The Evolution of Extortion in Iterated Prisoner's Dilemma Games

Iterated games are a fundamental component of economic and evolutionary game theory. They describe situations where two players interact repeatedly and have the possibility to use conditional strategies that depend on the outcome of previous interactions. In the context of evolution of cooperation, repeated games represent the mechanism of reciprocation. Recently a new class of strategies has been proposed, so called 'zero determinant strategies'. These strategies enforce a fixed linear relationship between one's own payoff and that of the other player. A subset of those strategies are 'extortioners' which ensure that any increase in the own payoff exceeds that of the other player by a fixed percentage. Here we analyze the evolutionary performance of this new class of strategies. We show that in reasonably large populations they can act as catalysts for the evolution of cooperation, similar to tit-for-tat, but they are not the stable outcome of natural selection. In very small populations, however, relative payoff differences between two players in a contest matter, and extortioners hold their ground. Extortion strategies do particularly well in co-evolutionary arms races between two distinct populations: significantly, they benefit the population which evolves at the slower rate - an instance of the so-called Red King effect. This may affect the evolution of interactions between host species and their endosymbionts.Comment: contains 4 figure

Comparing reactive and memory-one strategies of direct reciprocity

Direct reciprocity is a mechanism for the evolution of cooperation based on repeated interactions. When individuals meet repeatedly, they can use conditional strategies to enforce cooperative outcomes that would not be feasible in one-shot social dilemmas. Direct reciprocity requires that individuals keep track of their past interactions and find the right response. However, there are natural bounds on strategic complexity: Humans find it difficult to remember past interactions accurately, especially over long timespans. Given these limitations, it is natural to ask how complex strategies need to be for cooperation to evolve. Here, we study stochastic evolutionary game dynamics in finite populations to systematically compare the evolutionary performance of reactive strategies, which only respond to the co-player's previous move, and memory-one strategies, which take into account the own and the co-player's previous move. In both cases, we compare deterministic strategy and stochastic strategy spaces. For reactive strategies and small costs, we find that stochasticity benefits cooperation, because it allows for generous-tit-for-tat. For memory one strategies and small costs, we find that stochasticity does not increase the propensity for cooperation, because the deterministic rule of win-stay, lose-shift works best. For memory one strategies and large costs, however, stochasticity can augment cooperation.Comment: 18 pages, 7 figure

The signal-burying game can explain why we obscure positive traits and good deeds

People sometimes make their admirable deeds and accomplishments hard to spot, such as by giving anonymously or avoiding bragging. Such ‘buried’ signals are hard to reconcile with standard models of signalling or indirect reciprocity, which motivate costly pro-social behaviour by reputational gains. To explain these phenomena, we design a simple game theory model, which we call the signal-burying game. This game has the feature that senders can bury their signal by deliberately reducing the probability of the signal being observed. If the signal is observed, however, it is identified as having been buried. We show under which conditions buried signals can be maintained, using static equilibrium concepts and calculations of the evolutionary dynamics. We apply our analysis to shed light on a number of otherwise puzzling social phenomena, including modesty, anonymous donations, subtlety in art and fashion, and overeagerness

