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On The Existence Of Equilibrium In Bayesian Games Without Complementarities, Idione Meneghel, Rabee Tourky
On The Existence Of Equilibrium In Bayesian Games Without Complementarities, Idione Meneghel, Rabee Tourky
Cowles Foundation Discussion Papers
This paper presents new results on the existence of pure-strategy Bayesian equilibria in specified functional forms. These results broaden the scope of methods developed by Reny (2011) well beyond monotone pure strategies. Applications include natural models of first-price and all-pay auctions not covered by previous existence results. To illustrate the scope of our results, we provide an analysis of three auctions: (i) a first-price auction of objects that are heterogeneous and imperfect substitutes; (ii) a first-price auction in which bidders’ payoffs have a very general interdependence structure; and (iii) an all-pay auction with non-monotone equilibrium.
On The Existence Of Equilibrium In Bayesian Games Without Complementarities, Idione Meneghel, Rabee Tourky
On The Existence Of Equilibrium In Bayesian Games Without Complementarities, Idione Meneghel, Rabee Tourky
Cowles Foundation Discussion Papers
In a recent paper, Reny (2011) generalized the results of Athey (2001) and McAdams (2003) on the existence of monotone strategy equilibrium in Bayesian games. Though the generalization is subtle, Reny introduces far-reaching new techniques applying the fixed point theorem of Eilenberg and Montgomery (1946, Theorem 5). This is done by showing that with atomless type spaces the set of monotone functions is an absolute retract and when the values of the best response correspondence are non-empty sub-semilattices of monotone functions, they too are absolute retracts. In this paper, we provide an extensive generalization of Reny (2011), McAdams (2003), and …
On The Existence Of Equilibrium In Bayesian Games Without Complementarities, Idione Meneghel, Rabee Tourky
On The Existence Of Equilibrium In Bayesian Games Without Complementarities, Idione Meneghel, Rabee Tourky
Cowles Foundation Discussion Papers
This paper presents new results on the existence of pure-strategy Bayesian equilibria in specified functional forms. These results broaden the scope of methods developed by Reny (2011) well beyond monotone pure strategies. Applications include natural models of first-price and all-pay auctions not covered by previous existence results. To illustrate the scope of our results, we provide an analysis of three auctions: (i) a first-price auction of objects that are heterogeneous and imperfect substitutes; (ii) a first-price auction in which bidders’ payoffs have a very general interdependence structure; and (iii) an all-pay auction with non-monotone equilibrium.