Nash equilibria for relative investors with (non)linear price impact

Nicole B\"auerle and Tamara G\"oll

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Abstract: We consider the strategic interaction of $n$ investors who are able to influence a stock price process and at the same time measure their utilities relative to the other investors. Our main aim is to find Nash equilibrium investment strategies in this setting in a financial market driven by a Brownian motion and investigate the influence the price impact has on the equilibrium. We consider both CRRA and CARA utility functions. Our findings show that the problem is well-posed as long as the price impact is at most linear. Moreover, numerical results reveal that the investors behave very aggressively when the price impact is beyond a critical parameter.

Date: 2023-03, Revised 2024-04
New Economics Papers: this item is included in nep-gth, nep-mst and nep-upt
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Published in B\"auerle, N., G\"oll, T. Nash equilibria for relative investors with (non)linear price impact. Math Finan Econ (2024)

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