THE HISTORIC–STOCHASTIC STRATEGIST

2001 ◽  
Vol 11 (07) ◽  
pp. 2037-2050 ◽  
Author(s):  
RAMÓN ALONSO-SANZ ◽  
M. CARMEN MARTÍN ◽  
MARGARITA MARTÍN
Keyword(s):  
Prisoner's Dilemma ◽  
Evolutionary Dynamics ◽  
Prisoner’S Dilemma ◽  
One Dimensional ◽  
Historic Memory ◽  
Asynchronous Updating ◽  
Probabilistic Context ◽  
Spatial Formulation

The basic aim of this paper is to extend earlier work on assessing the effect of considering previous results (history) in the evolutionary dynamics of the spatial formulation of the Prisoner's Dilemma when players follow one-dimensional strategies. The historic strategist models considered before were deterministic, so the choices were fixed by the strategies in an automatic way. In the present work the strategies do not fix the choices but their probabilities. Both synchronous and asynchronous updating schemes have been taken into account. It is concluded here that the essential results found in the deterministic scenario remain valid in a probabilistic context: historic memory tends to favor the main features of the initial scenario.

THE HISTORIC STRATEGIST

2001 ◽  
Vol 11 (04) ◽  
pp. 943-966 ◽  
Author(s):  
RAMÓN ALONSO-SANZ ◽  
M. CARMEN MARTÍN ◽  
MARGARITA MARTÍN
Keyword(s):  
Prisoner's Dilemma ◽  
Evolutionary Dynamics ◽  
Prisoner’S Dilemma ◽  
One Dimensional ◽  
Historic Memory ◽  
Asynchronous Updating ◽  
Spatial Formulation

The basic aim of this paper is to extend earlier work on assessing the effect of considering previous results (history) in the evolutionary dynamics of the spatial formulation of the Prisoner's Dilemma. In the simpler historic models considered earlier, players did not elaborate strategies. In the present work one-dimensional strategies are followed by the players. Both synchronous and asynchronous updating schemes have been taken into account. It is concluded here that the essential result found in the no-strategies scenario remains valid when keeping historic memory of payoffs, moves and of the strategies themselves: history induces a preserving effect.

MEMORY BOOSTS COOPERATION IN THE STRUCTURALLY DYNAMIC PRISONER'S DILEMMA

2009 ◽  
Vol 19 (09) ◽  
pp. 2899-2926 ◽  
Author(s):  
RAMÓN ALONSO-SANZ
Keyword(s):  
Prisoner's Dilemma ◽  
Prisoner’S Dilemma ◽  
Iterated Prisoner's Dilemma ◽  
Historic Memory ◽  
Spatial Formulation ◽  
Iterated Prisoner’S Dilemma

In the conventional spatial formulation of the iterated prisoner's dilemma, only the results generated in the last round are taken into account in deciding the next choice. Historic memory of past iterations can be taken into account by featuring players by a summary of their previous winnings and choices. The effect of such a memory implementation when the players are allowed to follow a simple full-deterministic structurally coevolving dynamic is assessed in this work.

MEMORY BOOSTS COOPERATION

2006 ◽  
Vol 17 (06) ◽  
pp. 841-852 ◽  
Author(s):  
RAMÓN ALONSO-SANZ ◽  
MARGARITA MARTÍN
Keyword(s):  
Prisoner's Dilemma ◽  
Prisoner’S Dilemma ◽  
Iterated Prisoner's Dilemma ◽  
Historic Memory ◽  
Spatial Formulation ◽  
Iterated Prisoner’S Dilemma ◽  
Short Type

The standard spatial formulation of the iterated Prisoner's Dilemma is ahistoric (memoryless): i.e., only the results generated in the last round are taken into account in deciding the next choice. Historic memory can be implemented by featuring players by a summary of their previous winnigs and choices. Here we study the effect of limited trailing memory: only the last three iterations are recorded. The effects of full and discounted memory are assessed. It is concluded that this short-type memory stimulates cooperation.

scholarly journals Evolutionary prisoner's dilemma games with one-dimensional local interaction and imitation

2009 ◽  
Vol 41 (1) ◽  
pp. 154-176 ◽  
Author(s):  
Hsiao-Chi Chen ◽  
Yunshyong Chow
Keyword(s):  
Convergence Rate ◽  
Prisoner's Dilemma ◽  
Prisoner’S Dilemma ◽  
Local Interaction ◽  
One Dimensional ◽  
Long Run ◽  
Action Dynamics ◽  
The Impact ◽  
Full Cooperation ◽  
Long Run Equilibrium

