Adaptive simulation using mode identification

Adaptive simulation using modal clustering and method of potential function

Spatial patterns and scale freedom in a Prisoner's Dilemma cellular automata with Pavlovian strategies

A cellular automaton in which cells represent agents playing the Prisoner's Dilemma (PD) game following the simple "win-stay, loose-shift" strategy is studied. Individuals with binary behavior, such as they can either cooperate (C) or defect (D), play repeatedly with their neighbors (Von Neumann's and Moore's neighborhoods). Their utilities in each round of the game are given by a rescaled payoff matrix described by a single parameter Tau, which measures the ratio of 'temptation to defect' to 'reward for cooperation'. Depending on the region of the parameter space Tau, the system self-organizes - after a transient - into dynamical equilibrium states characterized by different definite fractions of C agents (2 states for the Von Neumann neighborhood and 4 for Moore neighborhood). For some ranges of Tau the cluster size distributions, the power spectrums P(f) and the perimeter-area curves follow power-law scalings. Percolation below threshold is also found for D agent clusters. We also analyze the asynchronous dynamics version of this model and compare results.Comment: Accepted for publication in JSTA

Similarity based cooperation and spatial segregation

We analyze a cooperative game, where the cooperative act is not based on the previous behaviour of the co-player, but on the similarity between the players. This system has been studied in a mean-field description recently [A. Traulsen and H. G. Schuster, Phys. Rev. E 68, 046129 (2003)]. Here, the spatial extension to a two-dimensional lattice is studied, where each player interacts with eight players in a Moore neighborhood. The system shows a strong segregation independent on parameters. The introduction of a local conversion mechanism towards tolerance allows for four-state cycles and the emergence of spiral waves in the spatial game. In the case of asymmetric costs of cooperation a rich variety of complex behavior is observed depending on both cooperation costs. Finally, we study the stabilization of a cooperative fixed point of a forecast rule in the symmetric game, which corresponds to cooperation across segregation borders. This fixed point becomes unstable for high cooperation costs, but can be stabilized by a linear feedback mechanism.Comment: 7 pages, 9 figure

Emotional Strategies as Catalysts for Cooperation in Signed Networks

The evolution of unconditional cooperation is one of the fundamental problems in science. A new solution is proposed to solve this puzzle. We treat this issue with an evolutionary model in which agents play the Prisoner's Dilemma on signed networks. The topology is allowed to co-evolve with relational signs as well as with agent strategies. We introduce a strategy that is conditional on the emotional content embedded in network signs. We show that this strategy acts as a catalyst and creates favorable conditions for the spread of unconditional cooperation. In line with the literature, we found evidence that the evolution of cooperation most likely occurs in networks with relatively high chances of rewiring and with low likelihood of strategy adoption. While a low likelihood of rewiring enhances cooperation, a very high likelihood seems to limit its diffusion. Furthermore, unlike in non-signed networks, cooperation becomes more prevalent in denser topologies.Comment: 24 pages, Accepted for publication in Advances in Complex System

“She Never Lets Me Write about It”: Children’s Perspectives on “Choice” in Their Writing Curriculum

Legislation and policies such as No Child Left Behind, Race to the Top, and the adoption of Common Core State Standards (CCSS) by the majority of states directly impact the educational experiences of children in classrooms. Current shifts in the U.S. education system include a greater focus on preparing all students to be college and career ready with increased expectations for teachers and children. With shifts in the curriculum and standards comes increased attention on writing performance, with a particular focus on measuring and tracking individual children’s progress in order to then evaluate teachers and classrooms (http://www.whitehouse.gov/blog/2010/01/19/speeding-race-top). Researchers and policymakers scramble to find ways to assess the increased amount of data that are collected; yet, children’s voices and their perceptions of their educational experiences are missing

I\u27m Not Allowed to Write about That in School but at Home I Can : Examining Elementary School Students\u27 Attitudes Toward Writing Instruction

