Single Crossing Properties and the Existence of Pure Strategy Equilibria in Games of Incomplete Information

By Susan Athey. 2001

684 citations recorded by the source corpus.

Subfields: Economics and Econometrics, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/24d1f36668dde7bd901ec9e9f9d795ec3c37b035

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Citations in the corpus

Asymmetric Auctions with Resale (2008, background): “0 = fi ( i (b)) 0 i (b) pj (b; vj) fi ( i (b)) i (b) b Fi ( i (b)) where pj (b; vj) is dened as the solution to (1).”
Nonparametric Identification of Risk Aversion in First‐Price Auctions Under Exclusion Restrictions (2009, background): “Athey and Haile (2002) and Haile, Hong and Shum (2003) exploit some exclusion restrictions to test for common values in first-price sealed-bid auctions.”
Monotone Comparative Statics under Uncertainty (2002, background): “Athey (forthcoming) applies this result to show that in auction games such as the first price auction described above, a PSNE exists.”
Global Games: Theory and Applications (2003, positive): “Now lemma 5 in Athey (2000b) implies that h(·, k, x ′) satisfies a single crossing property: there exists x∗(k, x ′) such that h(x, k, x ′) < 0 for all x < x∗(k, x ′), and h(x, k, x ′) > 0 for all x > x∗(k, x ′).”
Aggregating the single crossing property (2012, background): “…Nash equilibrium in which each player plays a monotone strategy (i.e., a strategy where the action increases with the player’s signal) hinges on whether a particular player has an optimal strategy that is monotone, given that other players are playing monotone strategies (see Athey (2001)).”
Auctions and Information acquisition: Sealed-bid or Dynamic Formats? (2007, methodology): “When there are no other uninformed bidders (n2 = 1), or when p > v, observing the current price p signals that θ((1)) > p, and it is readily verified that”
On the Existence of Pure Strategy Monotone Equilibria in Asymmetric First-Price Auctions (2004, methodology): “The reason for this is that standard proof techniques rely on the following single-crossing condition (SCC) exploited with great ingenuity in Athey (2001): If the others employ nondecreasing bid functions and one’s payoff from a high bid is no smaller than that from a lower bid, then the high bid…”
Auctions with Downstream Interaction Among Buyers (2000, background): “…Dyg > 0; we obtain ee¼ < G¡1(R): This means that a type slightly above ee¼ prefers to bid above R; but type G¡1(R) never bids above R: Hence the single crossing of incremental returns, which is a su¢cient condition for the existence of pure strategy equilibria, is not satis…ed (see Athey, 1999).”
Discrete Bids and Empirical Inference in Divisible Good Auctions (2011, methodology): “The difficulty with this approach, however, is that both the necessary condition (3) and inequalities implied by choosing qk rather than qk −∆ involve the gross utility V (·, si), which is an integral of the object of interest, v (·, si).”
Semiparametric Estimation of First-Price Auctions with Risk Averse Bidders* (2011, neutral): “Using US Forest Service auctions, Baldwin (1995) and Athey and Levin (2001) show that bidding diversification across species is consistent with bidders’ risk aversion.”
Toward a Strategic Foundation for Rational Expectations Equilibrium (2006, methodology): “By Athey (2001), to prove (i) and (ii) it suffices to show that u(p, x|x) satisfies single crossing in (p, x).”