The Price of Defense
نویسندگان
چکیده
We consider a game on graph $$G=\langle V, E\rangle $$ with two confronting classes of randomized players: $$\nu attackers, who choose vertices and seek to minimize the probability getting caught, single defender, chooses edges seeks maximize expected number attackers it catches. In Nash equilibrium, no player has an incentive unilaterally deviate from her strategy. The Price Defense is worst-case ratio, over all equilibria, utility defender at equilibrium. orchestrate strong interplay arguments Game Theory Graph obtain both general specific results in considered setting: (1) Via reduction Two-Players, Constant-Sum game, we observe that arbitrary equilibrium computable polynomial time. Further, prove lower bound $$\frac{\textstyle |V|}{\textstyle 2}$$ Defense. derive characterization graphs attaining this bound, which reveals promising connection Fractional Theory; thereby, implies efficient recognition algorithm for such Defense-Optimal graphs. (2) study some their computational complexity incurred are defined by imposing structure players’ strategies: either graph-theoretic supports, or symmetry uniformity probabilities. develop novel techniques trade-offs between these classes. Some touch upon classical milestones example, first game-theoretic König-Egerváry as admitting Matching
منابع مشابه
The Price of Defense
We consider a strategic game with two classes of confronting randomized players on a graph G(V,E): ν attackers, each choosing vertices and wishing to minimize the probability of being caught, and a defender, who chooses edges and gains the expected number of attackers it catches. The Price of Defense is the worst-case ratio, over all Nash equilibria, of the optimal gain of the defender over its...
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ژورنال
عنوان ژورنال: Algorithmica
سال: 2021
ISSN: ['1432-0541', '0178-4617']
DOI: https://doi.org/10.1007/s00453-020-00783-7