Competing for Consumer's Attention

Automatica, Vol. 44, No. 2, pp. 361-370, February 1, 2008

10 Pages Posted: 29 Jul 2010

See all articles by Guiomar Martin-Herran

Guiomar Martin-Herran

University of Valladolid - Faculty of Economic Science and Business Studies

Olivier Rubel

University of California, Davis

Georges Zaccour

HEC Montreal - Department of Decision Sciences

Date Written: February 1, 2008

Abstract

We consider an infinite-horizon differential game played by two direct marketers. Each player controls the number of emails sent to potential customers at each moment in time. There is a cost associated to the messages sent, as well as a potential reward. The latter is assumed to depend on the state variable defined as the level of the representative consumer's attention. Two features are included in the model, namely, marginal decreasing returns and bounded rationality. By the latter, we mean that the representative consumer has a limited capacity for processing the information received. The evolution of this capacity depends on its level, as well as on the emails sent by both players. This provides environmental flavour where, usually, one player's pollution emissions (here emails) also affect the payoff of the other player by damaging the common environment (here, the stock of consumer attention).

We characterize competitive equilibria for different scenarios based on each player's type, i.e., whether the player is a spammer or not. We define a spammer as a myopic player, i.e., a player who cares only about short-term payoff and ignores the impact of her action on the state dynamics. In all scenarios, the game turns out to be of the linear-quadratic variety. Feedback Nash equilibria for the different scenarios are characterized and the equilibrium strategies and outcomes are compared.

Finally, we analyze the game in normal form, where each player has the option of choosing between being a spammer or not, and we characterize Nash equilibria

Keywords: Electronic business dynamics, Electronic mail, Direct marketing, Differential games, Spam

Suggested Citation

Martin-Herran, Guiomar and Rubel, Olivier and Zaccour, Georges, Competing for Consumer's Attention (February 1, 2008). Automatica, Vol. 44, No. 2, pp. 361-370, February 1, 2008 . Available at SSRN: https://ssrn.com/abstract=1474404

Guiomar Martin-Herran

University of Valladolid - Faculty of Economic Science and Business Studies ( email )

Avenida Valle Esgueva, 6
Valladolid
Spain

Olivier Rubel (Contact Author)

University of California, Davis ( email )

One Shields Avenue
Davis, CA 95616
United States

Georges Zaccour

HEC Montreal - Department of Decision Sciences ( email )

HEC Montreal
3000, Chemin de la Côte-Sainte-Catherine
Montreal, Quebec H2X 2L3 H3T 2A7
Canada

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