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Published 7:20 PM EDT Sep 5, 2019

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MURPHY - Football coach David Gentry said he plans to keep Georgia's Life Christian Academy on the team's schedule, but will have 'increased security' during its Sept. 20 home game.

Mountain Heritage coach Joey Robinson told the Citizen Times on Sept. 4 that he had canceled the Cougars' home game on Sept. 6 against LCA after raising concerns that the team from Forest Park, Georgia, does not operate under a governing body.

LCA's Week 2 game against Robbinsville was cut short on Aug. 30 after reports of several on-the-field conflicts.

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'Things could change,' Gentry said. 'But as of right now, they are still on our schedule.'

Gentry said he preferred to not lose a home game from the schedule that brings in thousands of dollars to the athletic budget. Robinson said Sept. 4 that canceling this week's game with LCA cost him 'close to $5,000 in gate money.'

'My concern is safety on the field,' Gentry said. 'But we'll have extra security to make sure things go smoothly.'

Published 7:20 PM EDT Sep 5, 2019
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(Submitted on 22 Nov 2016 (v1), last revised 29 Oct 2017 (this version, v6))
Abstract: We study security games in which a defender commits to a mixed strategy forprotecting a finite set of targets of different values. An attacker, knowingthe defender's strategy, chooses which target to attack and for how long. Ifthe attacker spends time $t$ at a target $i$ of value $alpha_i$, and if heleaves before the defender visits the target, his utility is $t cdot alpha_i$; if the defender visits before he leaves, his utility is 0. The defender'sgoal is to minimize the attacker's utility. The defender's strategy consists ofa schedule for visiting the targets; it takes her unit time to switch betweentargets. Such games are a simplified model of a number of real-world scenariossuch as protecting computer networks from intruders, crops from thieves, etc.
We show that optimal defender play for this continuous time security gamesreduces to the solution of a combinatorial question regarding the existence ofinfinite sequences over a finite alphabet, with the following properties foreach symbol $i$: (1) $i$ constitutes a prescribed fraction $p_i$ of thesequence. (2) The occurrences of $i$ are spread apart close to evenly, in thatthe ratio of the longest to shortest interval between consecutive occurrencesis bounded by a parameter $K$. We call such sequences $K$-quasi-regular.
We show that, surprisingly, $2$-quasi-regular sequences suffice for optimaldefender play. What is more, even randomized $2$-quasi-regular sequencessuffice for optimality. We show that such sequences always exist, and can becalculated efficiently.
The question of the least $K$ for which deterministic $K$-quasi-regularsequences exist is fascinating. Using an ergodic theoretical approach, we showthat deterministic $3$-quasi-regular sequences always exist. For $2 leq K < 3$we do not know whether deterministic $K$-quasi-regular sequences always exist.

Submission history

From: David Kempe [view email]
[v1] Tue, 22 Nov 2016 07:16:22 UTC (45 KB)
[v2] Tue, 29 Nov 2016 07:43:48 UTC (46 KB)
[v3] Tue, 31 Jan 2017 22:11:49 UTC (45 KB)
[v4] Mon, 20 Feb 2017 03:07:34 UTC (46 KB)
[v5] Fri, 14 Jul 2017 03:35:22 UTC (48 KB)
[v6]Sun, 29 Oct 2017 00:29:29 UTC (49 KB)
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