Isotone Equilibrium in Games of Incomplete Information

By David McAdams. 2002

155 citations recorded by the source corpus.

An isotone pure strategy equilibrium exists in any game of incomplete information in which (1) each player i's action set is a finite sublattice of multi-dimensional Euclidean space, (2) types are multidimensional and atomless, and each player's interim expected payoff function satisfies two "non-primitive conditions" whenever others adopt isotone pure strategies: (3) single-crossing in own action and type and (4) quasisupermodularity in own action. Similarly, given that (134) and (2') types are multi-dimensional (with atoms) an isotone mixed strategy equilibrium exists. Conditions (34) are satisfied in supermodular and log-supermodular games given affiliated types, and in games with independent types in which each player's ex post payoff satisfies (a) supermodularity in own action and (b) non-decreasing differences in own action and type. These results also extend to games with a continuum action space when each player's ex post payoff is also continuous in his and others' actions.

Subfields: Economics and Econometrics, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/ff910005fa7aa20701558e9136b4798a691d765c

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Economics and Econometrics

1. Philip J. Reny
2. Xavier Vives
3. David McAdams
4. Elena Carletti
5. Rafael Repullo
6. Todd Keister

In Management Science and Operations Research

1. Philip J. Reny
2. Xavier Vives
3. David McAdams
4. Marek Weretka
5. Mar Reguant
6. Claudio Mezzetti
7. Marzena Rostek

Citations in the corpus

• On the Existence of Monotone Pure Strategy Equilibria in Bayesian Games (2009, methodology): “Both Athey (2001) and McAdams (2003), within the con nes of a lattice, make use of quasisupermodularity and single-crossing conditions on interim payo¤s.”
• Complementarities and Games: New Developments (2005, background): “• uniform price auctions with multiunit demand with non-private values and independent types (McAdams (2003)).”
• Monotone Equilibrium in Multi-Unit Auctions (2006, methodology): “…but, unlike this paper, do nothing to rule out the possibility of non-MPSE.4 More to the point of this paper, Rodriguez (2000) (for two bidders) and McAdams (2003a) (for n bidders) establish that all equilibria must be equivalent to MPSE (in the stronger sense of ex post allocation- and ex post…”