Correction: Forgiver Triumphs in Alternating Prisoner's Dilemma
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PROVIDER: S-EPMC3897288 | biostudies-literature | 2014 Jan
REPOSITORIES: biostudies-literature
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Project description:Cooperative behavior, where one individual incurs a cost to help another, is a wide spread phenomenon. Here we study direct reciprocity in the context of the alternating Prisoner's Dilemma. We consider all strategies that can be implemented by one and two-state automata. We calculate the payoff matrix of all pairwise encounters in the presence of noise. We explore deterministic selection dynamics with and without mutation. Using different error rates and payoff values, we observe convergence to a small number of distinct equilibria. Two of them are uncooperative strict Nash equilibria representing always-defect (ALLD) and Grim. The third equilibrium is mixed and represents a cooperative alliance of several strategies, dominated by a strategy which we call Forgiver. Forgiver cooperates whenever the opponent has cooperated; it defects once when the opponent has defected, but subsequently Forgiver attempts to re-establish cooperation even if the opponent has defected again. Forgiver is not an evolutionarily stable strategy, but the alliance, which it rules, is asymptotically stable. For a wide range of parameter values the most commonly observed outcome is convergence to the mixed equilibrium, dominated by Forgiver. Our results show that although forgiving might incur a short-term loss it can lead to a long-term gain. Forgiveness facilitates stable cooperation in the presence of exploitation and noise.
| S-EPMC3861238 | biostudies-literature
Project description:As tumors outgrow their blood supply and become oxygen deprived, they switch to less energetically efficient but oxygen-independent anaerobic glucose metabolism. However, cancer cells maintain glycolytic phenotype even in the areas of ample oxygen supply (Warburg effect). It has been hypothesized that the competitive advantage that glycolytic cells get over aerobic cells is achieved through secretion of lactic acid, which is a by-product of glycolysis. It creates acidic microenvironment around the tumor that can be toxic to normal somatic cells. This interaction can be seen as a prisoner's dilemma: from the point of view of metabolic payoffs, it is better for cells to cooperate and become better competitors but neither cell has an incentive to unilaterally change its metabolic strategy. In this paper a novel mathematical technique, which allows reducing an otherwise infinitely dimensional system to low dimensionality, is used to demonstrate that changing the environment can take the cells out of this equilibrium and that it is cooperation that can in fact lead to the cell population committing evolutionary suicide.
| S-EPMC3237466 | biostudies-literature
Project description:Iterated games are a fundamental component of economic and evolutionary game theory. They describe situations where two players interact repeatedly and have the ability to use conditional strategies that depend on the outcome of previous interactions, thus allowing for 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 allows "extortioners" to ensure that any increase in one player's 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 that they are not the stable outcome of natural selection. In very small populations, however, extortioners hold their ground. Extortion strategies do particularly well in coevolutionary arms races between two distinct populations. Significantly, they benefit the population that evolves at the slower rate, an example of the so-called "Red King" effect. This may affect the evolution of interactions between host species and their endosymbionts.
| S-EPMC3637695 | biostudies-literature
Project description:BackgroundThe neuropeptides oxytocin and vasopressin have been repeatedly implicated in social decision making by enhancing social salience and, generally, cooperation. The iterated and sequential version of the prisoner's dilemma (PD) game is a social dilemma paradigm eliciting strategies of cooperation versus competition.AimsWe aimed to characterise the role of PD players' sex, game partner type (computer vs. human) and oxytocin or vasopressin inhalation on the player's strategy preference.MethodsParticipants (153 men; 151 women) were randomised to intranasal 24 IU oxytocin, 20 IU vasopressin or placebo, double-blind, and played the PD. We examined main and interactive effects of sex, drug and partner type on strategy preference.ResultsWe found a pervasive preference for a tit-for-tat strategy (i.e. general sensitivity to the partner's choices) over unconditional cooperation, particularly when against a human rather than a computer partner. Oxytocin doubled this sensitivity in women (i.e. the preference for tit-for-tat over unconditional cooperation strategies) when playing against computers, which suggests a tendency to anthropomorphise them, and doubled women's unconditional cooperation preference when playing against humans. Vasopressin doubled sensitivity to the partner's previous choices (i.e. for tit-for-tat over unconditional cooperation) across sexes and partner types.ConclusionsThese findings suggest that women may be more sensitive to oxytocin's social effects of anthropomorphism of non-humans and of unconditional cooperation with humans, which may be consistent with evolutionary pressures for maternal care, and that vasopressin, irrespective of sex and partner type, may be generally sensitising humans to others' behaviour.
