Strategies In Prisoner's Dilemma Research Articles

Application of the Iterated Prisoner's Dilemma and Evolutionary Game Theory in Siting Nuclear Power Plants in South Korea

The quality of an urban living environment largely depends on the planning and development of public facilities, which are often halted or delayed due to the NIMBY (not in my backyard) phenomenon. In such facilities, environmental costs are borne solely by the residents of proximity to the facility, while public goods/services produced by the facility are reaped equally by residents across the greater region, which in turn presents a complex dynamic of public and self-interest. This paper uses repeated games and evolutionary game theory to identify the optimal negotiation strategy for the government when siting nuclear power plant facilities in South Korea. This study simulated a tournament containing 36 selected iterated prisoner's dilemma strategies and considered factors including mean payoff values, payoff matrices, and Axelrod's Ecological Variant to deduce an optimal strategy. The results showed that AON2, a memory-2 strategy of direct reciprocity, would provide the most stable and high return negotiations.

Prime numbers and the evolution of cooperation, II: Advantages to cooperators using prime-number period lengths in a finite population constrained to prisoner's dilemma strategies that alternate between periods of activity and inactivity

• The paper reports a model of a finite population of agents constrained to strategies that alternate between activity and inactivity (a.k.a. temporal partitioning) in a social environment where multiple one-shot prisoner's dilemma games occur across discrete, intra-generational time points. • Numerical simulation of the model indicates that cooperators reach fixation with far greater frequency when using schedules with prime-number period lengths. • Simulation results dovetail with the findings of a recent analytic model that confirmed a longstanding, hypothesized link between the prime numbers and the evolution of cooperation. • The findings suggest that schedules with prime-number period lengths constitute a new mechanism for the evolution of cooperation. • Viewed in concert with the findings of past-predator prey models, the results raise the possibility that cyclical behavior with prime-number period lengths might serve as an adaptive solution to a range of challenges that lifeforms face. This paper presents a model of a finite population of agents constrained to strategies that alternate between activity and inactivity (a.k.a. temporal partitioning) in a social environment where multiple one-shot prisoner's dilemma games occur across discrete, intra-generational time points. Evolutionary selection acts on agents’ behavioral dispositions to cooperate/defect and the schedules that determine when agents periodically implement that behavior. Numerical simulation of the model indicates that cooperators reach fixation with far greater frequency when using schedules with prime-number period lengths. These findings reinforce recent analytic findings that indicate a connection between the evolution of cooperation and the prime numbers, plus they offer new empirical predictions about the timing of social behavior.

Oyun: A New, Free Program for Iterated Prisoner's Dilemma Tournaments in the Classroom

Abstract Evolutionary applications of game theory present one of the most pedagogically accessible varieties of genuine, contemporary theoretical biology. We present here Oyun (oy-oon, http://charlespence.net/oyun), a program designed to run iterated prisoner's dilemma tournaments, competitions between prisoner's dilemma strategies developed by the students themselves. Using this software, students are able to readily design and tweak their own strategies, and to see how they fare both in round-robin tournaments and in “evolutionary” tournaments, where the scores in a given “generation” directly determine contribution to the population in the next generation. Oyun is freely available, runs on Windows, Mac, and Linux computers, and the process of creating new prisoner's dilemma strategies is both easy to teach and easy for students to grasp. We illustrate with two interesting examples taken from actual use of Oyun in the classroom.

