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

Geometric Prequantization of the Moduli Space of the Vortex equations on a Riemann surface

The moduli space of solutions to the vortex equations on a Riemann surface are well known to have a symplectic (in fact K\"{a}hler) structure. We show this symplectic structure explictly and proceed to show a family of symplectic (in fact, K\"{a}hler) structures $\Omega_{\Psi_0}$ on the moduli space, parametrised by $\Psi_0$, a section of a line bundle on the Riemann surface. Next we show that corresponding to these there is a family of prequantum line bundles ${\mathcal P}_{\Psi_0}$on the moduli space whose curvature is proportional to the symplectic forms $\Omega_{\Psi_0}$.Comment: 8 page

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

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 diversity and promotion of cooperation in the spatial prisoner's dilemma game

The diversity in wealth and social status is present not only among humans, but throughout the animal world. We account for this observation by generating random variables that determ ine the social diversity of players engaging in the prisoner's dilemma game. Here the term social diversity is used to address extrinsic factors that determine the mapping of game pay offs to individual fitness. These factors may increase or decrease the fitness of a player depending on its location on the spatial grid. We consider different distributions of extrin sic factors that determine the social diversity of players, and find that the power-law distribution enables the best promotion of cooperation. The facilitation of the cooperative str ategy relies mostly on the inhomogeneous social state of players, resulting in the formation of cooperative clusters which are ruled by socially high-ranking players that are able to prevail against the defectors even when there is a large temptation to defect. To confirm this, we also study the impact of spatially correlated social diversity and find that coopera tion deteriorates as the spatial correlation length increases. Our results suggest that the distribution of wealth and social status might have played a crucial role by the evolution of cooperation amongst egoistic individuals.Comment: 5 two-column pages, 5 figure

Administrative Law—Variable Annuity Held to Be Subject to Federal Securities Regulation

Securities and Exchange Commission v. United Benefit Life Insurance Company, 387 U.S. 202 (1967)

Evolutionary prisoner's dilemma game on hierarchical lattices

An evolutionary prisoner's dilemma (PD) game is studied with players located on a hierarchical structure of layered square lattices. The players can follow two strategies [D (defector) and C (cooperator)] and their income comes from PD games with the ``neighbors.'' The adoption of one of the neighboring strategies is allowed with a probability dependent on the payoff difference. Monte Carlo simulations are performed to study how the measure of cooperation is affected by the number of hierarchical levels (Q) and by the temptation to defect. According to the simulations the highest frequency of cooperation can be observed at the top level if the number of hierarchical levels is low (Q<4). For larger Q, however, the highest frequency of cooperators occurs in the middle layers. The four-level hierarchical structure provides the highest average (total) income for the whole community.Comment: appendix adde

Altruistic Contents of Quantum Prisoner's Dilemma

We examine the classical contents of quantum games. It is shown that a quantum strategy can be interpreted as a classical strategies with effective density-dependent game matrices composed of transposed matrix elements. In particular, successful quantum strategies in dilemma games are interpreted in terms of a symmetrized game matrix that corresponds to an altruistic game plan.Comment: Revised according to publisher's request: 4 pgs, 2 fgs, ReVTeX4. For more info, go to http://www.mech.kochi-tech.ac.jp/cheon

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