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First, as existing multipath routing protocols usually produce large amount of route reply packets in a short period of time, which may cause traffic congestion, a cumulative route reply strategy (CRR) is employed in this work.

In this paper, we explore the link between Mean-Field Games and the Best Reply Strategy approach.

That is to say, truthful revelation for the public good is the best reply strategy in the piecewise intertemporal game, and it is the only best reply strategy when x > 0. Remark 10 Theorem 10 means that the best reply strategy at τ s for each player is to reveal his/her true MRS for the public good to be provided at date τ s + 1, i.e., π i ( τ s + 1 ), but not π i ( τ s ).

Under nonmyopia assumption, a sincere revelation of preference for the public good at any discrete date of the λMDP Process is the best reply strategy for each player.

Under Nonmyopia assumption, each player's best reply strategy at any discrete date is to reveal his/her anticipated marginal rate of substitution for a public good at the end of a current time interval of the λ MDP Procedure.

end{aligned} (87 Since (left( sum _{iin mathbf {N}}psi _{i}-gamma right) ^{beta }ne 0) holds out of equilibrium, the best reply strategy for player i is begin{aligned} psi _{i}=pi _{i}+frac{beta -n+1}{beta n}.

It is verified that the best reply strategy for each player at each discrete date is to reveal his/her anticipated true MRS for the public good at the end of the current time interval, which maximizes each player's payoff in the piecewise intertemporal incentive game.

In order to introduce Condition ACR, I need (phi _{i}) as a best reply strategy given by begin{aligned} phi _{i}=frac{1}{n(delta _{i}-1)}left{ 1-n pii _{i}-(1-n pita _{i}- 1-ndelta _{i}- 1-ndeltaj}-gamma right) right},quad forall iin mathbf {N}.

The behavioral hypothesis underlying the above equation is the nonmyopia assumption, i.e., each player determines his/her best reply strategy at the beginning of each interval [ τ s, τ s + 1 ) in order to maximize his/her payoff, V i ( τ s + 1 ), at the beginning of the next interval [ τ s + 1, τ s + 2 ).

Results show that for intermediate and high levels of information accuracy, joint strategy fictitious play best predicts the respondents' route choice behaviour under information provision, suggesting that a best-reply strategy is used by travellers for their route choices.

Recently, simpler approaches relying on the Best-Reply Strategy have been proposed.

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