The Value of Ambiguous Commitments in Multi-Follower Games
Natalie Collina, Rabanus Derr, Aaron Roth

TL;DR
This paper explores how ambiguous commitment strategies in multi-follower games can significantly enhance a leader's utility, especially when commitments are coupled across followers, with implications for game theory and strategic decision-making.
Contribution
It extends the understanding of ambiguous commitments from single to multiple followers, demonstrating potential unbounded utility gains and providing algorithms for specific cases.
Findings
Ambiguous commitment can greatly increase leader's utility in multi-follower games.
Coupling commitments across followers can yield unbounded advantages, unlike in zero-sum games.
Efficient algorithms exist for specific cases, but the general problem is NP-hard.
Abstract
We study games in which a leader makes a single commitment, and then multiple followers (each with a different utility function) respond. In particular, we study ambiguous commitment strategies in these games, in which the leader may commit to a set of mixed strategies, and ambiguity-averse followers respond to maximize their worst-case utility over the set of leader strategies. Special cases of this setting have previously been studied when there is a single follower: in these cases, it is known that the leader can increase her utility by making an ambiguous commitment if the follower is restricted to playing a pure strategy, but that no gain can be had from ambiguity if the follower may mix. We confirm that this result continues to hold in the setting of general Stackelberg games. We then develop a theory of ambiguous commitment in games with multiple followers. We begin by…
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Taxonomy
TopicsGame Theory and Applications · Digital Platforms and Economics · Business Strategy and Innovation
