Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userReciprocal and Extortive Strategies: Infinitely Iterated Prisoners Dilemma
91
0
0.0
(
0
)
Authors
Robert D. Young
Ask ChatGPT about the research
No Arabic abstract
The Prisoners Dilemma game has a long history stretching across the social, biological, and physical sciences. In 2012, Press and Dyson developed a method for analyzing the mapping of the 8-dimensional strategy profile onto the 2-dimensional payoff space in an infinitely iterated Prisoners Dilemma game, based on Markov chain analysis and memory-one strategies. We generalize this approach and introduce the concept of strategy parameter to show that linear relations among player payoffs are a ubiquitous feature of the infinitely iterated Prisoners Dilemma game. Our extended analysis is applied to various strategy profiles including tit-for-tat, win-stay-lose-shift, and other randomized strategy sets. Strategy profiles are identified that map onto the vertices, edges, and interior of the Prisoners Dilemma quadrilateral in the 2-dimensional payoff (score) space. A DaMD strategy is defined based solely on Defection after Mutual Defection and leads to linear relations between player scores using strategy parameter analysis. The DaMD strategy is shown to result in an equal (reciprocal) or larger (extortive) score for its user compare to the other player, independent of the strategy of the other player. The extortive scores occur when the probabilities for the DaMD player to cooperate after conflicting plays (cooperate-defect or defect-cooperate) sum to less than 1. The equal reciprocal scores occur when the probabilities for the DaMD player to cooperate after conflicting plays (cooperate-defect or defect-cooperate) sum to 1. When one player selects the extortive DaMD, the opposing player can force the equal punishment payoffs for both players in the infinitely iterated Prisoners dilemma by also choosing the DaMD strategy. Possible pathways to mutual cooperation based on DaMD are discussed.
rate research
Read More
We present tournament results and several powerful strategies for the Iterated Prisoners 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.
The conventional wisdom is that scale-free networks are prone to cooperation spreading. In this paper we investigate the cooperative behaviors on the structured scale-free network. On the contrary of the conventional wisdom that scale-free networks are prone to cooperation spreading, the evolution of cooperation is inhibited on the structured scale-free network while performing the prisoners dilemma (PD) game. Firstly, we demonstrate that neither the scale-free property nor the high clustering coefficient is responsible for the inhibition of cooperation spreading on the structured scale-free network. Then we provide one heuristic method to argue that the lack of age correlations and its associated `large-world behavior in the structured scale-free network inhibit the spread of cooperation. The findings may help enlighten further studies on evolutionary dynamics of the PD game in scale-free networks.
The paradox of cooperation among selfish individuals still puzzles scientific communities. Although a large amount of evidence has demonstrated that cooperator clusters in spatial games are effective to protect cooperators against the invasion of defectors, we continue to lack the condition for the formation of a giant cooperator cluster that assures the prevalence of cooperation in a system. Here, we study the dynamical organization of cooperator clusters in spatial prisoners dilemma game to offer the condition for the dominance of cooperation, finding that a phase transition characterized by the emergence of a large spanning cooperator cluster occurs when the initial fraction of cooperators exceeds a certain threshold. Interestingly, the phase transition belongs to different universality classes of percolation determined by the temptation to defect $b$. Specifically, on square lattices, $1<b<4/3$ leads to a phase transition pertaining to the class of regular site percolation, whereas $3/2<b<2$ gives rise to a phase transition subject to invasion percolation with trapping. Our findings offer deeper understanding of the cooperative behaviors in nature and society.
The Axelrod library is an open source Python package that allows for reproducible game theoretic research into the Iterated Prisoners Dilemma. This area of research began in the 1980s but suffers from a lack of documentation and test code. The goal of the library is to provide such a resource, with facilities for the design of new strategies and interactions between them, as well as conducting tournaments and ecological simulations for populations of strategies. With a growing collection of 139 strategies, the library is a also a platform for an original tournament that, in itself, is of interest to the game theoretic community. This paper describes the Iterated Prisoners Dilemma, the Axelrod library and its development, and insights gained from some novel research.
Since the introduction of zero-determinant strategies, extortionate strategies have received considerable interest. While an interesting class of strategies, the definitions of extortionate strategies are algebraically rigid, apply only to memory-one strategies, and require complete knowledge of a strategy (memory-one cooperation probabilities). We describe a method to detect extortionate behaviour from the history of play of a strategy. When applied to a corpus of 204 strategies this method detects extortionate behaviour in well-known extortionate strategies as well others that do not fit the algebraic definition. The highest performing strategies in this corpus are able to exhibit selectively extortionate behavior, cooperating with strong strategies while exploiting weaker strategies, which no memory-one strategy can do. These strategies emerged from an evolutionary selection process and their existence contradicts widely-repeated folklore in the evolutionary game theory literature: complex strategies can be extraordinarily effective, zero-determinant strategies can be outperformed by non-zero determinant strategies, and longer memory strategies are able to outperform short memory strategies. Moreover, while resistance to extortion is critical for the evolution of cooperation, the extortion of weak opponents need not prevent cooperation between stronger opponents, and this adaptability may be crucial to maintaining cooperation in the long run.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
