by Nowak and May (1992). They used the prisoner s dilemma as an update rule for two dimensional cellular automata. In their simulations, cells could be in one of two states (cooperate or defect) and at each time step, every cell was replaced by the cell bordering it that had the highest summed payoff from playing the ....

Nowak, M. and R. May (1992). Evolutionary games and spatial chaos. Nature 359, 826--829.

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M. A. Nowak and R. M. May, Evolutionary games and spatial chaos, Nature 359 (1992) 826--829.

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M. A. Nowak & R. M. May, Evolutionary games and spatial chaos, Nature 359 (1993) 826--829.

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Nowak, M. A., & May, R. M. (1992). Evolutionary games and spatial chaos. Nature, 359, 826-- 829.

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NOWAK, M. A., AND R. M. MAY (1992): "Evolutionary Games and Spatial Chaos," Nature, 359, 826--829.

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M. Nowak and R. May. Evolutionary games and spatial chaos. Nature, 359:826-829, 1992.

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M. Nowak and R. May, "Evolutionary games and spatial chaos," Nature, vol. 359, no. 6398, pp. 826--829, Oct. 1992.

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M. A. Nowak and R. M. May. Evolutionary games and spatial chaos. Nature, 359:826-829, 1992.

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Nowak, M. A. and May, R. M. (1992). Evolutionary Games and Spatial Chaos. Nature 359. pp 826-829.

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Nowak, M. A. & May, R. M. 1992 Evolutionary Games and Spatial Chaos. Nature 359 826-829 and to appear in Int. J. Chaos Bifurc.

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TREE 10: 336-339. Nowak, M. A. and R. M. May 1992. Evolutionary games and spatial chaos. Nature 359: 826-829.

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