Public good games with incentives

Public good games dienen als Modell für den Konflikt zwischen Allgemeinwohl und individuellem Vorteil: Während der Erfolg eines gemeinschaftlichen Projekts oft vom Einsatz aller Beteiligten abhängt, kann für den Einzelnen der Anreiz zum Trittbrettfahren bestehen. In dieser Dissertation untersuche ich das Zusammenspiel von Kooperation und Anreizsystemen mit Hilfe der evolutionären Spieltheorie. Es wird gezeigt, dass Belohnungen zwar individuelle Kooperation anstoßen können, dass aber Bestrafungsmöglichkeiten notwendig sind um die Zusammenarbeit aufrechtzuerhalten. Dabei liefert die individuelle Reputation der Spieler einen Anreiz, die Einhaltung von Normen zu überwachen und Abweichungen zu sanktionieren. Im Gegensatz zu früheren Studien werden Bestrafungsmechanismen jedoch nicht zur Stabilisierung von beliebigen Normen und Verhaltensvorschriften verwendet. Stattdessen werden Sanktionen gezielt dazu eingesetzt um die soziale Wohlfahrt zu verbessern. In dieser Dissertation stelle ich auch einige mathematischeWerkzeuge und methodische Konzepte vor, die bei der Untersuchung von Public good games hilfreich sind. Dazu wird die Theorie der Rollenspiele erweitert und eine modifizierte Replikatorgleichung eingeführt. Unter dieser lokalen Replikatordynamik können sich selbst dominierte Strategien durchsetzen, falls diese zu einem relativen Vorteil führen.Public good games reflect the common conflict between group interest and self interest: While collaborative projects depend on joint efforts of all participants, each individual performs best by free-riding on the others’ contributions. In this thesis I use evolutionary game dynamics to study the interplay of cooperation and incentives. I demonstrate that rewards may act as a catalyst for individual contributions, while punishment is needed to maintain mutual cooperation. In this process, reputation plays a key role: It helps to mitigate the second-order free-rider problem and prevents subjects from being spiteful. In contrast to previous studies, I do not find that punishment can promote any behaviour (as long as deviations from that norm are punished). Instead, sanctions are targeted at noncooperators only, and lead to stable cooperation. Furthermore, this thesis provides some mathematical tools for the study of public good games with incentives. It extends the theory of role games and it introduces a modified replicator dynamcis that allows to investigate the consequences of local competition. Under this local replicator dynamics, even dominated strategies may prevail if they lead to a relative payoff advantage – which can be considered as a basic model for the evolution of spite

Partners and rivals in direct reciprocity

Reciprocity is a major factor in human social life and accounts for a large part of cooperation in our communities. Direct reciprocity arises when repeated interactions occur between the same individuals. The framework of iterated games formalizes this phenomenon. Despite being introduced more than five decades ago, the concept keeps offering beautiful surprises. Recent theoretical research driven by new mathematical tools has proposed a remarkable dichotomy among the crucial strategies: successful individuals either act as partners or as rivals. Rivals strive for unilateral advantages by applying selfish or extortionate strategies. Partners aim to share the payoff for mutual cooperation, but are ready to fight back when being exploited. Which of these behaviours evolves depends on the environment. Whereas small population sizes and a limited number of rounds favour rivalry, partner strategies are selected when populations are large and relationships stable. Only partners allow for evolution of cooperation, while the rivals’ attempt to put themselves first leads to defection. Hilbe et al. synthesize recent theoretical work on zero-determinant and ‘rival’ versus ‘partner’ strategies in social dilemmas. They describe the environments under which these contrasting selfish or cooperative strategies emerge in evolution

Coevolutionary interactions between farmers and mafia induce host acceptance of avian brood parasites

Brood parasites exploit their host in order to increase their own fitness. Typically, this results in an arms race between parasite trickery and host defence. Thus, it is puzzling to observe hosts that accept parasitism without any resistance. The ‘mafia’ hypothesis suggests that these hosts accept parasitism to avoid retaliation. Retaliation has been shown to evolve when the hosts condition their response to mafia parasites, who use depredation as a targeted response to rejection. However, it is unclear if acceptance would also emerge when ‘farming’ parasites are present in the population. Farming parasites use depredation to synchronize the timing with the host, destroying mature clutches to force the host to re-nest. Herein, we develop an evolutionary model to analyse the interaction between depredatory parasites and their hosts. We show that coevolutionary cycles between farmers and mafia can still induce host acceptance of brood parasites. However, this equilibrium is unstable and in the long-run the dynamics of this host–parasite interaction exhibits strong oscillations: when farmers are the majority, accepters conditional to mafia (the host will reject first and only accept after retaliation by the parasite) have a higher fitness than unconditional accepters (the host always accepts parasitism). This leads to an increase in mafia parasites’ fitness and in turn induce an optimal environment for accepter hosts

Wiederholte Spiele mit Fehlern

Die Diplomarbeit widmet sich einem wiederholten Spiel, dem wiederholten donation game, einer Variante des Gefangenen-Dilemmas. Der Zug eines Spielers hängt annahmegemäß nur vom Ausgang der Vorrunde ab. Unter diesen Umständen wird untersucht, welche Strategie den größten Erfolg verspricht, wenn berücksichtigt wird, dass von Zeit zu Zeit Fehler passieren und z.B. der gegnerische Zug falsch interpretiert wird

