Efficient Strategy Computation in Zero-Sum Asymmetric Information Repeated Games

Abstract

Zero-sum asymmetric games model decision making scenarios involving two competing players who have different information about the game being played. A particular case is that of nested information, where one (informed) player has superior information over the other (uninformed) player. This paper considers the case of nested information in repeated zerosum games and studies the computation of strategies for both the informed and uninformed players for finite-horizon and discounted infinite-horizon nested information games. For finitehorizon settings, we exploit that for both players, the security strategy, and also the opponent's corresponding best response depend only on the informed player's history of actions. Using this property, we refine the sequence form, and formulate an LP computation of player strategies that is linear in the size of the uninformed player's action set. For the infinite-horizon discounted game, we construct LP formulations to compute the approximated security strategies for both players, and provide a bound on the performance difference between the approximated security strategies and the security strategies. Finally, we illustrate the results on a network interdiction game between an informed system administrator and uniformed intruder.

Can Competition Outperform Collaboration? The Role of Misbehaving Agents

“…A third research avenue involves zero-sum games to model interactions among agents [43,44]. In particular, in asymmetric zero-sum games, one player has more knowledge than the other, which is a suitable model for worst-case attacks.…”

“…In our case, misbehaving agents are stubborn on average but behave in a less trivial (noisy) way. On the other hand, smart (malicious) adversaries may need to be contrasted by sophisticated strategies [43,44]. This case is outside the scope of this article, where we explore competition as a tool to enhance resilience, and we defer a comprehensive study with intelligent attacks to future work.…”

Can Competition Outperform Collaboration? The Role of Malicious Agents

“…A third research avenue involves zero-sum games [60], [61] to alternatively model the system dynamics. In particular, asymmetric zero-sum games let one player have more knowledge than other, which may be a suitable model for worst-case attacks.…”

Analyzing pre-commitment strategies in General Lotto games

“…Related works: This manuscript takes steps towards understanding the competitive allocation of resources in multistage scenarios. There is widespread interest in this research objective that involves the analysis of zero-sum games [14], [20], [21], differential or repeated games [13], [27], and Colonel Blotto games [1], [19], [26], [29]. The goal of many of these works is to develop tools to compute decision-making policies for agents in adversarial and uncertain environments.…”