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International Conference on Web and Internet Economics

WINE 2016: Web and Internet Economics pp 1–14Cite as

Computing Equilibria with Partial Commitment

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10123))

Abstract

In security games, the solution concept commonly used is that of a Stackelberg equilibrium where the defender gets to commit to a mixed strategy. The motivation for this is that the attacker can repeatedly observe the defender’s actions and learn her distribution over actions, before acting himself. If the actions were not observable, Nash (or perhaps correlated) equilibrium would arguably be a more natural solution concept. But what if some, but not all, aspects of the defender’s actions are observable? In this paper, we introduce solution concepts corresponding to this case, both with and without correlation. We study their basic properties, whether these solutions can be efficiently computed, and the impact of additional observability on the utility obtained.

I dedicate this paper to my sister Jessica, her fiancé Jeremy, and their upcoming full commitment. I wish them a lifetime of happiness.

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Notes

  1. 1.

    As is commonly assumed in this model, ties for the column player are broken in the row player’s favor; if not, the row player can simply commit to \(1/2-\epsilon \) on a and \(1/2+\epsilon \) on b.

  2. 2.

    It is easy to get confused here—does the column player not learn more in a round purely by virtue of his own payoff from that round? It is important to remember that we are not considering repeated play by the column player. The idea is that the column player can observe over time the signals and how the row player acts before the column player ever acts. For discussion of security contexts in which certain types of players can receive messages that are inaccessible to other types, see Xu et al. [24].

  3. 3.

    This was verified to be optimal using the linear program in Fig. 1; same for the next case.

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Acknowledgments

I am thankful for support from ARO under grants W911NF-12-1-0550 and W911NF-11-1-0332, NSF under awards IIS-1527434, IIS-0953756, CCF-1101659, and CCF-1337215, and a Guggenheim Fellowship.

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  1. Duke University, Durham, North Carolina, USA

    Vincent Conitzer

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  1. Vincent Conitzer
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Correspondence to Vincent Conitzer .

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Editors and Affiliations

  1. School of Computer Science, McGill University, Montreal, Québec, Canada

    Yang Cai

  2. Department of Mathematics and Statistics, and School of Computer Science, McGill University, Montreal, Québec, Canada

    Adrian Vetta

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Conitzer, V. (2016). Computing Equilibria with Partial Commitment. In: Cai, Y., Vetta, A. (eds) Web and Internet Economics. WINE 2016. Lecture Notes in Computer Science(), vol 10123. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-54110-4_1

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  • DOI: https://doi.org/10.1007/978-3-662-54110-4_1

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