Nash equilibria for dividend distribution with competition
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866911037098295296 |
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| author | De Angelis, Tiziano Gensbittel, Fabien Villeneuve, Stéphane |
| author_facet | De Angelis, Tiziano Gensbittel, Fabien Villeneuve, Stéphane |
| contents | We construct Nash equilibria in feedback form for a class of two-person stochastic games of singular control with absorption, arising from a stylized model for corporate finance. More precisely, the paper focusses on a strategic dynamic game in which two financially-constrained firms operate in the same market. The firms distribute dividends and are faced with default risk. The strategic interaction arises from the fact that if one firm defaults, the other one becomes a monopolist and increases its profitability. The firms choose their dividend distribution policies from a class of randomised strategies and we identify two types of equilibria, depending on the firms' initial endowments. In both situations the optimal strategies and the equilibrium payoffs are found explicitly. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_07703 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Nash equilibria for dividend distribution with competition De Angelis, Tiziano Gensbittel, Fabien Villeneuve, Stéphane Optimization and Control Probability Mathematical Finance 91A15, 93E20, 91G50, 60J60, 35R35 We construct Nash equilibria in feedback form for a class of two-person stochastic games of singular control with absorption, arising from a stylized model for corporate finance. More precisely, the paper focusses on a strategic dynamic game in which two financially-constrained firms operate in the same market. The firms distribute dividends and are faced with default risk. The strategic interaction arises from the fact that if one firm defaults, the other one becomes a monopolist and increases its profitability. The firms choose their dividend distribution policies from a class of randomised strategies and we identify two types of equilibria, depending on the firms' initial endowments. In both situations the optimal strategies and the equilibrium payoffs are found explicitly. |
| title | Nash equilibria for dividend distribution with competition |
| topic | Optimization and Control Probability Mathematical Finance 91A15, 93E20, 91G50, 60J60, 35R35 |
| url | https://arxiv.org/abs/2312.07703 |