scholarly journals Screening in Vertical Oligopolies

Econometrica ◽  
2021 ◽  
Vol 89 (3) ◽  
pp. 1265-1311
Author(s):  
Hector Chade ◽  
Jeroen Swinkels
Keyword(s):  
Finite Number ◽  
Private Information ◽  
Mixed Strategy ◽  
Necessary Conditions ◽  
Welfare Effects ◽  
Outside Option ◽  
Strategy Equilibrium ◽  
Simple Set ◽  
Higher Types ◽  
Efficient Level

A finite number of vertically differentiated firms simultaneously compete for and screen agents with private information about their payoffs. In equilibrium, higher firms serve higher types. Each firm distorts the allocation downward from the efficient level on types below a threshold, but upward above. While payoffs in this game are neither quasi‐concave nor continuous, if firms are sufficiently differentiated, then any strategy profile that satisfies a simple set of necessary conditions is a pure‐stategy equilibrium, and an equilibrium exists. A mixed‐strategy equilibrium exists even when firms are less differentiated. The welfare effects of private information are drastically different than under monopoly. The equilibrium approaches the competitive limit quickly as entry costs grow small. We solve the problem of a multi‐plant firm facing a type‐dependent outside option and use this to study the effect of mergers.

scholarly journals Coordination and Private Information Revelation: Failure of Information Unraveling

2018 ◽  
Author(s):  
Debdatta Saha ◽  
Prabal Roy Chowdhury
Keyword(s):  
Asymmetric Information ◽  
Private Information ◽  
Mixed Strategy ◽  
Coordination Game ◽  
Information Revelation ◽  
Strategic Uncertainty ◽  
Two Agents ◽  
Strategy Equilibrium ◽  
Battle Of The Sexes ◽  
Central Result

This paper examines a persuasion game between two agents with one-sided asymmetric information, where the informed agent can reveal her private information prior to playing a Battle-of-the-Sexes coordination game. We find that in the presence of strategic uncertainty in coordination there exists an equilibrium where there is no 'unraveling' of information. We provide a purification argument for this mixed strategy equilibrium to strengthen the central result, which is robust to several extensions, including both-sided asymmetric information and imprecise information revelation.

scholarly journals Flags of holomorphic foliations

2011 ◽  
Vol 83 (3) ◽  
pp. 775-786 ◽  
Author(s):  
Rogério S. Mol
Keyword(s):  
Finite Number ◽  
Complex Manifold ◽  
Necessary Conditions ◽  
Holomorphic Foliations ◽  
Lower Dimension ◽  
Higher Dimension ◽  
Basic Properties ◽  
Codimension One ◽  
Tangent Sheaf ◽  
Polar Classes

A flag of holomorphic foliations on a complex manifold M is an object consisting of a finite number of singular holomorphic foliations on M of growing dimensions such that the tangent sheaf of a fixed foliation is a subsheaf of the tangent sheaf of any of the foliations of higher dimension. We study some basic properties oft hese objects and, in <img src="/img/revistas/aabc/2011nahead/aop2411pcn.jpg" align="absmiddle" />, n > 3, we establish some necessary conditions for a foliation, we find bounds of lower dimension to leave invariant foliations of codimension one. Finally, still in <img src="/img/revistas/aabc/2011nahead/aop2411pcn.jpg" align="absmiddle" /> involving the degrees of polar classes of foliations in a flag.

scholarly journals Mixed Equilibrium in a Pure Location Game: The Case of n≥4$$n \ge 4$$ Firms

2015 ◽  
Vol 15 (2) ◽  
Author(s):  
Christian Ewerhart
Keyword(s):  
Political Theory ◽  
Mixed Strategy ◽  
Spatial Competition ◽  
Mixed Strategy Equilibrium ◽  
Strategy Equilibrium ◽  
Mixed Equilibrium

AbstractThe Hotelling game of pure location allows interpretations in spatial competition, political theory, and strategic forecasting. In this paper, the doubly symmetric mixed-strategy equilibrium for

scholarly journals Biological auctions with multiple rewards

2015 ◽  
Vol 282 (1812) ◽  
pp. 20151041 ◽  
Author(s):  
Johannes G. Reiter ◽  
Ayush Kanodia ◽  
Raghav Gupta ◽  
Martin A. Nowak ◽  
Krishnendu Chatterjee
Keyword(s):  
Mixed Strategy ◽  
Evolutionarily Stable Strategy ◽  
Fundamental Characteristic ◽  
Stable Strategy ◽  
Bidding Strategies ◽  
Multiple Resources ◽  
Mixed Strategy Equilibrium ◽  
Strategy Equilibrium ◽  
Evolutionarily Stable ◽  
Competition For Resources

The competition for resources among cells, individuals or species is a fundamental characteristic of evolution. Biological all-pay auctions have been used to model situations where multiple individuals compete for a single resource. However, in many situations multiple resources with various values exist and single reward auctions are not applicable. We generalize the model to multiple rewards and study the evolution of strategies. In biological all-pay auctions the bid of an individual corresponds to its strategy and is equivalent to its payment in the auction. The decreasingly ordered rewards are distributed according to the decreasingly ordered bids of the participating individuals. The reproductive success of an individual is proportional to its fitness given by the sum of the rewards won minus its payments. Hence, successful bidding strategies spread in the population. We find that the results for the multiple reward case are very different from the single reward case. While the mixed strategy equilibrium in the single reward case with more than two players consists of mostly low-bidding individuals, we show that the equilibrium can convert to many high-bidding individuals and a few low-bidding individuals in the multiple reward case. Some reward values lead to a specialization among the individuals where one subpopulation competes for the rewards and the other subpopulation largely avoids costly competitions. Whether the mixed strategy equilibrium is an evolutionarily stable strategy (ESS) depends on the specific values of the rewards.

