217. Playing the Budget-Constrained Multi-Battle Contest with Randomized Strategies for Maximizing Winning Probabilities
Invited abstract in session TD-4: Multiobjective Optimization III, stream Multiobjective optimization.
Thursday, 14:10 - 15:50Room: M:M
Authors (first author is the speaker)
| 1. | Chien-Hsin Chen
|
| Computer Science, National Tsing Hua University | |
| 2. | Po-An Chen
|
| Institute of Information Management, National Chiao Tung University | |
| 3. | Wing-Kai Hon
|
| Computer Science, National Tsing Hua University |
Abstract
The result of our previous work on budget-constrained multi-battle contests is basically the optimal budget ratio that guarantees the first-mover to win against an adversarial follower and the corresponding bidding strategy. One may wonder what a player should do when their initial budget is not high enough. Our model and results in this paper provide a more general way to discuss what a player with only a relatively moderate amount of budget would do: our goal is to derive "the leader's mixed strategy that maximizes the winning probability for the whole game, under each rule for tie-breaking", assuming the follower plays adversarially. Moreover, we express such a maximum winning probability in terms of the amount of extra money.
In particular, the winning probabilities when several basic and more complicated rules are applied will "not" be affected by the role of players; only which game rule is used and the amount of extra money of the rich player matters. When the reciprocal of the extra amount of money is integral and the most complicated rule is applied, instead of giving a closed-form solution, the winning probability can be characterized by a recursive formula.
Keywords
- SS - Multi-Criteria Optimization and Real-World Applications
- Multi- and many-objective optimization
Status: accepted
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