Leadership games with convex strategy sets

Abstract

This document is the author's final manuscript accepted version of the journal article, incorporating any revisions agreed during the peer review process. Some differences between this version and the published version may remain. You are advised to consult the publisher's version if you wish to cite from it. Leadership Games with Convex Strategy Sets AbstractA basic model of commitment is to convert a two-player game in strategic form to a "leadership game" with the same payoffs, where one player, the leader, commits to a strategy, to which the second player always chooses a best reply. This paper studies such leadership games for games with convex strategy sets. We apply them to mixed extensions of finite games, which we analyze completely, including nongeneric games. The main result is that leadership is advantageous in the sense that, as a set, the leader's payoffs in equilibrium are at least as high as his Nash and correlated equilibrium payoffs in the simultaneous game. We also consider leadership games with three or more players, where most conclusions no longer hold.

Commitment in first-price auctions

“…The result derived in this paper is quantitatively similar to those established in 2 We note that the complete information setting is somewhat standard in the literature on commitments in Stackelberg games (see [5,12]), and often yields a nontrivial optimal commitment for the leader.…”

“…In work that partially motivates the present study, von Stengel and Zamir [12] show that in a two-player Stackelberg game with finite action space, the leader always benefits from the power to commit to mixed strategies; when there is more than one follower, however, a leader may strictly lose by being required to commit to a mixed strategy. Unlike in [12], the focus of this paper is on deriving a complete characterization of optimal commitments, for a more technically challenging setting with continuous action space. We also show that pre-play commitment in firstprice auctions always strictly benefits the leader even if there is more than one follower, as long as the leader's valuation is among the top two.…”

“…Before proceeding, we emphasize that the tie-breaking assumption and the assumption that bidder 2 always chooses the leader's favorite best response 4 are 4 Indeed, as noted by Maschler [19] and von Stengel and Zamir [12], if the follower did not choose the best response that is most favorable to the leader, the leader could induce such behavior at an SPE by slightly modifying her commitment. only used to characterize the SPE that maximizes the leader's expected payoff.…”

The Exact Computational Complexity of Evolutionarily Stable Strategies

“…In any case, equilibria are often seen as a state to which play could reasonably converge, rather than an outcome that can necessarily be arrived at immediately by deduction. Many other solution concepts have been studied from a computational perspective, including refinements of Nash equilibrium [Hansen et al, 2010;Sørensen, 2012], coarsenings of Nash equilibrium (such as correlated equilibrium [Papadimitriou and Roughgarden, 2008;Jiang and Leyton-Brown, 2013] and equilibria of repeated games [Littman and Stone, 2005;Borgs et al, 2010;Kontogiannis and Spirakis, 2008]), and incomparable concepts such as Stackelberg equilibrium [Conitzer and Sandholm, 2006;von Stengel and Zamir, 2010].…”

Lead, Follow or Cooperate? Sequential versus Collusive Payoffs in Symmetric Duopoly Games

“…In particular, by relaxing the assumption of complements or substitutes actions, [13] proves that either the leader's payoff dominates that of the follower (which is also dominated by the simultaneous Nash) or, in turn, is dominated by the follower's. Dowrick [16], Amir [17], Amir and Grilo [18], Amir et al [15], Currarini and Marini [19,20], and Von Stengel and Zamir [21] all present various leader-follower payoff comparisons between single players or coalitions. On the other hand, the relationship between fully cooperative and sequential payoffs has been scarcely explored.…”