Mutation enhances cooperation in direct reciprocity

Direct reciprocity is a powerful mechanism for evolution of cooperation based on repeated interactions between the same individuals. But high levels of cooperation evolve only if the benefit-to-cost ratio exceeds a certain threshold that depends on memory length. For the best-explored case of one-round memory, that threshold is two. Here we report that intermediate mutation rates lead to high levels of cooperation, even if the benefit-to-cost ratio is only marginally above one, and even if individuals only use a minimum of past information. This surprising observation is caused by two effects. First, mutation generates diversity which undermines the evolutionary stability of defectors. Second, mutation leads to diverse communities of cooperators that are more resilient than homogeneous ones. This finding is relevant because many real world opportunities for cooperation have small benefit-to-cost ratios, which are between one and two, and we describe how direct reciprocity can attain cooperation in such settings. Our result can be interpreted as showing that diversity, rather than uniformity, promotes evolution of cooperation.Comment: 37 pages, 14 figure

The evolution of indirect reciprocity under action and assessment generosity

Indirect reciprocity is a mechanism for the evolution of cooperation based on social norms. This mechanism requires that individuals in a population observe and judge each other’s behaviors. Individuals with a good reputation are more likely to receive help from others. Previous work suggests that indirect reciprocity is only effective when all relevant information is reliable and publicly available. Otherwise, individuals may disagree on how to assess others, even if they all apply the same social norm. Such disagreements can lead to a breakdown of cooperation. Here we explore whether the predominantly studied ‘leading eight’ social norms of indirect reciprocity can be made more robust by equipping them with an element of generosity. To this end, we distinguish between two kinds of generosity. According to assessment generosity, individuals occasionally assign a good reputation to group members who would usually be regarded as bad. According to action generosity, individuals occasionally cooperate with group members with whom they would usually defect. Using individual-based simulations, we show that the two kinds of generosity have a very different effect on the resulting reputation dynamics. Assessment generosity tends to add to the overall noise and allows defectors to invade. In contrast, a limited amount of action generosity can be beneficial in a few cases. However, even when action generosity is beneficial, the respective simulations do not result in full cooperation. Our results suggest that while generosity can favor cooperation when individuals use the most simple strategies of reciprocity, it is disadvantageous when individuals use more complex social norms

Small intestinal volvulus in 47 cows

OBJECTIVE: To describe the findings, treatment, and outcome of small intestinal volvulus (SIV) in 47 cows. ANIMALS AND PROCEDURE: Retrospective analysis of medical records. Comparison of the findings for 18 surviving and 29 non-surviving cows. RESULTS: The most common abnormal vital signs were tachycardia (68.0%), tachypnea (59.6%), and decreased rectal temperature (51.1%). Signs of colic occurred in 66.0% of cows in the study. Rumen motility was reduced or absent in 93.6% of cows, and intestinal motility in 76.6%. Clinical signs on ballottement and/or percussion and simultaneous auscultation were positive on the right side in 78.7% of cows. Transrectal examination showed dilated small intestines in 48.9% of cows. The rectum contained little or no feces in 93.6% of cows. The principal laboratory abnormalities were hypocalcemia (74.1%), hypokalemia (73.8%), azotemia (62.8%), hypermagnesemia (61.6%), and hemoconcentration (60.0%). The principal ultrasonographic findings were dilated small intestines (87.1%) and reduced or absent small intestinal motility (85.2%). Forty-one of the 47 cows underwent right flank laparotomy and the SIV was reduced in 21 cows. When comparing the clinical and laboratory findings of 18 surviving and 29 non-surviving cows, the groups differed significantly with respect to severely abnormal general condition (16.7 versus 37.9%), rumen stasis (22.2 versus 79.3%), intestinal atony (16.7 versus 48.3%), serum urea concentration (6.5 versus 9.8 mmol/L), and serum magnesium concentration (0.98 versus 1.30 mmol/L). In summary, 38.3% of the cows were discharged and 61.7% were euthanized before, during, or after surgery. CONCLUSION AND CLINICAL RELEVANCE: An acute course of disease, little or no feces in the rectum, and dilated small intestines were characteristic of SIV in this study population