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on Contract Theory and Applications |
| By: | Alessandro Chiusolo; Emma Hubert |
| Abstract: | The recent work by Cvitani\'c, Possama\"i, and Touzi (2018) [9] presents a general approach for continuous-time principal-agent problems, through dynamic programming and second-order backward stochastic differential equations (BSDEs). In this paper, we provide an alternative formulation of the principal-agent problem, which can be solved simply by relying on the theory of BSDEs. This reformulation is strongly inspired by an important remark in [9], namely that if the principal observes the output process in continuous-time, she can compute its quadratic variation pathwise. While in [9], this information is used in the contract, our reformulation consists in assuming that the principal could directly control this process, in a `first-best' fashion. The resolution approach for this alternative problem actually follows the line of the so-called `Sannikov's trick' in the literature on continuous-time principal-agent problems, as originally introduced by Sannikov (2008) [28]. We then show that the solution to this `first-best' formulation is identical to the solution of the original problem. More precisely, using the contract form introduced in [9] as `penalisation contracts', we highlight that this `first-best' scenario can be achieved even if the principal cannot directly control the quadratic variation. Nevertheless, we do not have to rely on the theory of 2BSDEs to prove that such contracts are optimal, as their optimality is ensured by showing that the `first-best' scenario is achieved. We believe that this more straightforward approach to solve continuous-time principal-agent problems with volatility control will facilitate the dissemination of these problems across many fields, and its extension to even more intricate problems. |
| Date: | 2024–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2407.09471 |
| By: | Jose M. Betancourt; Ali Hortaçsu; Aniko Öry; Kevin R. Williams |
| 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. |
| JEL: | C7 D04 D6 L0 |
| Date: | 2024–07 |
| URL: | https://d.repec.org/n?u=RePEc:nbr:nberwo:32673 |
| By: | Rosina Rodríguez Olivera |
| Abstract: | I study the incentives of an informed firm to share its private information with its competitor and the incentives of a regulator to constrain or enforce disclosure in order to benefit consumers. Firms offer differentiated goods, compete a là Bertrand and one firm has an information advantage about demand over its competitor. I show that full disclosure of information is optimal for the informed firm, because it increases price correlation and surplus extraction from consumers. A regulator can increase expected consumer surplus and welfare by restricting disclosure, but consumers can benefit from the regulator privately disclosing some information to the competitor. Disclosure increases the ability of firms to extract surplus from consumers, but private disclosure creates a coordination failure in firm pricing. The optimal disclosure policy is chosen to induce goods to be closer substitutes and intensify the competition across firms. |
| Keywords: | Competition, Information |
| JEL: | D18 D43 |
| Date: | 2024–07 |
| URL: | https://d.repec.org/n?u=RePEc:bon:boncrc:crctr224_2024_578 |