In this paper we explore the impact of imitation rules on players' long-run behaviors in evolutionary prisoner's dilemma games. All players sit sequentially and equally spaced around a circle. Players are assumed to interact only with their neighbors, and to imitate either their successful neighbors and/or themselves or the successful actions taken by their neighbors and/or themselves. In the imitating-successful-player dynamics, full defection is the unique long-run equilibrium as the probability of players' experimentations (or mutations) tend to 0. By contrast, full cooperation could emerge in the long run under the imitating-successful-action dynamics. Moreover, it is discovered that the convergence rate to equilibrium under local interaction could be slower than that under global interaction.

scholarly journals Learning dynamics explains human behaviour in Prisoner's Dilemma on networks

2014 ◽  
Vol 11 (94) ◽  
pp. 20131186 ◽  
Author(s):  
Giulio Cimini ◽  
Angel Sánchez
Keyword(s):  
Social Factors ◽  
Prisoner's Dilemma ◽  
Evolutionary Dynamics ◽  
Prisoner’S Dilemma ◽  
Conditional Cooperation ◽  
The Past ◽  
Extensive Analysis ◽  
Emergence Of Cooperation ◽  
Experimental Findings ◽  
Evolutionarily Stable

Cooperative behaviour lies at the very basis of human societies, yet its evolutionary origin remains a key unsolved puzzle. Whereas reciprocity or conditional cooperation is one of the most prominent mechanisms proposed to explain the emergence of cooperation in social dilemmas, recent experimental findings on networked Prisoner's Dilemma games suggest that conditional cooperation also depends on the previous action of the player—namely on the ‘mood’ in which the player is currently in. Roughly, a majority of people behave as conditional cooperators if they cooperated in the past, whereas they ignore the context and free ride with high probability if they did not. However, the ultimate origin of this behaviour represents a conundrum itself. Here, we aim specifically to provide an evolutionary explanation of moody conditional cooperation (MCC). To this end, we perform an extensive analysis of different evolutionary dynamics for players' behavioural traits—ranging from standard processes used in game theory based on pay-off comparison to others that include non-economic or social factors. Our results show that only a dynamic built upon reinforcement learning is able to give rise to evolutionarily stable MCC, and at the end to reproduce the human behaviours observed in the experiments.

EVOLUTIONARY ANALYSIS ON SPATIAL LOCALITY IN N-PERSON ITERATED PRISONER'S DILEMMA

2003 ◽  
Vol 03 (02) ◽  
pp. 177-188 ◽  
Author(s):  
REIJI SUZUKI ◽  
TAKAYA ARITA
Keyword(s):  
Prisoner's Dilemma ◽  
Cooperative Behavior ◽  
Prisoner’S Dilemma ◽  
Dynamic Evolution ◽  
Evolutionary Analysis ◽  
One Dimensional ◽  
Spatial Locality ◽  
Iterated Prisoner's Dilemma ◽  
Two Factors ◽  
Iterated Prisoner’S Dilemma

The purpose of this paper is to consider the effects of spatial locality on the evolution of cooperative behavior in the N-person iterated Prisoner's Dilemma (N-IPD) by focusing on two essentially distinct factors: the scale of interaction (which decides the neighboring members playing the N-person games) and the scale of reproduction (which decides the neighboring candidates for an offspring in each cell). We conducted evolutionary experiments of strategies for one-dimensional N-IPD game with various settings of these two factors. Experimental results revealed that these two factors bring qualitatively different effects to the emergence of cooperative behavior. Furthermore, we investigated the dynamics of the evolution of spatial locality in N-IPD. When we introduced the evolution of the scale of interaction into our model, the dynamic evolution of the scale of interaction through generation facilitated the emergence of global cooperation when the scale of reproduction was relatively small. Experiments with the evolution of the scale of reproduction are also discussed.

THE HISTORIC PRISONER'S DILEMMA

1999 ◽  
Vol 09 (06) ◽  
pp. 1197-1210 ◽  
Author(s):  
RAMÓN ALONSO-SANZ
Keyword(s):  
Prisoner's Dilemma ◽  
Prisoner’S Dilemma ◽  
Spatial Formulation

The effect of considering previous results (history) in the spatial formulation of the Prisoner's Dilemma is assessed. It is concluded that history protects homogeneous populations against the irruption of mutant behavior.

scholarly journals Evolutionary dynamics of the prisoner's dilemma with expellers

2019 ◽  
Vol 3 (1) ◽  
pp. 015011 ◽  
Author(s):  
Xiaofeng Wang ◽  
Guofeng Zhang ◽  
Weijian Kong
Keyword(s):  
Prisoner's Dilemma ◽  
Evolutionary Dynamics ◽  
Prisoner’S Dilemma
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