### Abstract

A theory of existence and characterization of equilibria is developed for stochastic zero-sum differential games when the players operate under different (probabilistic) models for the underlying system and the measurement process(es). The main objective of this study is to identify salient features of such an extended formulation for zero-sum stochastic differential games with noisy measurements, and to analyze the equilibria that emerge from possible inconsistent modeling. After a general discussion on the implications of subjective probabilistic modeling on saddle-point equilibria, the authors carefully study the class of zero-sum differential games where the players have a common (noisy) measurement of the state, but different (subjective) statistics on the system measurement noise processes. The author obtains a characterization of the equilibrium solution in the presence of such a discrepancy and studies the structural consistency of the solution and its convergence to the saddle-point solution of the nominal game as the discrepancy becomes (in some norm) vanishingly small.

Original language | English (US) |
---|---|

Pages (from-to) | 1425-1429 |

Number of pages | 5 |

Journal | Proceedings of the IEEE Conference on Decision and Control |

State | Published - Dec 1 1988 |

Event | Proceedings of the 27th IEEE Conference on Decision and Control - Austin, TX, USA Duration: Dec 7 1988 → Dec 9 1988 |

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### ASJC Scopus subject areas

- Control and Systems Engineering
- Modeling and Simulation
- Control and Optimization

### Cite this

**Probabilistic multimodeling in zero-sum differential games.** / Basar, M Tamer.

Research output: Contribution to journal › Conference article

}

TY - JOUR

T1 - Probabilistic multimodeling in zero-sum differential games

AU - Basar, M Tamer

PY - 1988/12/1

Y1 - 1988/12/1

N2 - A theory of existence and characterization of equilibria is developed for stochastic zero-sum differential games when the players operate under different (probabilistic) models for the underlying system and the measurement process(es). The main objective of this study is to identify salient features of such an extended formulation for zero-sum stochastic differential games with noisy measurements, and to analyze the equilibria that emerge from possible inconsistent modeling. After a general discussion on the implications of subjective probabilistic modeling on saddle-point equilibria, the authors carefully study the class of zero-sum differential games where the players have a common (noisy) measurement of the state, but different (subjective) statistics on the system measurement noise processes. The author obtains a characterization of the equilibrium solution in the presence of such a discrepancy and studies the structural consistency of the solution and its convergence to the saddle-point solution of the nominal game as the discrepancy becomes (in some norm) vanishingly small.

AB - A theory of existence and characterization of equilibria is developed for stochastic zero-sum differential games when the players operate under different (probabilistic) models for the underlying system and the measurement process(es). The main objective of this study is to identify salient features of such an extended formulation for zero-sum stochastic differential games with noisy measurements, and to analyze the equilibria that emerge from possible inconsistent modeling. After a general discussion on the implications of subjective probabilistic modeling on saddle-point equilibria, the authors carefully study the class of zero-sum differential games where the players have a common (noisy) measurement of the state, but different (subjective) statistics on the system measurement noise processes. The author obtains a characterization of the equilibrium solution in the presence of such a discrepancy and studies the structural consistency of the solution and its convergence to the saddle-point solution of the nominal game as the discrepancy becomes (in some norm) vanishingly small.

UR - http://www.scopus.com/inward/record.url?scp=0024169846&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0024169846&partnerID=8YFLogxK

M3 - Conference article

AN - SCOPUS:0024169846

SP - 1425

EP - 1429

JO - Proceedings of the IEEE Conference on Decision and Control

JF - Proceedings of the IEEE Conference on Decision and Control

SN - 0191-2216

ER -