Existence of equilibrium in common agency games with adverse selection

Carmona, Guilherme; Fajardo, José

doi:10.1016/j.geb.2008.10.003

Cited by 17 publications

(17 citation statements)

References 13 publications

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“…2 In particular, Page and Monteiro (2003) first establish, under some additional conditions on primitives, that no matter what the tie-breaking rule (or mechanism), catalog games are uniformly payoff secure. 3 Next they show that if the catalog game is uniformly payoff secure, then no matter what the tie-breaking rule the mixed extension of the game is payoff secure. 4 Together these two results imply that the question of existence of Nash equilibrium in discontinuous mixed catalog games reduces (via Reny (1999)) to a search for tie-breaking mechanisms which guarantee that the induced expected profit functions over catalogs are at least reciprocally upper semicontinuous -a property guaranteed by the upper semicontinuity of expected profits under the optimistic tie-breaking rule.…”

Section: Related Literaturementioning

confidence: 99%

“…Reciprocal upper semicontinuity is implied by upper semicontinuity (but the converse does not hold in general). 3 A catalog game is uniformly payoff secure if for every firm j, every catalog C * j , and every ε > 0, there exists a catalog C j such that for any catalogs C −j offered by other firms there is a neighborhood of C−j such that…”

Section: Related Literaturementioning

confidence: 99%

“…The work most closely related to our analysis here is that of Carmona and Fajardo (2006). Their strategy for solving the Nash problem differs from our strategy.…”

Section: Related Literaturementioning

confidence: 99%

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Endogenous mechanisms and Nash equilibrium in competitive contracting games

Monteiro

Page

2009

Journal of Mathematical Economics

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We model strategic competition in a market with asymmetric information as a noncooperative game in which each firm competes for the business of a buyer of unknown type by offering the buyer a catalog of products and prices. The timing in our model is Stackelberg: in the first stage, given the distribution of buyer types known to all firms and the deducible, type-dependent best responses of the agent, firms simultaneously and noncooperatively choose their catalog offers. In the second stage the buyer, knowing his type, chooses a single firm and product-price pair from that firm's catalog. By backward induction, this Stackelberg game with asymmetric information reduces to a game over catalogs with payoff indeterminacies. In particular, due to ties within catalogs and/or across catalogs, corresponding to any catalog profile offered by firms there may be multiple possible expected firm payoffs, all consistent with the rational optimizing behavior of the agent for each of his types. The resolution of these indeterminacies depends on the tie-breaking mechanism which emerges in the market. Because each tie-breaking mechanism induces a particular game over catalogs, a reasonable candidate would be a tie-breaking mechanism which supports a Nash equilibrium in the corresponding catalog game. We call such a mechanism an endogenous Nash mechanism. The fundamental question we address in this paper is, does there exist an endogenous Nash mechanism -and therefore, does there exist a Nash equilibrium for the catalog game? We show under fairly mild conditions on primitives that catalog games naturally possess tie-breaking mechanisms which support Nash equilibria.

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Section: Related Literaturementioning

confidence: 99%

Section: Related Literaturementioning

confidence: 99%

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Endogenous mechanisms and Nash equilibrium in competitive contracting games

Monteiro

Page

2009

Journal of Mathematical Economics

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“…The results of Bagh & Jofré in [5], and of Page Jr. & Monteiro in [29] and [30] provide testable conditions that allow for Reny's results to be used in multi-firm-agent games. An alternate route has been taken by Carmona & Fajardo in [10]. The authors provide an existence result of sub-game perfect equilibria in common agency games.…”

Section: Introductionmentioning

confidence: 99%

Efficiency and equilibria in games of optimal derivative design

Horst

Moreno-Bromberg

2011

Math Finan Econ

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In this paper the problem of optimal derivative design, profit maximization and risk minimization under adverse selection when multiple agencies compete for the business of a continuum of heterogenous agents is studied. In contrast with the principal-agent models that are extended within, here the presence of ties in the agents' best-response correspondences yields discontinuous payoff functions for the agencies. These discontinuities are dealt with via efficient tie-breaking rules. The main results of this paper are a proof of existence of (mixed-strategies) Nash equilibria in the case of profit-maximizing agencies, and of socially efficient allocations when the firms are risk minimizers. It is also shown that in the particular case of the entropic risk measure, there exists an efficient "fix-mix" tie-breaking rule, in which case firms share the whole market over given proportions. Preliminary -Comments WelcomeJEL classification: C62, C72, D43, D82, G14.

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“…Along those lines, Stole (1991) and Martimort (1992) characterized equilibria for games of private agency (each principal contracts on a specific activity of their common agent) whereas Martimort and Stole (2010) focused on public agency (all principals contract on the same variables). The existence of equilibrium in more general menu games, or more precisely for their mixedstrategy extensions, was investigated by Page and Monteiro (2003), Monteiro and Page (2005), Page (2008) and Carmona and Fajardo (2009). While the first contributions take as fixed the strategy by the common agent, Carmona and Fajardo (2009) determined this strategy endogenously as part of the solution concept.…”

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confidence: 99%

Representing equilibrium aggregates in aggregate games with applications to common agency

Martimort

Stole²

2012

Games and Economic Behavior

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International audienceAn aggregate game is a normal-form game with the property that each playerʼs payoff is a function of only his own strategy and an aggregate of the strategy profile of all players. Such games possess properties that can often yield simple characterizations of equilibrium aggregates without requiring that one solves for the equilibrium strategy profile. When payoffs have a quasi-linear structure and a degree of symmetry, we construct a self-generating maximization program over the space of aggregates with the property that the solution set corresponds to the set of equilibrium aggregates of the original n-player game. We illustrate the value of this approach in common-agency games where the playersʼ strategy space is an infinite-dimensional space of nonlinear contracts. We derive equilibrium existence and characterization theorems for both the adverse selection and moral hazard versions of these games

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Existence of equilibrium in common agency games with adverse selection

Cited by 17 publications

References 13 publications

Endogenous mechanisms and Nash equilibrium in competitive contracting games

Endogenous mechanisms and Nash equilibrium in competitive contracting games

Efficiency and equilibria in games of optimal derivative design

Representing equilibrium aggregates in aggregate games with applications to common agency

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