Title: The%20Evolution%20of%20Cooperation%20within%20the%20Iterated%20Prisoner
1The Evolution of Cooperation within the Iterated
Prisoners dilemmaon a Social Network
2Introduction
- The evolution of cooperation in the iterated
prisoners dilemma is a well researched and
documented phenomenon. - However, by changing a few of the underlying
assumptions a more realistic and intriguing
result regarding the emergence of competitive and
cooperative behaviors is found. - The first and foremost change posited is
reevaluating the notion of utility. - In this paper, utility is developed in terms of a
mathematical belief structure.
3Changes to the Game Structure
- Classical Evolutionary Game Theory
- Use of Replicator Equations
- Birth/Death Process Population Demographics
Change - Random Draw to determine player pairings
- Infinite Population Sizes
- Strategies Constant
- Belief Based Utility Approach
- Use of difference equations
- Populations are constant (no birth/death process)
- Player pairings retain memory (i.e. a network
structure evolves) - Initial pairings based on nearest neighbor search
- Strategies change as beliefs are changed
4Belief Based Utility
- In the absence of external constraints, people
tend to act in accordance with their beliefs. - Needs and external driving factors may force
people to act against their beliefs. - In this model of the iterated prisoners dilemma
two beliefs are modeled hostility and
retribution. - Changes between belief and need can be modeled
using a catastrophe geometry
5Belief Structures
Impacted by Socialization and Interaction
- In the case of the iterated prisoners dilemma we
are interested in networked patterns of action
that arise - through competition and collaboration among
actors. - These interactions may impact the degree of
cognitive dissonance among actors and (through
loss) give rise to a need function altering their
normal modes of behavior. - The primary factors that drives this in the
iterated prisoners dilemma is the accumulated
wealth of a player. - The manner in which wealth is generated is
impacted by several factors that determine how a
social network is constructed by actors.
Shifts Behavioral Patterns
Characterized By
- The shadow zone. Where patterns of behavior
converges to need driven behavior (belief
structures overridden). - The illuminated zone. Patterns of behavior
correspond to beliefs (cognitive dissonance is
measured by amplitude.) - The caustic The dividing line between belief
driven response and need driven response.
6Results
Initially, cooperative players P1 and P2 are
overwhelmed by hostile players P3 and P4.
However, shortly into the game P1 and P2 players
begin to form coalitions and through favorable
outcomes, arising from the tit-for-tat and
cooperative P1 strategies, continue to grow
relationships and accumulate wealth. As P1
players have a higher reputation among P2 players
they are more readily accepted into the P2
coalition. Hostile players P1 and P2 attempt to
invade these cooperative networks, but are not
allowed due to their low reputation scores. Over
time, hostile players go against their beliefs,
first the P4 and later the P3 players, and begin
to mimic the behavior of cooperative players.
When this happens the social network is in
equilibrium.
- The presence of critical points, seen in chart 6,
that are chaotic attractors in the iterated
Prisoners Dilemma implies many interesting
things. - Self-organized criticality (SOC) is introduced
into the evolution of cooperation in the iterated
prisoners dilemma. - The distribution of the attractors over the
games evolution implies a sense of temporal
scale-invariance. - That is the characteristic of adaptive behavior
arising the temporal distribution of attractors
came into being from a series of phase
transitions that occurred during the evolution of
the game itself. - This implies self-adaptation on the part of the
players.