Accurate reactions open up the way for more cooperative societies

We consider a prisoner's dilemma model where the interaction neighborhood is defined by a square lattice. Players are equipped with basic cognitive abilities such as being able to distinguish their partners, remember their actions, and react to their strategy. By means of their short-term memory, they can remember not only the last action of their partner but the way they reacted to it themselves. This additional accuracy in the memory enables the handling of different interaction patterns in a more appropriate way and this results in a cooperative community with a strikingly high cooperation level for any temptation value. However, the more developed cognitive abilities can only be effective if the copying process of the strategies is accurate enough. The excessive extent of faulty decisions can deal a fatal blow to the possibility of stable cooperative relations

Diverging fluctuations in a spatial five-species cyclic dominance game

A five-species predator-prey model is studied on a square lattice where each species has two prey and two predators on the analogy to the Rock-Paper-Scissors-Lizard-Spock game. The evolution of the spatial distribution of species is governed by site exchange and invasion between the neighboring predator-prey pairs, where the cyclic symmetry can be characterized by two different invasion rates. The mean-field analysis has indicated periodic oscillations in the species densities with a frequency becoming zero for a specific ratio of invasion rates. When varying the ratio of invasion rates, the appearance of this zero-eigenvalue mode is accompanied by neutrality between the species associations. Monte Carlo simulations of the spatial system reveal diverging fluctuations at a specific invasion rate, which can be related to the vanishing dominance between all pairs of species associations.Comment: accepted for publication in Physical Review

From pairwise to group interactions in games of cyclic dominance

We study the rock-paper-scissors game in structured populations, where the invasion rates determine individual payoffs that govern the process of strategy change. The traditional version of the game is recovered if the payoffs for each potential invasion stem from a single pairwise interaction. However, the transformation of invasion rates to payoffs also allows the usage of larger interaction ranges. In addition to the traditional pairwise interaction, we therefore consider simultaneous interactions with all nearest neighbors, as well as with all nearest and next-nearest neighbors, thus effectively going from single pair to group interactions in games of cyclic dominance. We show that differences in the interaction range affect not only the stationary fractions of strategies, but also their relations of dominance. The transition from pairwise to group interactions can thus decelerate and even revert the direction of the invasion between the competing strategies. Like in evolutionary social dilemmas, in games of cyclic dominance too the indirect multipoint interactions that are due to group interactions hence play a pivotal role. Our results indicate that, in addition to the invasion rates, the interaction range is at least as important for the maintenance of biodiversity among cyclically competing strategies.Comment: 7 two-column pages, 6 figures; accepted for publication in Physical Review

Evolúciós játékok gráfokon = Evolutionary games on graphs

Kutatási programunkban az evolúciós játékok különböző változatait vizsgáltuk hálózatokon. Az evolúciós Fogolydilemma játékok elemzését kiterjesztettük más társadalmi dilemmák tanulmányozására, hogy pontosabb képet kapjunk a közösség javát szolgáló magatartás fenntartásának körülményeiről. Vizsgáltuk, hogy mi történik akkor, ha bővítjük a stratégiateret különböző jellegű büntetések lehetőségével. A koevolúciós játékok szellemében tanulmányoztuk azokat az eseteket, amikor játékosaink nemcsak a stratégiájukat, hanem kapcsolataikat illetve az egyéni evolúciós szabályt is változtathatták. Bevezettünk olyan modelleket, amelyek a személyes tulajdonságok (pl. tekintély, kor, testvériesség) következményeinek tanulmányozását is lehetővé tették. Ezek a vizsgálatok mind azt példázták, hogy az említett jelenségek figyelembe vétele segíti a társadalom számára előnyös magatartás fennmaradását. Az elmúlt két évben érdeklődésünk a többszereplős közlegelő játékra épülő kölcsönhatások felé fordult. Ezek a rendszerek közelebb vannak a valósághoz, az eredmények kevésbé érzékenyek a kapcsolatrendszer topológiai tulajdonságaira és a hatótávolság növelése miatt érdekes határfelületi jelenségek szerepére hívták fel a figyelmünket. A stratégiák számának növelése olyan komplex mintázatok megjelenésével járt együtt, amelyek leírásánál már a stratégia-társulások közötti versenyzést is figyelembe kellett venni. Röviden, írtunk 34 cikket, amelyekre eddig kb. 750 hivatkozást kaptunk. | We have studied different versions of evolutionary games on networks. In order to have more accurate pictures about the conditions supporting the cooperative behaviors the investigation of the Prisoner's Dilemma is extended to other social dilemmas. In addition we have studied what happens when increasing the number of strategies, for example, by allowing the chance of different punishments. Within the framework of the coevolutionary games we have investigated models where the players are allowed to modify their connections and their individual evolutionary rules. We have extended these models to study the consequences of some personal features, including reputation, age, and fraternity. All the mentioned models have exemplified ways how the cooperative behavior can be maintained in societies. In the last two years we begun to study systematically the spatial versions of public goods games because this types of multi-player games are more realistic, these models are less sensitive to the connectivity structure, and yield the appearance of interesting interfacial phenomena due to the enhanced range of interactions. The increase in the number of strategies results in complex patterns that can be interpreted as a competition between strategy associations. In short, the above results are published in 34 articles cited about 750 times up to now

