pressed and tested for their ability to
destabilize a desired equilibrium.
To accommodate this, we encode
change to the population over time (for
example, by invasion of mutants) over
repeated games by using deterministic finite automata (DFA). The DFA
strategy space offers a vastly reachable
space of dynamic strategic structures.
This provides the means to explore
the uses of identity in repeated signaling interactions.
The DFA state codes noted in the
table determine the (type, signal) of a
sender’s controlling agent, or the action as receiver. Each DFA encounter
determines a sequence of outcomes
as illustrated in the example that follows. Consider the strategy of Figure
3(c) as sender matched against strategy of (d) as receiver with a transaction
budget of two units. The sender starts
in state s1, and the receiver starts in
state s3; they play at the cost of one
unit against the transaction budget.
Note that the discount for deception
will entail additional communication
efforts. Next, the sender transitions
to state s7 by following the s3 labeled
transition, and the receiver loops
back to state s3; they both play at the
cost of a half unit since state s7 uses
deception. Next, the sender transitions to state s1 while the receiver transitions to state s6 to exhaust the transaction budget and complete the game.
The computed outcome sequence is
o1, o7, o2, resulting in a sender aggregate utility of (A + B) and receiver aggregate utility of (B − (A + C)).
Evolutionary strategy. Evolutionary
game theory models a dynamic population of agents capable of modifying their strategy and predicts popu-lation-level effects. 2, 3, 5, 19, 32 Formally,
evolutionary games are a dynamic
system with stochastic variables. The
agents in evolutionary games may
(both individually and collectively) explore strategy structures directly (via
mutation and peer-informed reselection), and they may exploit strategies
where and when competitive advantages are found.
To implement this system, the time
domain is divided into intervals called
generations. The system is initialized by
fixing a finite set of agents and assigning each agent a strategy determined
with a seeding probability distribution.
During a generation, pairs of agents
will encounter one another to play repeated signaling games; the encounters are determined by an encounter
distribution. At the completion of a
generation, agents evaluate rewards
obtained from their implemented
strategies. This evaluation results in
their performance measure. Next, performance measures are compared
within a set of peer agents that coop-erte to inform each agents’ reselection
stage. During the reselection stage,
agents determine a strategy to use in
the next generation, as achieved by a
boosting probability distribution that
preferentially selects strategies based
on performance. After reselection,
some agents are mutated with a
mutation probability distribution. This step
completes the generation and establishes the strategies implemented during the next generation.
The agents evolve discrete strategic
forms (DFA); a strategic mutation network is graphed in Figure 3(e) to provide
a sense of scale. The dynamic system
thus evolves a population measure over
strategies. Within the WANET, nodes
freely mutate, forming deceptive strategies as often as they augment cooperative ones. Evolutionary games allow us
to elucidate the stability and resilience
of various strategies arising from mutations and a selection process ruled by
non-cooperation and rationality.
We augment the basic structure of
reselection by considering carefully
how strategic information is shared.
Upon noticing that deceptive and
cooperative strategies differ fundamentally in their information asymmetric requirements, we introduce a
technique referred to as split-boosting,
which modulates the information flow
components of the network.
Recreate by split-boosting. During the
Recreate phase, agents select strategies
preferentially by comparing performance
measured only among a set of agents that
share this pooled information.
Splitting the set of agents into
components we limit the boosting
to include only strategies available
from the component. Within a component (subset) S, let vi be the performance measure for strategy used
by agents i ∈ S. Letting
and we can safely transfer the performance measures to the
When a deceptive
it will be used
as there is no
reason to abandon
it after one
Moreover, it is
are needed to