| S-EPMC7583454 | biostudies-literature
Project description:Currently, there is no satisfying answer to how cooperation arises rationally in a single-play prisoner's dilemma game with complete information. When player types are known, as well as payoffs and actions, economic analysis through payoff-optimizing computation does not provide a clear path for cooperation. We propose a new form of game-the 'expected' game-and illustrate its implications for theory and practice based on the prisoner's dilemma example. We prove that cooperation can be a rational choice for players in reality in such games defined by a weighted set of payoffs of two or more different reference games.
| S-EPMC7526889 | biostudies-literature
Project description:Cooperation is a central mechanism for evolution. It consists of an individual paying a cost in order to benefit another individual. However, natural selection describes individuals as being selfish and in competition among themselves. Therefore explaining the origin of cooperation within the context of natural selection is a problem that has been puzzling researchers for a long time. In the paradigmatic case of the Prisoner's Dilemma (PD), several schemes for the evolution of cooperation have been proposed. Here we introduce an extension of the Replicator Equation (RE), called the Optimal Replicator Equation (ORE), motivated by the fact that evolution acts not only at the level of individuals of a population, but also among competing populations, and we show that this new model for natural selection directly leads to a simple and natural rule for the emergence of cooperation in the most basic version of the PD. Contrary to common belief, our results reveal that cooperation can emerge among selfish individuals because of selfishness itself: if the final reward for being part of a society is sufficiently appealing, players spontaneously decide to cooperate.
| S-EPMC5792647 | biostudies-literature
Project description:We study a spatial, one-shot prisoner's dilemma (PD) model in which selection operates on both an organism's behavioral strategy (cooperate or defect) and its decision of when to implement that strategy, which we depict as an organism's choice of one point in time, out of a set of discrete time slots, at which to carry out its PD strategy. Results indicate selection for cooperators across various time slots and parameter settings, including parameter settings in which cooperation would not evolve in an exclusively spatial model-as in work investigating exogenously imposed temporal networks. Moreover, in the presence of time slots, cooperators' portion of the population grows even under different combinations of spatial structure, transition rules, and update dynamics, though rates of cooperator fixation decline under pairwise comparison and synchronous updating. These findings indicate that, under certain evolutionary processes, merely existing in time and space promotes the evolution of cooperation.
| S-EPMC8589994 | biostudies-literature
Project description:Zero-determinant (ZD) strategies, as discovered by Press and Dyson, can enforce a linear relationship between a pair of players' scores in the iterated prisoner's dilemma. Particularly, the extortionate ZD strategies can enforce and exploit cooperation, providing a player with a score advantage, and consequently higher scores than those from either mutual cooperation or generous ZD strategies. In laboratory experiments in which human subjects were paired with computer co-players, we demonstrate that both the generous and the extortionate ZD strategies indeed enforce a unilateral control of the reward. When the experimental setting is sufficiently long and the computerized nature of the opponent is known to human subjects, the extortionate strategy outperforms the generous strategy. Human subjects' cooperation rates when playing against extortionate and generous ZD strategies are similar after learning has occurred. More than half of extortionate strategists finally obtain an average score higher than that from mutual cooperation.
| S-EPMC4832060 | biostudies-literature
Project description:We present tournament results and several powerful strategies for the Iterated Prisoner's Dilemma created using reinforcement learning techniques (evolutionary and particle swarm algorithms). These strategies are trained to perform well against a corpus of over 170 distinct opponents, including many well-known and classic strategies. All the trained strategies win standard tournaments against the total collection of other opponents. The trained strategies and one particular human made designed strategy are the top performers in noisy tournaments also.
| S-EPMC5724862 | biostudies-literature
Project description:Recent work has revealed a new class of "zero-determinant" (ZD) strategies for iterated, two-player games. ZD strategies allow a player to unilaterally enforce a linear relationship between her score and her opponent's score, and thus to achieve an unusual degree of control over both players' long-term payoffs. Although originally conceived in the context of classical two-player game theory, ZD strategies also have consequences in evolving populations of players. Here, we explore the evolutionary prospects for ZD strategies in the Iterated Prisoner's Dilemma (IPD). Several recent studies have focused on the evolution of "extortion strategies," a subset of ZD strategies, and have found them to be unsuccessful in populations. Nevertheless, we identify a different subset of ZD strategies, called "generous ZD strategies," that forgive defecting opponents but nonetheless dominate in evolving populations. For all but the smallest population sizes, generous ZD strategies are not only robust to being replaced by other strategies but can selectively replace any noncooperative ZD strategy. Generous strategies can be generalized beyond the space of ZD strategies, and they remain robust to invasion. When evolution occurs on the full set of all IPD strategies, selection disproportionately favors these generous strategies. In some regimes, generous strategies outperform even the most successful of the well-known IPD strategies, including win-stay-lose-shift.
| S-EPMC3780848 | biostudies-literature