Analyzing Social Network Structures in the Iterated Prisoner's Dilemma with Choice and Refusal

The Iterated Prisoner's Dilemma with Choice and Refusal (IPD/CR) is an extension of the Iterated Prisoner's Dilemma with evolution that allows players to choose and to refuse their game partners. From individual behaviors, behavioral population structures emerge. In this report, we examine one particular IPD/CR environment and document the social network methods used to identify population behaviors found within this complex adaptive system. In contrast to the standard homogeneous population of nice cooperators, we have also found metastable populations of mixed strategies within this environment. In particular, the social networks of interesting populations and their evolution are examined.Comment: 37 pages, uuencoded gzip'd Postscript (1.1Mb when gunzip'd) also available via WWW at http://www.cs.wisc.edu/~smucker/ipd-cr/ipd-cr.htm

The robustness of the "Raise-The-Stakes" strategy - Coping with exploitation in noisy Prisoner's Dilemma Games.

Recent models of altruism point out the success of a strategy called 'Raise-The- Stakes' (RTS) in situations allowing variability in cooperation. In theory, RTS is difficult to exploit because it begins with a small investment in an iterated Prisoner's Dilemma Game. When its cooperation is reciprocated, RTS increases its generosity, thereby taking advantage of cooperative opportunities. Previous research has shown that human subjects indeed adopt RTS but start out moderately cooperative rather than with a minimal investment. This raises the question how robust RTS is against exploitation, certainly in a noisy situation. In a behavioral experiment we investigate whether human subjects vary their cooperation in interaction with reciprocators and cheaters in an iterated non-discrete version of a Prisoner's Dilemma Game. When confronted with a strategy that matches the investment of the subject on the previous round, we find that subjects are likely to increase cooperation. However, cooperation gradually breaks down in interaction with a strategy that undercuts the level of cooperation of the subjects, indicating the robustness of RTS. In line with RTS modeling studies, but in contrast with the cheater detection literature, we find that human subjects are less willing to increase cooperation when the perceived likelihood of mistakes increases.Cheating; Evolution of cooperation; Noise; Prisoner's dilemma; Reciprocal altruism;

Prospects and Pitfalls of Statistical Testing: Insights from Replicating the Demographic Prisoner's Dilemma

This paper documents our efforts (and troubles) in replicating Epstein's (1998) demographic prisoner's dilemma model. Confronted with a number of ambiguous descriptions of model features we introduce a method for systematically generating a large number of model replications and testing for their equivalence to the original model. While, qualitatively speaking, a number of our replicated models resemble the results of the original model reasonably well, statistical testing reveals that in quantitative terms our endeavor was only partially successful. This fact hints towards some unstated assumptions regarding the original model. Finally we conduct a number of statistical tests with respect to the influence of certain design choices like the method of updating, the timing of events and the randomization of the activation order. The results of these tests highlight the importance of an explicit documentation of design choices and especially of the timing of events. A central lesson learned from this exercise is that the power of statistical replication analysis is to a large degree determined by the available data.Agent-Based Model, Verification, Comparative Computational Methodology, Prisoners Dilemma, Replication, Demographic Prisoners Dilemma

The Viability of Cooperation Based on Interpersonal Commitment

A prominent explanation of cooperation in repeated exchange is reciprocity (e.g. Axelrod, 1984). However, empirical studies indicate that exchange partners are often much less intent on keeping the books balanced than Axelrod suggested. In particular, there is evidence for commitment behavior, indicating that people tend to build long-term cooperative relationships characterised by largely unconditional cooperation, and are inclined to hold on to them even when this appears to contradict self-interest. Using an agent-based computational model, we examine whether in a competitive environment commitment can be a more successful strategy than reciprocity. We move beyond previous computational models by proposing a method that allows to systematically explore an infinite space of possible exchange strategies. We use this method to carry out two sets of simulation experiments designed to assess the viability of commitment against a large set of potential competitors. In the first experiment, we find that although unconditional cooperation makes strategies vulnerable to exploitation, a strategy of commitment benefits more from being more unconditionally cooperative. The second experiment shows that tolerance improves the performance of reciprocity strategies but does not make them more successful than commitment. To explicate the underlying mechanism, we also study the spontaneous formation of exchange network structures in the simulated populations. It turns out that commitment strategies benefit from efficient networking: they spontaneously create a structure of exchange relations that ensures efficient division of labor. The problem with stricter reciprocity strategies is that they tend to spread interaction requests randomly across the population, to keep relations in balance. During times of great scarcity of exchange partners this structure is inefficient because it generates overlapping personal networks so that often too many people try to interact with the same partner at the same time.Interpersonal Commitment, Fairness, Reciprocity, Agent-Based Simulation, Help Exchange, Evolution

Toward a Cognitive Experimental Economics

This paper aims to analyze and exemplify some methodological implications on the way to conduct experiments related to the adoption of a cognitive approach in Economics. Many differences arise in relation to a more traditional way. In fact cognitive economics has strong descriptive attention and aims at beeing closer to reality than the mainstream. Besides the idea of representative agents is questioned. Different kind of experiments, differents analysis and new tools are so required. The paper proposes also some notes on the relation between experimental economics and simulation with artificial agents.cognitive economics, experimental economics, learning

Learning Games

This paper proposes a model of learning about a game. Players initially have littleknowledge about the game. Through playing the identical game repeatedly, eachplayer not only learns which action to choose but also constructs his personal viewon the game. The model is studied using a hybrid payoff matrix of the prisoner’sdilemma and coordination games. Results of computer simulations show (1) when allthe players are slow in learning the game, they have only a partial understanding ofthe game, but may enjoy higher payoffs than the cases with full or no understandingof the game; (2) when one of the players is quick in learning the game, he obtains ahigher payoff than the others. However, all of them can receive lower payoffs than thecase where all the players are slow learners

Learning and innovative elements of strategy adoption rules expand cooperative network topologies

Cooperation plays a key role in the evolution of complex systems. However, the level of cooperation extensively varies with the topology of agent networks in the widely used models of repeated games. Here we show that cooperation remains rather stable by applying the reinforcement learning strategy adoption rule, Q-learning on a variety of random, regular, small-word, scale-free and modular network models in repeated, multi-agent Prisoners Dilemma and Hawk-Dove games. Furthermore, we found that using the above model systems other long-term learning strategy adoption rules also promote cooperation, while introducing a low level of noise (as a model of innovation) to the strategy adoption rules makes the level of cooperation less dependent on the actual network topology. Our results demonstrate that long-term learning and random elements in the strategy adoption rules, when acting together, extend the range of network topologies enabling the development of cooperation at a wider range of costs and temptations. These results suggest that a balanced duo of learning and innovation may help to preserve cooperation during the re-organization of real-world networks, and may play a prominent role in the evolution of self-organizing, complex systems.Comment: 14 pages, 3 Figures + a Supplementary Material with 25 pages, 3 Tables, 12 Figures and 116 reference