Equilibrium pricing with positive externalities

We study the problem of selling an item to strategic buyers in the presence of positive historical externalities, where the value of a product increases as more people buy and use it. This increase in the value of the product is the result of resolving bugs or security holes after more usage. We consider a continuum of buyers that are partitioned into types where each type has a valuation function based on the actions of other buyers. Given a fixed sequence of prices, or price trajectory, buyers choose a day on which to purchase the product, i.e. they have to decide whether to purchase the product early in the game or later after more people already own it. We model this strategic setting as a game, study existence and uniqueness of the equilibria, and design an FPTAS to compute an approximately revenue-maximizing pricing trajectory for the seller in two special cases: the symmetric settings in which there is just a single buyer type, and the linear settings that are characterized by an initial type-independent bias and a linear type-dependent influenceability coefficient.

[1]  Mohammad Ghodsi,et al.  Optimal Iterative Pricing over Social Networks (Extended Abstract) , 2010, WINE.

[2]  Joseph Farrell,et al.  Standardization, Compatibility, and Innovation , 1985 .

[3]  Asuman E. Ozdaglar,et al.  Optimal Pricing in the Presence of Local Network Effects , 2010, WINE.

[4]  Vincent Conitzer,et al.  Computing the optimal strategy to commit to , 2006, EC '06.

[5]  D. North.  Competing Technologies , Increasing Returns , and Lock-In by Historical Events , 1994 .

[6]  Sarit Kraus,et al.  Efficient Algorithms to Solve Bayesian Stackelberg Games for Security Applications , 2008, AAAI.

[7]  Robin Mason,et al.  Network externalities and the Coase conjecture , 2000 .

[8]  Matthew Richardson,et al.  Mining the network value of customers , 2001, KDD '01.

[9]  B. Bensaid,et al.  Dynamic monopoly pricing with network externalities , 1996 .

[10]  Éva Tardos,et al.  Influential Nodes in a Diffusion Model for Social Networks , 2005, ICALP.

[11]  C. Shapiro,et al.  Network Externalities, Competition, and Compatibility , 1985 .

[12]  H. Stackelberg,et al.  Marktform und Gleichgewicht , 1935 .

[13]  Elchanan Mossel,et al.  Submodularity of Influence in Social Networks: From Local to Global , 2010, SIAM J. Comput..

[14]  Atri Rudra,et al.  Dynamic pricing for impatient bidders , 2007, SODA '07.

[15]  Luís M. B. Cabral,et al.  Monopoly Pricing With Network Externalities , 1999 .

[16]  Vincent Conitzer,et al.  Computing optimal strategies to commit to in extensive-form games , 2010, EC '10.

[17]  Pekka Sääskilahti,et al.  Monopoly Pricing of Social Goods , 2015 .

[18]  S. Kakutani.  A generalization of Brouwer’s fixed point theorem , 1941 .

[19]  J. yon Neumann.  A GENERALIZATION OF BROUWERS FIXED POINT THEOREM BY SHIZUO IAKUTANI , .

[20]  Vahab S. Mirrokni,et al.  Optimal marketing strategies over social networks , 2008, WWW.

[21]  Nima Haghpanah,et al.  Optimal iterative pricing over social networks , 2010 .

[22]  A. Mas-Colell.  On a theorem of Schmeidler , 1984 .