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Team, Game, and Negotiation based UAV Task Allocation 63
where,
˜ ˆ β i
β =1 − (1 − β j ); β i = (33)
β j
j∈A
j∈A
j
So, given N routes P 1 ,P 2 ,P 3 ,...,P N of the N agents, where P i is any P ∈
i
q j
i i
P (we drop the C s i argument from the path notation P (C s i ) as well as
q
i
from P (C s i ), the set of all possible paths, for simplicity), the reduction in
uncertainty achieved by A i at each step t (t =1, 2,... ,q) is given by v i (t)
and is computed using Case 1 or Case 2 as the case may be. Note that this
computation has to be done simultaneously for all the agents. The total benefit
to A i due to path P i is
q

i
m (P 1 ,...,P N )= v i (t) (34)
t=1
which represents the payoff obtained by A i as the agents choose strategies
+
i
P 1 ,P 2 , ...,P N . The functions m : P q → R ,fromthe setof
i=1,...,N i
paths to the uncertainty reduction value, are called the search effectiveness
functions.
5.2 Solution Concepts
The decision to choose a particular path that would provide the maximum
information gain (or uncertainty reduction) can be based on various strategies.
We consider the following strategies: Noncooperative Nash strategy, coali-
tional Nash strategy, security strategy, cooperative strategy, greedy strategy,
and globally optimal strategy. The Nash, security, coalitional Nash, and greedy
strategies do not require any kind of communication to arrive at an optimal
decision, while cooperative and globally optimal strategies require communi-
cation to implement the decision making process.
(i) Noncooperative Nash Equilibrium Strategy: When the agents do not com-
municate with each other to decide on their future action at time t, and each
agent assumes that the other N − 1 agents take actions that are beneficial to
them, then we can use the concept of noncooperative Nash equilibrium.
(ii) Coalitional Nash Strategy: This is similar to the non-cooperative Nash
equilibrium strategy, except that each agent assumes the other N − 1 agents
to form a coalition and take actions jointly that are jointly beneficial to them.
(iii) Security Strategy: This strategy becomes relevant when, as before, the
agents do not communicate with each other and each agent assumes the other
N − 1 agents to be adversaries. In such a situation the best strategy for the
agent is to secure its minimal benefit. Hence, it is logical for the agent to use
security strategy that would guarantee a minimal payoff.