scholarly journals Bundling and Competition for Slots

2012 ◽  
Vol 102 (5) ◽  
pp. 1957-1985 ◽  
Author(s):  
Doh-Shin Jeon ◽  
Domenico Menicucci
Keyword(s):  
Marginal Cost ◽  
Mixed Strategy ◽  
Pure Strategy ◽  
Policy Implications ◽  
Digital Goods ◽  
Efficient Technology ◽  
Pure Strategy Equilibrium ◽  
Clear Cut ◽  
Mixed Strategy Equilibrium ◽  
Strategy Equilibrium

We consider competition between sellers selling multiple distinct products to a buyer having k slots. Under independent pricing, a pure strategy equilibrium often does not exist, and equilibrium in mixed strategy is never efficient. When bundling is allowed, each seller has an incentive to bundle his products, and an efficient “technology-renting” equilibrium always exists. Furthermore, in the case of digital goods or when sales below marginal cost are banned, all equilibria are efficient. Comparing the mixed-strategy equilibrium with the technology-renting equilibrium reveals that bundling often increases the buyer's surplus. Finally, we derive clear-cut policy implications.(JEL D43, D86, K21, L13, L14, L41, L82)

scholarly journals External Economies and International Trade Redux: Comment*

2013 ◽  
Vol 128 (4) ◽  
pp. 1895-1905 ◽  
Author(s):  
Gary Lyn ◽  
Andrés Rodríguez-Clare
Keyword(s):  
International Trade ◽  
Multiple Equilibria ◽  
Mixed Strategy ◽  
Equilibrium Analysis ◽  
Perfect Competition ◽  
Transport Costs ◽  
Trade Patterns ◽  
Strategy Equilibrium ◽  
Pure Strategies ◽  
Alternative Set

Abstract Recently, Gene Grossman and Esteban Rossi-Hansberg (GRH; “External Economies and International Trade: Redux,” Quarterly Journal of Economics 125 [2010], 829–858) proposed a novel way to think about the implications of international trade in the presence of national external economies at the industry level. Instead of perfect competition and two industries, GRH assume Bertrand competition and a continuum of industries. GRH conclude that the equilibrium is unique if transport costs are low, that there is no trade for high transport costs, and that there is no equilibrium in pure strategies when transport costs are intermediate. In this note we reexamine the equilibrium analysis under different transport costs for a single industry (partial equilibrium) version of GRH’s model. We confirm many of GRH’s results, but also find that there are circumstances under which there are multiple equilibria, including equilibria in which trade patterns run counter to “natural” comparative advantage, and also find that there is a profitable deviation to the mixed-strategy equilibrium postulated by GRH for intermediate trading costs. We propose an alternative set of strategies for this case and establish that they constitute an equilibrium.

On the Foundations of Nash Equilibrium

1996 ◽  
Vol 12 (1) ◽  
pp. 67-88 ◽  
Author(s):  
Hans Jørgen Jacobsen
Keyword(s):  
Game Theory ◽  
Nash Equilibrium ◽  
Cooperative Game Theory ◽  
Mixed Strategy ◽  
Pure Strategy ◽  
Mixed Strategies ◽  
Positive Theory ◽  
Equilibrium Concept ◽  
Strategy Equilibrium ◽  
Pure Strategies

The most important analytical tool in non-cooperative game theory is the concept of a Nash equilibrium, which is a collection of possibly mixed strategies, one for each player, with the property that each player's strategy is a best reply to the strategies of the other players. If we do not go into normative game theory, which concerns itself with the recommendation of strategies, and focus instead entirely on the positive theory of prediction, two alternative interpretations of the Nash equilibrium concept are predominantly available.In the more traditional one, a Nash equilibrium is a prediction of actual play. A game may not have a Nash equilibrium in pure strategies, and a mixed strategy equilibrium may be difficult to incorporate into this interpretation if it involves the idea of actual randomization over equally good pure strategies. In another interpretation originating from Harsanyi (1973a), see also Rubinstein (1991), and Aumann and Brandenburger (1991), a Nash equilibrium is a ‘consistent’ collection of probabilistic expectations, conjectures, on the players. It is consistent in the sense that for each player each pure strategy, which has positive probability according to the conjecture about that player, is indeed a best reply to the conjectures about others.

scholarly journals Random Actions in Experimental Zero-Sum Games

2021 ◽  
Vol 13 (1(J)) ◽  
pp. 69-81
Author(s):  
Jung S. You
Keyword(s):  
Nash Equilibrium ◽  
Mixed Strategy ◽  
Theoretical Models ◽  
Zero Sum Games ◽  
Strategy Equilibrium ◽  
Mixed Strategy Nash Equilibrium ◽  
Matching Pennies ◽  
Business Politics ◽  
The Game Theory ◽  
Zero Sum

A mixed strategy, a strategy of unpredictable actions, is applicable to business, politics, and sports. Playing mixed strategies, however, poses a challenge, as the game theory involves calculating probabilities and executing random actions. I test i.i.d. hypotheses of the mixed strategy Nash equilibrium with the simplest experiments in which student participants play zero-sum games in multiple iterations and possibly figure out the optimal mixed strategy (equilibrium) through the games. My results confirm that most players behave differently from the Nash equilibrium prediction for the simplest 2x2 zero-sum game (matching-pennies) and 3x3 zero-sum game (e.g., the rock-paper-scissors game). The results indicate the need to further develop theoretical models that explain a non-Nash equilibrium behavior.

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