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on Contract Theory and Applications |
| By: | Moshe Babaioff; Linda Cai; Brendan Lucier |
| Abstract: | We consider a principal seller with $m$ heterogeneous products to sell to an additive buyer over independent items. The principal can offer an arbitrary menu of product bundles, but faces competition from smaller and more agile single-item sellers. The single-item sellers choose their prices after the principal commits to a menu, potentially under-cutting the principal's offerings. We explore to what extent the principal can leverage the ability to bundle product together to extract revenue. Any choice of menu by the principal induces an oligopoly pricing game between the single-item sellers, which may have multiple equilibria. When there is only a single item this model reduces to Bertrand competition, for which the principal's revenue is $0$ at any equilibrium, so we assume that no single item's value is too dominant. We establish an upper bound on the principal's optimal revenue at every equilibrium: the expected welfare after truncating each item's value to its revenue-maximizing price. Under a technical condition on the value distributions -- that the monopolist's revenue is sufficiently sensitive to price -- we show that the principal seller can simply price the grand-bundle and ensure (in any equilibrium) a constant approximation to this bound (and hence to the optimal revenue). We also show that for some value distributions violating our conditions, grand-bundle pricing does not yield a constant approximation to the optimal revenue in any equilibrium. |
| Date: | 2024–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2406.13835&r= |
| By: | Johannes Schneider; \'Alvaro Delgado-Vega |
| Abstract: | We study an organization with a principal and two agents. All three have a long-run agenda which drives their repeated interactions. The principal can influence the competition for agency by endorsing an agent. Her agenda is more aligned with her ``friend'' than with her ``enemy.'' Even when fully aligned with the friend, the principal embraces the enemy by persistently endorsing him once an initial ``cordon sanitaire'' to exclude the enemy breaks exogenously. A dynamically optimizing principal with extreme agenda either implements the commitment solution or reverts to static Nash. For less extreme principals, losing commitment power has more gradual effects. |
| Date: | 2024–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2406.09734&r= |
| By: | Jose M. Betancourt (Yale University); Ali Horta su (University of Chicago); Aniko …ry (Carnegie Mellon University); Kevin R. Williams (Yale University) |
| Abstract: | We study dynamic price competition between sellers offering differentiated products with limited capacity and a common sales deadline. In every period, firms simultaneously set prices, and a randomly arriving buyer decides whether to purchase a product or leave the market. Given remaining capacities, firms trade off selling today against shifting demand to competitors to obtain future market power. We provide conditions for the existence and uniqueness of pure-strategy Markov perfect equilibria. In the continuous-time limit, prices solve a system of ordinary differential equations. We derive properties of equilibrium dynamics and show that prices increase the most when the product with the lowest remaining capacity sells. Because firms do not fully internalize the social option value of future sales, equilibrium prices can be inefficiently low such that both firms and consumers would benefit if firms could commit to higher prices. We term this new welfare effect the Bertrand scarcity trap. |
| Date: | 2024–06 |
| URL: | https://d.repec.org/n?u=RePEc:cwl:cwldpp:2394&r= |