Page 79 - Innovations in Intelligent Machines

68 P.B. Sujit et al.
Cooperative Strategy

In this strategy the agents communicate during the decision process. The
agents jointly choose a strategy such that the joint payoff of the game is maxi-
mized. Each agent computes the same search effectiveness function M and
decides it’s q step look ahead path using the function M.For N agents, let the
1
N
search effectiveness function be M = m (P 1 ,...,P N )+ ... + m (P 1 ,...,P N )
which represents the joint payoff due to all the agents’ actions. A N-tuple of
∗
∗
strategies (P ,...,P ) is said to be a cooperative strategy, if the following
N
1
condition is satisfied:
1 ∗ ∗ N ∗ ∗ ∗ ∗
m (P ,...,P )+ ... + m (P ,...,P )= M(P ,...,P ) ≥
1 N 1 N 1 N
1 N q
M(P 1 ,...,P N )= m (P 1 ,...,P N )+ ... + m (P 1 ,...,P N ), ∀ P i ∈P (46)
i
The cooperative strategy used in game theory involves communication
between the players to coordinate their actions and arrive at a mutually
acceptable decision. The drawback of cooperative strategy, when used in eco-
nomics, where the players are selfish by nature, is that player may violate
the mutually decided upon agreement to earn larger benefits at the cost of
others. In our scenario, since the agents are automated, they can be assumed
to be altruistic and hence they do not violate the decided upon agreement.
Hence, using the search effectiveness functions, each agent can also compute
the cooperative strategy without explicit communication between the agents.
The equilibrium solution remains the same whether communication is present
or not, provided that all the agents possess the same uncertainty map.

Greedy Strategy

In this case, the agents do not communicate among themselves and use a
greedy strategy to determine their future actions. This is similar to the non-
cooperative strategy used in [32]. The agent chooses a path P i k with a look
ahead policy of q, using the following relation:

i k i j q
m (P ) ≥ m (P ), ∀ j =1, 2,..., |P | (47)
i i i
i
k
where m (P ) is the benefit obtained by agents A i using path P k and it is
i i
evaluated using Eqn. (29).
Selection of Strategies

When there are multiple solutions, the selection of strategies by players
becomes a crucial issue. The security and greedy strategies are straightfor-
ward to implement. If there exists multiple security or greedy strategies, any
one of them will guarantee the same payoff level. In fact, for security strategies
the actual payoff is bound to be higher for the players so long as they stick to