Research on writing indicates that children’s attitudes about writing have an impact on their writing achievement (Knudson, 1995; Graham, Berninger & Fan, 2007). At the same time, we see the narrowing of curricular practices, especially in literacy, giving children less input into their educational experience and fewer choices about how and what they are learning (Genishi & Dyson, 2012). The purpose of this study was to examine children’s attitudes towards writing and the experiences that have shaped these attitudes and their identities as writers. We conducted grade level focus group interviews with children in an elementary school to learn more about their writing practices (in and out of school), their perceptions of themselves as writers, and the experiences that have influenced their views on writing and their writing practices. The goal was o learn about writing experiences that motivate children to write and lead to children\u27s positive and/or negative attitudes towards writing in order to think about ways that teachers’ can help to support writing development in classrooms across the elementary school grades

Exploring the cooperative regimes in a model of agents without memory or "tags": indirect reciprocity vs. selfish incentives

The self-organization in cooperative regimes in a simple mean-field version of a model based on "selfish" agents which play the Prisoner's Dilemma (PD) game is studied. The agents have no memory and use strategies not based on direct reciprocity nor 'tags'. Two variables are assigned to each agent $i$ at time $t$, measuring its capital $C(i;t)$ and its probability of cooperation $p(i;t)$. At each time step $t$ a pair of agents interact by playing the PD game. These 2 agents update their probability of cooperation $p(i)$ as follows: they compare the profits they made in this interaction $\delta C(i;t)$ with an estimator $\epsilon(i;t)$ and, if $\delta C(i;t) \ge \epsilon(i;t)$, agent $i$ increases its $p(i;t)$ while if $\delta C(i;t) < \epsilon(i;t)$ the agent decreases $p(i;t)$. The 4!=24 different cases produced by permuting the four Prisoner's Dilemma canonical payoffs 3, 0, 1, and 5 - corresponding,respectively, to $R$ (reward), $S$ (sucker's payoff), $T$ (temptation to defect) and $P$ (punishment) - are analyzed. It turns out that for all these 24 possibilities, after a transient,the system self-organizes into a stationary state with average equilibrium probability of cooperation $\bar{p}_\infty$ = constant $> 0$.Depending on the payoff matrix, there are different equilibrium states characterized by their average probability of cooperation and average equilibrium per-capita-income ($\bar{p}_\infty,\bar{\delta C}_\infty$).Comment: 11 pages, 5 figure

Prisoner's Dilemma cellular automata revisited: evolution of cooperation under environmental pressure

We propose an extension of the evolutionary Prisoner's Dilemma cellular automata, introduced by Nowak and May \cite{nm92}, in which the pressure of the environment is taken into account. This is implemented by requiring that individuals need to collect a minimum score $U_{min}$, representing indispensable resources (nutrients, energy, money, etc.) to prosper in this environment. So the agents, instead of evolving just by adopting the behaviour of the most successful neighbour (who got $U^{msn}$), also take into account if $U^{msn}$ is above or below the threshold $U_{min}$. If $U^{msn}<U_{min}$ an individual has a probability of adopting the opposite behaviour from the one used by its most successful neighbour. This modification allows the evolution of cooperation for payoffs for which defection was the rule (as it happens, for example, when the sucker's payoff is much worse than the punishment for mutual defection). We also analyse a more sophisticated version of this model in which the selective rule is supplemented with a "win-stay, lose-shift" criterion. The cluster structure is analyzed and, for this more complex version we found power-law scaling for a restricted region in the parameter space.Comment: 15 pages, 8 figures; added figures and revised tex

Social games in a social network

We study an evolutionary version of the Prisoner's Dilemma game, played by agents placed in a small-world network. Agents are able to change their strategy, imitating that of the most successful neighbor. We observe that different topologies, ranging from regular lattices to random graphs, produce a variety of emergent behaviors. This is a contribution towards the study of social phenomena and transitions governed by the topology of the community