A Note on Negative Electoral Advertising

In their seminal paper, Harrington and Hess (1996) discuss a model where candidates differ along two dimensions - ideology which is modeled by the standard Hotelling-Downs formulation and valence factors which encompass traits which all voters agree as desirable. While valence factor is given, the voter perception of a candidate’s ideology can be influenced via advertising. In this expository note, we extend the model model to take account of valence as well as ideological advertising but we restrict our attention only to negative advertising. We find that when the available resources are sufficiently small and certain technical conditions are fulfilled, the expected result holds, namely, the candidate with the higher initial valence index will run a relatively personal campaign while the candidate with the lower initial valence index will run an ideological campaign.Negative Advertising, Electoral Contests

Private Peering Among Internet Backbone Providers

We develop a model, in which Internet backbone providers decide on private peering agreements, comparing the benefits of private peering relative to being connected only through National Access Points. Backbone providers compete by setting capacities for their networks, capacities on the private peering links, if they choose to peer privately, and access prices. The model is formulated as a multistage game. We examine the model from two alternative modelling perspectives - a purely non-cooperative game, where we solve for Subgame Perfect Nash Equilibria through backward induction, and a network theoretic perspective, where we examine pairwise stable and efficient networks. While there are a large number of Subgame Perfect Nash Equilibria, both the pairwise stable and the efficient network are unique and the stable network is not efficient and vice versa. The stable network is the complete network, where all the backbone providers choose to peer with each other, while the efficient network is the one, where the backbone providers are connected to each other only through the National Access Points.Subgame perfect Nash equilibrium, networks, pairwise stability, efficiency

Intra-backbone and Inter-backbone Peering Among Internet Service Providers

We consider a model with two backbones and a finite number of Internet Service Providers (ISPs) connected to the backbones. ISPs decide on private peering agreements, comparing the benefits of private peering to costs. Intra-backbone peering refers to peering between ISPs connected to the same backbone, whereas inter-backbone peering refers to peering between ISPs connected to different backbones. We formulate the model as a two-stage game. In the first stage, ISPs decide on peering agreements. In the second stage they compete in prices a la Bertrand. We examine the effects of peering on profits of ISPs. Peering affects profits through two channels - reduction of backbone congestion which we call the symmetric effect and ability to send traffic bypassing or circumventing congested backbones which we call the asymmetric effect. The first has a negative or ambiguous effect while the second has a generally positive effect on firm profits. The two often act against each other making the net effect ambiguous. We also conduct simulations to determine pairwise stable peering configurations in a six-provider model and find that there is a paucity of inter-backbone peering in asymmetric settings.Peering, Networks

Intra-backbone and Inter-backbone Peering Among Internet Service Providers

We consider a model with two backbones and a finite number of Internet Service Providers (ISPs) connected to the backbones. ISPs decide on private peering agreements, comparing the benefits of private peering to costs. Intra-backbone peering refers to peering between ISPs connected to the same backbone, whereas inter-backbone peering refers to peering between ISPs connected to different backbones. We formulate the model as a two-stage game. In the first stage, ISPs decide on peering agreements. In the second stage they compete in prices a la Bertrand. We examine the effects of peering on profits of ISPs. Peering affects profits through two channels - reduction of backbone congestion which we call the symmetric effect and ability to send traffic bypassing or circumventing congested backbones which we call the asymmetric effect. The first has a negative or ambiguous effect while the second has a generally positive effect on firm profits. The two often act against each other making the net effect ambiguous. We also conduct simulations to determine pairwise stable peering configurations in a six-provider model and find that there is a paucity of inter-backbone peering in asymmetric settings.Peering, Networks

Private Peering Among Internet Backbone Providers

We develop a model, in which Internet backbone providers decide on private peering agreements, comparing the benefits of private peering relative to being connected only through National Access Points. Backbone providers compete by setting capacities for their networks, capacities on the private peering links, if they choose to peer privately, and access prices. The model is formulated as a multistage game. We examine the model from two alternative modelling perspectives - a purely non-cooperative game, where we solve for Subgame Perfect Nash Equilibria through backward induction, and a network theoretic perspective, where we examine pairwise stable and efficient networks. While there are a large number of Subgame Perfect Nash Equilibria, both the pairwise stable and the efficient network are unique and the stable network is not efficient and vice versa. The stable network is the complete network, where all the backbone providers choose to peer with each other, while the efficient network is the one, where the backbone providers are connected to each other only through the National Access Points.Subgame perfect Nash equilibrium, networks, pairwise stability, efficiency

An Analysis of Advertising Wars

Comparative advertising by one brand against another showcases its merits versus the demerits of the other. In a two-stage game among finitely many firms, firms decide first how much to advertise against whom. In the second stage, given the advertising configuration, firms compete as Cournot oligopolists. In the symmetric case, equilibrium advertising constitutes a clear welfare loss. Equilibrium advertising levels and advertising expenditures decline with rising advertising costs. Whereas equilibrium levels of advertising decrease in the number of firms, aggregate advertising expenditures increase. We further relate effectiveness of advertising to proximity in product space. With two firms, comparative advertising and quality choice have similar effects. In a three stage game, where firms choose first locations (variety), then advertising levels (quality), and then quantities, we obtain maximum horizontal product differentiation and minimum vertical product differentiation.Advertising, Cournot Oligopoly, Product Differentiation

A Note on Negative Electoral Advertising

In their seminal paper, Harrington and Hess (1996) discuss a model where candidates differ along two dimensions - ideology which is modeled by the standard Hotelling-Downs formulation and valence factors which encompass traits which all voters agree as desirable. While valence factor is given, the voter perception of a candidate’s ideology can be influenced via advertising. In this expository note, we extend the model model to take account of valence as well as ideological advertising but we restrict our attention only to negative advertising. We find that when the available resources are sufficiently small and certain technical conditions are fulfilled, the expected result holds, namely, the candidate with the higher initial valence index will run a relatively personal campaign while the candidate with the lower initial valence index will run an ideological campaign

Networks of Collaboration in Multi-market Oligopolies

The result that firms competing in a Cournot oligopoly with pairwise collaboration form a complete network under zero or negligible link formation costs provided by Goyal and Joshi (2003) no longer hold in multi-market oligopolies. Link formation in one market affects a firm’s profitability in another market in a possibly negative way resulting in the fact that it is no longer always profitable in an unambiguous manner. With non-negative link formation costs, the stable networks have a dominant group architecture and efficient networks are charecterized by at most one non-singleton component with a geodesic distance between players that is less than three

An Analysis of Advertising Wars

Comparative advertising by one brand against another showcases its merits versus the demerits of the other. In a two-stage game among finitely many firms, firms decide first how much to advertise against whom. In the second stage, given the advertising configuration, firms compete as Cournot oligopolists. In the symmetric case, equilibrium advertising constitutes a clear welfare loss. Equilibrium advertising levels and advertising expenditures decline with rising advertising costs. Whereas equilibrium levels of advertising decrease in the number of firms, aggregate advertising expenditures increase. We further relate effectiveness of advertising to proximity in product space. With two firms, comparative advertising and quality choice have similar effects. In a three stage game, where firms choose first locations (variety), then advertising levels (quality), and then quantities, we obtain maximum horizontal product differentiation and minimum vertical product differentiation.Advertising, Cournot Oligopoly, Product Differentiation