1875. Generalized Nash Game under Uncertainty—a CVaR Based Approach
Invited abstract in session TC-53: New Trends in Game Theory VI, stream Game Theory and Mathematical Economics.
Tuesday, 12:30-14:00Room: Liberty Moot Court
Authors (first author is the speaker)
| 1. | Kishan Suthar
|
| Operations management and quantitative techniques area, Indian Institute of Management Indore | |
| 2. | Nagarajan Krishnamurthy
|
| Operations Management & Quantitative Techniques area, Indian Institute of Management Indore |
Abstract
A generalized Nash game is an N-player game with interdependent strategy sets. Such games are used to model and solve the tragedy of the commons, traffic congestion, and so on. A generalized Nash equilibrium (GNE) is an equilibrium solution to a generalized Nash game. While the existence of a GNE is well-established in the deterministic setting, its existence in the stochastic setting is not known in general. Moreover, guaranteeing the uniqueness of such an equilibrium, even in the deterministic setting, is challenging. Uniqueness can be established under certain conditions such as the quasi-concavity of the utility function and the convexity of the interdependent strategy sets. Under uncertainty, previous studies have used various approaches including almost-sure formulations, expected value formulations, and risk measure considerations. In this study, we first demonstrate the existence of a GNE in stochastic generalized Nash games and use the Conditional Value-at-Risk (CVaR) to solve these games. The equilibrium solution is characterized by players' risk aversion, and we identify the conditions required for the existence of a unique GNE in such games.
Keywords
- Game Theory
- Stochastic Models
- Risk Analysis and Management
Status: accepted
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