A Note on the Characterization of Optimal Return Functions and Optimal Strategies for Gambling Problems

Pursuit-evasion games are used to define guidance strategies for multi-agent planning problems. Although optimal strategies exist for deterministic scenarios, in the case when information about the opponent players is imperfect, it is important to evaluate the effect of uncertainties on the estimated variables. This paper proposes a method to characterize the game space of a pursuit-evasion game under a stochastic perspective. The Mahalanobis distance is used as a metric to determine the levels of confidence in the estimation of the Zero Effort Miss across the capture zone. This information can be used to gain an insight into the guidance strategy. A simulation is carried out to provide numerical results.

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A Stochastic Model for Service Contract

International Journal of Reliability Quality and Safety Engineering ◽

10.1142/s0218539398000054 ◽

1998 ◽

Vol 05 (01) ◽

pp. 29-45 ◽

Cited By ~ 25

Author(s):

D. N. P. Murthy ◽

E. Asgharizadeh

Keyword(s):

Sensitivity Analysis ◽

Simple Model ◽

Single Agent ◽

Optimal Strategies ◽

Complete Characterization ◽

Viable Option ◽

Service Contract ◽

External Agent ◽

Maintenance Service

When it is not economical to carry out maintenance in-house, out-sourcing to an external agent is an alternate viable option. In this paper, we study a simple maintenance service contract involving a single agent (providing the maintenance service) and a single customer (owner of the equipment and recipient of the maintenance service). We develop a simple model to obtain the optimal strategies for both the customer and the agent. We give a complete characterization of the strategies along with some sensitivity analysis and discuss some extensions.

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Characterization of Optimal Strategies in Dynamic Games

Discrete Applied Mathematics ◽

10.1016/0166-218x(82)90063-4 ◽

1982 ◽

Vol 4 (4) ◽

pp. 343

Keyword(s):

Dynamic Games ◽

Optimal Strategies

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Characterization and simplification of optimal strategies in positive stochastic games

Journal of Applied Probability ◽

10.1017/jpr.2018.47 ◽

2018 ◽

Vol 55 (3) ◽

pp. 728-741 ◽

Cited By ~ 2

Author(s):

János Flesch ◽

Arkadi Predtetchinski ◽

William Sudderth

Keyword(s):

State Space ◽

Optimal Strategy ◽

Stochastic Games ◽

Optimal Strategies ◽

Action Space ◽

Positive Zero ◽

Countable State ◽

Zero Sum ◽

Action Spaces

Abstract We consider positive zero-sum stochastic games with countable state and action spaces. For each player, we provide a characterization of those strategies that are optimal in every subgame. These characterizations are used to prove two simplification results. We show that if player 2 has an optimal strategy then he/she also has a stationary optimal strategy, and prove the same for player 1 under the assumption that the state space and player 2's action space are finite.

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