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

Yue YIN 1,2,*, Bo AN 1,3,
• AcceptedJun 27, 2016
• PublishedFeb 23, 2017
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• 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 –

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