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SCIENTIA SINICA Informationis, Volume 47 , Issue 4 : 492-506(2017) https://doi.org/10.1360/N112016-00088

Designing game-theoretic security strategies for large public events

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  • ReceivedApr 8, 2016
  • AcceptedJun 27, 2016
  • PublishedFeb 23, 2017

Abstract


Funded by

国家自然科学基金(61202212)

  • Figure 5

    (Color online) Minimax assignment

  • Table 1   Resources assigned to $i, j, l$ in $S$
    Time period $q_i^t(S)$ $q_j^t(S)$ $q_l^t(S)$
    Before $t_1$ $a_i$ $a_j$ $a_l$
    $[t_1, t_1 + d_{ij})$ $a_i - 1$ $a_j$ $a_l$
    $[t_1 + d_{ij}, t_2)$ $a_i-1$ $a_j +1$ $a_l$
    $[t_2, t_2 + d_{jl})$ $a_i - 1$ $a_j$ $a_l$
    After $t_2 + d_{jl}$ $a_i - 1$ $a_j$ $a_l + 1$
  •   

    Algorithm 1 SCOUT-A

    for all $i \in \mathcal{T}$

    $V_i \leftarrow v_i(0), a_i \leftarrow 0$

    end for

    ${\rm left} \leftarrow m$

    while ${\rm left} > 0$ do

    $i \leftarrow \arg\!\max_{i \in \mathcal{T} }V_i$, $a_i \leftarrow a_i + 1$, ${\rm left} \leftarrow {\rm left} - 1$, $V_i \leftarrow W_i^{a_i}(0)$

    end while

    $t_m \leftarrow 0$, $k \leftarrow 0$

    while $t_m< t_{\rm e}$ do

    ${\boldsymbol I} \leftarrow \emptyset$

    for all $\forall i, j \in \mathcal{T}$

    if $\exists t$ such that $\frac{\partial W_i^{a_i - 1}(t)}{\partial t} < \frac{\partial W_j^{a_j}(t)}{\partial t}$ then

    $I_{ij} \leftarrow I_{ij}(A, t_m)$

    if $I_{ij} < t_{\rm e}$ then

    ${\boldsymbol I} \leftarrow {\boldsymbol I} \cup I_{ij}$

    end if

    end if

    end for

    if ${\boldsymbol I} = \emptyset$ then

    break

    end if

    $I_{ij} \leftarrow \min({\boldsymbol I})$

    if $W_i^{a_i - 1}(I_{ij} - \Delta t) \ge W_j^{a_j}(I_{ij} - \Delta t)$ then

    $\tau_k \leftarrow I_{ij}, t_m \leftarrow I_{ij}, a_i \leftarrow a_i - 1, a_j \leftarrow a_j + 1, c_{ij}^k \leftarrow 1, k \leftarrow k + 1$

    end if

    end while

  • Table 2   Resources assigned to $i, j, l$ in $S^1$
    Time period $q_i^t(S)$ $q_j^t(S)$ $q_l^t(S)$
    Before $t_3$ $a_i$ $a_j$ $a_l$
    $[t_3, t_3 + d_{il})$ $a_i-1$ $a_j$ $a_l$
    After $t_3 + d_{il}$ $a_i - 1$ $a_j$ $a_l + 1$
  •   

    Algorithm 2 SCOUT-C

    $\Psi \leftarrow \emptyset$

    for all $\rho \in \{0, \ldots, R_i\}, \rho&apos; \in \{0, \ldots, R_j\}$

    $\Psi \leftarrow \Psi \cup \{\theta({\rm Tr})\} \cup \{\theta({\rm Tr}) + d_{ij}\},$ where ${\rm Tr} = (i, j, a_i, a_j, \rho, \rho&apos;)$

    end for

    run SCOUT-D, using $\Psi$ as the time points set

  • Table 3   Transfer time between studios (min, from google map)
    鸟巢 奥林匹克公园 首体 工体 五棵松
    鸟巢 8 14 17 29
    奥林匹克公园 8 20 24 33
    首体 14 20 24 17
    工体 17 24 24 36
    五棵松 29 33 17 36