Diverse and varied cyber-attacks challenge the operation of the smart-world system that is supported by Internet-of-Things (IoT) (smart cities, smart grid, smart transportation, etc.) and must be carefully and thoughtfully addressed before widespread adoption of the smart-world system can be fully realized. Although a number of research efforts have been devoted to defending against these threats, a majority of existing schemes focus on the development of a specific defensive strategy to deal with specific, often singular threats. In this paper, we address the issue of coalitional attacks, which can be launched by multiple adversaries cooperatively against the smart-world system such as smart cities. Particularly, we propose a game-theory based model to capture the interaction among multiple adversaries, and quantify the capacity of the defender based on the extended Iterated Public Goods Game (IPGG) model. In the formalized game model, in each round of the attack, a participant can either cooperate by participating in the coalitional attack, or defect by standing aside. In our work, we consider the generic defensive strategy that has a probability to detect the coalitional attack. When the coalitional attack is detected, all participating adversaries are penalized. The expected payoff of each participant is derived through the equalizer strategy that provides participants with competitive benefits. The multiple adversaries with the collusive strategy are also considered. Via a combination of theoretical analysis and experimentation, our results show that no matter which strategies the adversaries choose (random strategy, win-stay-lose-shift strategy, or even the adaptive equalizer strategy), our formalized game model is capable of enabling the defender to greatly reduce the maximum value of the expected average payoff to the adversaries via provisioning sufficient defensive resources, which is reflected by setting a proper penalty factor against the adversaries. In addition, we extend our game model and analyze the extortion strategy, which can enable one participant to obtain more payoff by extorting his/her opponents. The evaluation results show that the defender can combat this strategy by encouraging competition among the adversaries, and significantly suppress the total payoff of the adversaries via setting the proper penalty factor.
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