Fingerprinting: Visualization and Automatic Analysis of Prisoner's Dilemma Strategies

Fingerprinting is a technique for generating a representation-independent functional signature for a game playing agent. Fingerprints can be used to compare agents across representations in an automatic fashion. The theory of fingerprints is developed for software agents that play the iterated prisoner's dilemma. Examples of the technique for computing fingerprints are given. This paper summarizes past results and introduces the following new results. Fingerprints of prisoner's dilemma strategies that are represented as finite-state machines must be rational functions. An example of a strategy that does not have a finite-state representation and which does not have a rational fingerprint function is given: the majority strategy. It is shown that the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">AllD</i> - and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">AllC</i> -based fingerprints can be derived from the tit-for-tat fingerprint by a simple substitution. Fingerprints for four new probe strategies are introduced, generalizing previous work in which tit-for-tat is the sole probe strategy. A trial comparison is made of evolved prisoner's dilemma strategies across three representations: finite-state machines, feedforward neural nets, and lookup tables. Fingerprinting demonstrates that all three representations sample the strategy space in a radically different manner, even though the neural net's and lookup table's parameters are alternate encodings of the same strategy space. This space of strategies is also a subset of those encoded by the finite-state representation. Shortcomings of the fingerprint technique are outlined, with illustrative examples, and possible paths to overcome these shortcomings are given.

Evolution of prisoner's dilemma strategies on scale-free networks

The evolution of strategies in the iterated prisoner's dilemma on scale-free networks is investigated. It is found that the smaller the average degree is, the easier it is to promote cooperation by natural selection. Cooperation on scale-free networks built upon big clustering coefficients is enhanced and maintained at a high level. The introduction of punishment strategy for unsatisfied agents also increases cooperation and improves its persistence on scale-free networks.

The undecidability of the spatialized prisoner's dilemma

In the spatialized Prisoner's Dilemma, players compete against their immediate neighbors and adopt a neighbor's strategy should it prove locally superior. Fields of strategies evolve in the manner of cellular automata (Nowak and May, 1993; Mar and St. Denis, 1993a,b; Grim 1995, 1996). Often a question arises as to what the eventual outcome of an initial spatial configuration of strategies will be: Will a single strategy prove triumphant in the sense of progressively conquering more and more territory without opposition, or will an equilibrium of some small number of strategies emerge? Here it is shown, for finite configurations of Prisoner's Dilemma strategies embedded in a given infinite background, that such questions are formally undecidable: there is no algorithm or effective procedure which, given a specification of a finite configuration, will in all cases tell us whether that configuration will or will not result in progressive conquest by a single strategy when embedded in the given field. The proof introduces undecidability into decision theory in three steps: by (1) outlining a class of abstract machines with familiar undecidability results, by (2) modelling these machines within a particular family of cellular automata, carrying over undecidability results for these, and finally by (3) showing that spatial configurations of Prisoner's Dilemma strategies will take the form of such cellular automata.

Editorial Comments on the Article by Hirshleifer and Martinez Coll

The ecological approach to experimental games has added another dimension to the study of conflict and cooperation. In their seminal paper, J. Maynard Smith and G. R. Price (1973) demonstrated the differential viability (represented by relative numbers of progeny reflecting the payoffs of encounters) of selected simple governing interactions between individuals of a species. Particularly successful was the strategy of the so called Retaliator, later called TIT-FOR-TAT. The round-robin contests of iterated Prisoner's Dilemma strategies organized by R. Axelrod (1984) and the subsequent simulations of such contests attracted wide attention. The success of TIT-FOR-TAT in those contests and in the simulations led to speculations about the significance of these results in relation to the conduct of real-life conflicts. Needless to say, no categorical policy-related conclusions are warranted. It is foolhardy to translate the drastically simplified models represented by the simplest conceivable matrix games into real-life situations that defy any reasonably complete description, let alone suggest ways of testing theories. (The virtual nonreproducibility of such situations should spike any such hopes.) What, then, is the relevance of such experiments and simulations to the conduct of human affairs, particularly in international relations, where the fate of civilization, perhaps of humanity, seems to be at stake? It is impossible on the basis of observed results to say what will happen in consequence of particular policies. Surely it would be futile to conclude that because TIT-FOR-TAT performed best in the contests and simulations, an eye-for-an-eye policy works, or that it is most effective in eliciting cooperation. Yet suggestions to this effect have been made. The ease with which the shakiness of these conjectures can be