Evolutionary prisoner's dilemma game on hierarchical lattices

An evolutionary prisoner's dilemma (PD) game is studied with players located on a hierarchical structure of layered square lattices. The players can follow two strategies [D (defector) and C (cooperator)] and their income comes from PD games with the ``neighbors.'' The adoption of one of the neighboring strategies is allowed with a probability dependent on the payoff difference. Monte Carlo simulations are performed to study how the measure of cooperation is affected by the number of hierarchical levels (Q) and by the temptation to defect. According to the simulations the highest frequency of cooperation can be observed at the top level if the number of hierarchical levels is low (Q<4). For larger Q, however, the highest frequency of cooperators occurs in the middle layers. The four-level hierarchical structure provides the highest average (total) income for the whole community.Comment: appendix adde

Evolutionary Prisoner's Dilemma game on the Newman-Watts networks

Maintenance of cooperation was studied for a two-strategy evolutionary Prisoner's Dilemma game where the players are located on a one-dimensional chain and their payoff comes from games with the nearest and next-nearest neighbor interactions. The applied host geometry makes possible to study the impacts of two conflicting topological features. The evolutionary rule involves some noise affecting the strategy adoptions between the interacting players. Using Monte Carlo simulations and the extended versions of dynamical mean-field theory we determined the phase diagram as a function of noise level and a payoff parameter. The peculiar feature of the diagram is changed significantly when the connectivity structure is extended by extra links as suggested by Newman and Watts.Comment: 4 figure

Adaptív ökológia változó környezetben = Adaptive ecology in variable environment

A pályázat alapkérdése a versengés és együttélés, szelekció és sokféleség viszonya úgy ökológiai, mint evolúciós szempontból: ökológiában niche elmélet; evolúcióelméletben fajkeletkezés. Ökológiai eredményeink legfontosabbika a korlátozott hasonlóság modell-független elmélete, amely az együttélés robusztusságát összeköti az együttélő fajok közötti - pontos matematikai értelemben vett - niche szegregációval. Az általános összefüggés konkrét megnyilvánulásait specifikus esetekben vizsgáltuk, a klasszikus Lotka-Volterra versengési modelltől a térben strukturált, illetve időben fluktuáló esetekig. Evolúciós kutatásaink a divergens evolúció lehetőségéről szólnak. Az adaptív dinamika elméletének egy új megalapozását adtuk meg, amely azt a populációdinamikából vezeti le a kis evolúciós lépések feltételezésével. Biológiailag ez a populációreguláció és az adaptív tájkép fogalma összekapcsolásának felel meg és megalapozza a szétágazó evolúció niche-szétválásként való értelmezését. A fajkeletkezési probléma másik oldalát, a reproduktív izoláció létrejöttét egy analitikusan kezelhető minimál-modellben vizsgáltuk. A pályázat eredményeiből 13 nemzetközi publikáció született, amelyek együttes impakt faktora 38. | The basic issue of the work, reported here, is the relationship between competition and coexistence; selection and diversity from ecological as well as from evolutionary point of view. In ecology it corresponds to niche theory; in evolutionary theory it is speciation. Our most important ecological result is a model-independent theory of limiting similarity. It connects robustness of coexistence to niche differentiation in a precise mathematical way. We studied the implementations of this general framework in several specific cases from the classical Lotka-Voltarra model to spatially explicit and temporally fluctuating situations. Our evolutionary investigations are concerned about divergent evolution. A new underpinning of adaptive dynamics was introduced: it was derived from the explicitly considered underlying population dynamics with the single assumption of evolution via small steps. From biological point of view it corresponds to establishing a connection between the notions of adaptive landscape and population regulation. The other side of the speciation problem, the emergence of reproductive isolation was studied in an analytically tractable minimal model. We published 13 papers with cumulative impact factor 38